Papers

In [arXiv:2605.26185 [hep-th]] it is pointed out how the tensionless string with a gauged scale symmetry discussed in the recent articles, [arXiv:2605.12414 [hep-th]], [arXiv:2605.25817 [hep-th]], [arXiv:2605.26822 [hep-th]], is a reduction of the conformal string [arXiv:hep-th/9410143 [hep-th]] to Minkowski space. Here we corroborate this by choices of slices in Dirac $d+2$ dimensional conformal space. We perform a Dirac reduction of the model and its algebra of constraints and see how they map to the constraints in $d$ dimensions, including how the semidirect product of the Virasoro algebra with a su(1,1) Kac-Moody algebra becomes the Corrollian-Weyl symmetry in $d$ dimensions.

We investigate a holographic s+p superconductor model coupled to nonlinear electrodynamics in the probe limit. The equations of motion are solved numerically, and the condensates as well as the grand potential curves for phase transitions at different values of the nonlinear parameter $b$ are illustrated. It is found that as $b$ increases, both the pure s-wave and p-wave condensates are suppressed. From the $b-T$ phase diagram, we observe that the region of the pure s-wave phase gradually shrinks with increasing $b$, which is attributed to the stronger suppression on the s-wave condensate compared to the one on the p-wave. Moreover, a smaller charge ratio $q_p/q_s$ is needed for the s+p coexistent phase to appear as $b$ grows. A particularly interesting feature is that, due to the nonlinear self-interaction of the electromagnetic field, charge accumulates spontaneously outside the event horizon from the bulk perspective even in the absence of scalar and vector condensates, thereby invalidating the conventional formula for the superconducting charge density. We improve the definition of the superconducting charge density as the background-subtracted value of the accumulated charge outside the horizon with respect to that in the normal phase. Furthermore, the optical conductivity in the normal phase is also modified by this accumulated charge for finite $b$, and its imaginary part develops a minimum at a finite frequency. This minimum persists in the superconducting phase near the critical point, confusing the extraction of the gap frequency.

This dissertation aims to put forth a systematic construction of a fractional-calculus extension of holographic dark energy (HDE). We show that linking late-time cosmic acceleration to non-local or memory effects encoded in a fractional (Riesz) derivative within black hole thermodynamics produces deviations from standard HDE and can address some challenges of the Hubble cutoff. In particular, a Riesz fractional spatial derivative is introduced into the Hamiltonian constraint of a Schwarzschild black hole in quantum geometrodynamics, leading to a Fractional Wheeler–DeWitt equation whose solutions yield fractionally corrected thermodynamic quantities, notably fractional Bekenstein–Hawking entropy governed by the Lévy index \(\alpha\), with \(1<\alpha\leq2\). Using this entropy with Cohen's inequality, a new dark energy density is constructed, defining the Fractional Holographic Dark Energy (FHDE) framework. The cosmological implications of FHDE are then investigated. Within the Hubble cutoff, its late-time evolution is analysed through cosmological observables, and the model is reconstructed using effective field descriptions with spin-\(0\) and spin-\(1\) candidates, allowing kinetic and potential terms to be extracted as functions of redshift \(z\) and \(\alpha\). The framework is then extended to BD, DGP, EPN, and Horndeski theories to derive the equation-of-state and deceleration parameters in terms of \(z\) and \(\alpha\). In addition, the fate of the Universe is studied through late-time singularities, namely the big, little, and pseudo-rip, within the Granda–Oliveros FHDE setting. In short, this dissertation proposes FHDE as a theoretically motivated extension of HDE, bridging non-locality in quantum gravity with the late-time dynamics of the Universe, and offering a route toward understanding cosmic acceleration beyond \(\Lambda\)CDM.

We investigate the constraining power of scalaron-driven inflation on asymptotically safe scalar-tensor theories. Starting from a Horndeski-type theory and applying a renormalization group improvement procedure generates higher-derivative couplings which are fixed in terms of the microscopic parameters - a structure that is expected to occur also within first principle computations based on the asymptotic safety mechanism. The latter are taken to be the free parameters appearing at the Gaussian fixed point. We find that the free parameter initially associated with the non-minimal gravity-matter coupling is not confined to the gravity-matter sector of the theory and also enters the effective higher-derivative couplings in the gravitational sector. We review the setting of multi-field inflationary models which is appropriate to analyze the inflationary dynamics in this context and illustrate their applicability by working out the explicit bounds on the non-minimal gravity-matter coupling resulting from cosmological observations. Given the fixed point structure of asymptotically safe scalar-tensor theories, the results indicate that UV-completions by two of the three available non-Gaussian fixed points can be ruled out while pinpointing phenomenologically viable RG trajectories emanating from the third fixed point.

The simplest nontrivial amplitude in planar $\mathcal{N}=4$ super-Yang-Mills theory is six-gluon scattering in the maximally-helicity-violating configuration. It has been computed to 8 loops with the help of antipodal duality, which relates it to the three-point form factor of a protected operator, the chiral stress tensor super-multiplet, represented also as ${\rm tr} \phi^2$. In this talk, we describe the computation to 8 loops of another three-point form factor, for the operator ${\rm tr}\phi^3$. This form factor lives in the same restricted space of polylogarithms as the ${\rm tr}\phi^2$ form factor. We also report on all-order patterns for sequences of coefficients in the symbols of these polylogarithmic results, for the leading discontinuity of the ${\rm tr}\phi^3$ form factor.

We study how the Ostrogradsky modes can be removed in multi-field higher-order scalar-tensor theories. For a general class of theories with an arbitrary number $\mathcal{N}$ of scalar fields and quadratic dependence on their second derivatives, we perform an ADM decomposition and carry out the Hamiltonian analysis in the branch where the metric kinetic block is invertible. The primary degeneracy condition is a matrix condition in field space. Previous studies of coupled higher-derivative systems have shown that primary degeneracy need not by itself be sufficient. In the generally covariant multi-scalar-tensor setting considered here, where the scalar and metric velocities mix in the ADM decomposition, preservation of the primary degeneracy constraints generates additional consistency conditions. We obtain these conditions explicitly in terms of the ADM coefficient blocks generated by the covariant action. Some of these conditions are antisymmetric in the field-space indices and vanish in the single-field limit. A rank condition on the constraint algebra is required in addition. Under the assumptions used in the Hamiltonian counting, in particular that the scalar second-class sector leaves the diffeomorphism constraints first class, the theory then propagates $2+\mathcal{N}$ degrees of freedom, the two tensor modes of gravity and one scalar mode per field, with no additional Ostrogradsky mode. We check the conditions in the single-field limit and in a multi-field quadratic Horndeski-type subclass. We also give a subclass with nonzero scalar-metric kinetic mixing, constructed directly at the level of the ADM coefficient blocks, showing that the Hamiltonian conditions admit nontrivial solutions at the ADM-block level.

Line bundle cohomology on complete intersection Calabi–Yau threefolds is an important input in string phenomenology. Previous work, based on direct extrapolation and on machine-learning analyses of finite data sets, has shown that these cohomology dimensions often admit chamber-wise polynomial descriptions on the Picard lattice. In this paper we explain this structure through the Hilbert functions associated with the non-trivial maps in the Koszul spectral sequence. Once Bott–Borel–Weil theory determines the non-vanishing ambient cohomology groups, the rank defects of the relevant Koszul maps are governed by Hilbert functions of cokernel or kernel modules. This turns many empirical chamber formulae into explicit rank-defect statements, with proofs that are either analytic or certified on finite boxes. Using this approach, we recover analytically almost all of the piecewise formulae appearing in the existing literature. For the remaining cases, we prove finite-box certificate theorems for infinite families of line bundles in the specified regions. We also identify new wall structures on certain CICYs which refine the chamber decompositions suggested by finite-range data. Finally, we use the same framework to construct line bundle cohomology formula libraries for two CICY threefolds which had not previously been analysed in this way. These results suggest that Hilbert-function methods can provide promising faster inputs for future string model-building scans based on line bundle constructions.

The conventional and topological phase transitions of a four-dimensional asymptotically AdS black hole with a non-minimal coupling term $F^{\alpha\beta}F^{\gamma\lambda}R_{\alpha\gamma}R_{\beta\lambda}$ are investigated. Using a perturbative approach to first order in the coupling $\epsilon$, the thermodynamic quantities are derived and the first law and Smarr relation are verified. Intriguingly, while the $\epsilon = 0$ limit yields the standard Reissner–Nordström–AdS black hole belonging to the $W^{1+}$ topological class ($W = +1$), switching on the non-minimal coupling fundamentally transforms the topology to the $W^{0-}$ class ($W = 0$). This transition occurs while the van der Waals-type first-order phase transition survives in the intermediate region, embedded within the overall Hawking–Page pattern, rendering the system a hybrid black hole thermodynamic system. The coupling $\epsilon$ thus acts as a topological deformation parameter that alters the universal classification of the system, despite the perturbative nature of the solution.

Warm inflation is usually expected to completely deplete the inflaton condensate by dissipating its energy into radiation. We show that this expectation fails in a simple and observationally viable regime. In a strongly dissipative warm inflationary scenario, the dissipative ratio, $Q=\Upsilon/(3H)$, can fall rapidly after the end of inflation as the system approaches radiation domination, thereby suppressing further energy transfer to the thermal bath. This leads to a residual inflaton condensate, which subsequently evolves as an effectively non-dissipative scalar field. For potentials with a stable quadratic minimum, this remnant inflaton manifests as a cold dark matter component. We establish this mechanism for the minimal renormalizable potential, with a dissipative coefficient $\Upsilon\propto T^3$. In this case, current cosmological data allow strong dissipation while leaving the inflaton mass weakly constrained by inflationary observables. The observed dark matter abundance then fixes its mass to be $m \approx 0.02\,{\rm MeV}$, while larger masses overclose the Universe. The transition to matter-like scaling occurs well before BBN, avoiding a long-lived inflaton dark radiation component. Relic inflaton dark matter therefore turns the post-inflationary dynamics of warm inflation into a new late time constraint on its parameter space.

We use numerical minimization of the lattice action of trace-deformed Yang-Mills theory on $T^4$ with twisted boundary conditions to find the classical minimum action configurations of fractional topological charge. We vary the twists and ratios of torus periods to interpolate between different $R^{4-k} \times T^k$ geometries. This allows us to see how the corresponding minimum action saddle point configurations – monopole-instantons ($k=1$), center vortices ($k=2$), and fractional instantons ($k=3,4$) – morph into each other. We also study how the transition between them depends on the presence of a deformation potential. In particular, we argue that the recent analytic picture of chains of monopole-instantons collimating their flux into center-vortex sheets, while technically relying on the deformation potential, also holds in pure Yang-Mills theory, for tori whose shape causes the abelianization due to the deformation to align with the one due to the twists. Our results also indicate that with nonzero deformation potential, some transitions between different minimal-action fractional charge configurations may be discontinuous and involve level crossing.

We give a summary of our work [3] and [4] with Geoffrey Compère and Sk Jahanur Hoque. After quickly reviewing the $\Lambda$-BMS solution space and why it is not trivial to define an analogue of Bondi mass loss, we discuss how this can be resolved by studying the linearized solutions. Then we describe how to solve the linearized Einstein s equations in the generalized harmonic gauge and the set of assumptions such as adiabaticity and being at a large distance from the source that allows us to write the metric perturbations in terms of the source multipole moments. We point out how to consistently truncate the multipole expansion. We then discuss the net change of the metric perturbation at future infinity due to a source that is time-varying in a finite time interval that will be connected to the memory effect. We explain how to define charge flows using the holographic stress tensor and what form they take in terms of multipole moments at second order in perturbations. We conclude with a some remarks on the results.

We construct magnetic and electric Carrollian Maxwell theories by performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry. The procedure preserves the original first-class U(1) Gauss constraint in the standard Carrollian Maxwell theories and deformed Carrollian Maxwell theories with a decoupled electric/magnetic scalar $A_-$. We emphasize that $A_-$ can be rendered non-dynamical by imposing additional ad hoc constraints. This corresponds to imposing the light-cone gauge $A_- = 0$ prior to the KK-like null reduction. For an electric pseudo-coupled theory without gauge symmetry, after imposing the ad hoc constraints the theory becomes the standard electric Maxwell theory together with a decoupled zero-energy scalar $A_-$. Furthermore, our work provides an explicit example of the correct application of this approach, thereby broadening the scope of its applicability to gauge theories.

We investigate a discrete warped Chern-Simons description of three-dimensional warped gravity based on boundary holonomies and monodromy sectors. Starting from the lower-spin SL(2, R) + U(1) gauge structure associated with warped AdS(3) holography and warped conformal field theories (WCFTs), we construct a discrete boundary framework in which ordered products of link holonomies replace continuous gauge connections along noncontractible cycles. In this setting, boundary monodromies become the primary gauge-invariant observables characterizing the physical sectors of the theory. We show that the hyperbolic, eliliptic, and parabolic sectors naturally arise from the conjugacy classes of the discrete SL(2, R) monodromy, while the additional U(1) holonomy supplies the warped contribution to the boundary charges. Using these monodromy invariants, we derive a discrete entropy relation entirely from boundary holonomy data without relying on a smooth geometric thermal background. The resulting entropy reproduces the characteristic warped black-hole and WCFT structure in the continuum limit. We further demonstrate that the continuum warped holonomy conditions are recovered from the large-lattice limit of the ordered boundary products, establishing a direct correspondence between discrete monodromies and continuous Wilson loops. Our analysis suggests that warped gravitational thermodynamics may be understood from a fundamentally holonomy-based perspective in which boundary monodromy sectors provide an alternative organizational description of the physical states within the discrete warped framework. Keywords: warped Chern-Simons theory, boundary monodromies, holonomy sectors, Wilson loops, warped thermodynamics.

We study the resurgent structure of short–time heat kernel asymptotics from the viewpoint of Picard–Lefschetz theory. For a real analytic Riemannian manifold, we show the heat kernel admits a 1– Gevrey small–time expansion whose Borel transform detects complex–geometric data beyond the real geodesic sector. We formulate an infinite–dimensional Picard–Lefschetz problem of Morse–Floer type for the holomorphic energy functional on the complexified path space, and propose a heat–kernel analogue of the Picard–Lefschetz/Alien correspondence. In this framework, pointed alien operators acting on the asymptotic expansion associated with the real geodesic are predicted to produce the formal heat–kernel sectors associated with other holomorphic geodesics, with coefficients given by signed counts of connecting trajectories of the Morse flow. We perform a confirming test of this proposal on the hyperbolic plane $\mathbb{H}_{\R}^2$.

Scalar-induced gravitational waves (SIGWs) are usually characterized by their power spectrum, although their quadratic scalar source also carries higher-order correlation information. We investigate whether phase-sensitive correlations of a primordial Gaussian scalar state can survive decoherence and be transferred to the induced tensor sector. The scalar state is described in a fixed oscillator basis by the occupation $N_k^\zeta$ and anomalous moment $M_k^\zeta$, while the transfer is formulated through the unequal-time scalar Wightman function. The late-time tensor moments $d_k$ and $\gamma_k$ define an effective Gaussian reference state and its discord, whereas the exact SIGW state is generally non-Gaussian and contains an additional connected fourth-order cumulant. We therefore introduce the baseline-subtracted observable $\Delta\kappa_{\rm coh}=\kappa_N[G^>_{\rm coh}]-\kappa_N[G^>_{\rm ref}]$. For phase damping with $M_k^\zeta\propto e^{-D_k}$, the Gaussian-reference contribution conditionally scales as $|\gamma_k|\propto e^{-2D_k}$ and $\kappa_N^{\rm G}\propto e^{-4D_k}$. This provides a framework in which the SIGW spectrum fixes the signal band, while higher-order statistics probe residual coherence beyond the power spectrum.

Scalar-induced gravitational waves are usually treated as a classical stochastic background sourced by phase-random curvature perturbations. We show that this description can miss residual quantum information. Starting from a decohered two-mode Gaussian scalar state, we derive explicit transfer relations between the scalar anomalous coherence and the covariance matrix of induced tensor modes. For a localized scalar power spectrum, the ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by scalar anomalous-coherence contractions. This coherence can generate nonzero tensor discord and a connected tensor-power covariance even after scalar entanglement has vanished. We identify the connected covariance and phase-sensitive strain correlations as probes of primordial quantum coherence in secondary gravitational-wave backgrounds, and discuss their possible relevance for future space-based interferometers and pulsar timing arrays.

Recent baryon acoustic oscillation measurements from DESI provide important new clues for reassessing whether the standard $\Lambda$CDM model offers a sufficient description of the late-time expansion history of the Universe. When combined with cosmic microwave background and type Ia supernova data, these measurements show an apparent departure from the $\Lambda$CDM model, commonly described as dynamical dark energy (DDE) with equation of state crossing the phantom divide (i.e., quintom behavior). This review examines the current status of the DESI-motivated indications for DDE and their possible implications for physics beyond $\Lambda$CDM. We discuss how the strength of the preference for DDE depends on the adopted parametrization and dataset combination, and how residual systematics or internal tensions among datasets may affect its interpretation. At the background level, several mechanisms beyond $\Lambda$CDM can produce similar expansion histories. We therefore further discuss how the same effective departure from $w=-1$ may arise from physically distinct scenarios, including interacting dark energy, non-minimally coupled gravity, and non-standard dark matter. Meanwhile, these different new-physics interpretations may have different implications for current cosmological tensions, especially those involving $H_0$, $S_8$, and $\sum m_\nu$. In conclusion, the question posed by DESI is not merely whether dark energy evolves with time, but rather how, within the framework of precision cosmology, to disentangle new physics scenarios from systematic errors.

We investigate Krylov complexity for single-trace operators dual to open strings attached to giant gravitons in planar $\mathcal{N}=4$ super Yang-Mills theory. We show that in protected and few-body sectors, Krylov dynamics is governed by orthogonal polynomial theory associated to the seed spectral measure, leading to bounded Lanczos coefficients determined solely by spectral support. In particular, for fixed magnon number $M$ and open-string length $L\rightarrow\infty$, we derive $a_n=2Mg$ and $b_n\rightarrow Mg$, demonstrating integrable, band-limited dynamics. This establishes that such sectors are insufficient to test recently proposed gravity-side universality of operator complexity growth. We therefore formulate a finite-density program in which magnons scale with system size, and propose a concrete universality test: whether the leading Krylov growth depends only on coarse thermodynamic data $(\rho,\varepsilon)$ and not on microscopic probe structure. This provides a precise boundary-field-theory framework for testing gravitational universality conjectures.

Vacuum decay at zero temperature is generically described by a real $O(4)$-symmetric Coleman bounce. When the scalar field driving the decay carries a conserved global charge, this picture changes qualitatively: the path integral must be projected onto a definite charge sector, the Euclidean field obeys twisted boundary conditions, and the saddle is complex. For the simplest case of a $U(1)$ global symmetry, we first reformulate this problem in a two-field real Euclidean description with a real saddle. We then solve the resulting two-dimensional partial differential equation problem describing the decay of a homogeneous charged medium to a deeper vacuum via bubble nucleation. At finite charge the bounce departs from $O(4)$ symmetry, the barrier between vacua is lowered, and the decay rate increases. Continuing the solution to real time, we find that charge rearrangement around the expanding wall costs phase-gradient energy and drives the bubble to a subluminal terminal velocity even in vacuum. We also clarify how the fixed-charge construction interfaces with finite-temperature and finite-chemical-potential descriptions.

Extra-dimensional axions have coupling strength related to fundamental, ultraviolet physics. It has been proposed that the properties of such axions imply a bound on the quantum gravity cutoff: $\Lambda_\mathrm{QG} \lesssim 2\pi \sqrt{S} f$, where $f$ is the axion decay constant and $S$ is the instanton action. In the context of weakly-coupled string theory, we identify $\Lambda_\mathrm{QG}$ with the string scale $M_s$. In this paper, we carry out a quantitative study of this bound on the string scale in the context of Calabi-Yau compactifications of Type IIB string theory, considering both $C_2$ and $C_4$ axions. We show, both analytically and numerically, that the bound holds even near boundaries of the Kähler moduli space, including those where the co-scaling relationship for axion strings fails. This evidence bolsters previous arguments, based on naturalness and on unitarity, that the bound is a general feature of extra-dimensional axions in quantum gravity.

Modern cosmology is often taken to provide an increasingly accurate description of the universe's underlying ontology through progressively refined mathematical models. I challenge this interpretation by arguing that the empirical success of cosmology underdetermines not only ontology but also the mathematical and conceptual frameworks used to represent observational data. I propose instead that the objective content of cosmology is best identified with cross-representational informational invariants-features of observational structure that persist across empirically adequate descriptions. These invariants can be characterized in information-theoretic terms, including correlation structure, statistical distinguishability, and limits on accessible information, and formalized using tools such as the Fisher-Rao metric on model space. On this view, cosmological models are best understood as efficient encodings of observational structure rather than uniquely privileged descriptions of fundamental reality. Scientific progress, accordingly, consists not in convergence toward a fixed ontology, but in the progressive refinement of the informational structure accessible to observation.

We revisit the topic of false vacuum decay in field theory. We focus on a toy model of a real massive scalar field with an unstable quartic potential. This model has a false vacuum, and decay out of the false vacuum can be described via the method of constrained instantons, which work by introducing a constraint on the path integral. We identify and develop three different asymptotic limits which enable analytic construction of approximate {constrained} solutions. The first, in which the constrained solution is small compared to the inverse mass of the scalar field, is an application of the perturbative methods of Affleck, although we re-derive the main results and identify several terms which were previously neglected. Second, for very large constrained solutions we adapt the thin-wall approximation of Coleman. However, we find that the large instanton limit does not always exist. In this case we identify another useful limit, in which the Lagrange multiplier used to implement the constraint is large. In this limit, the solution's scaling with the parameters may be found via dimensional analysis and an exact solution is obtained with a single numerical computation.

We investigate the head-on coalescence of charged binary black holes in Einstein-Maxwell-Scalar (EMS) theory using numerical relativity. The binaries are built from charged puncture initial data representing two Reissner-Nordström black holes immersed in a purely kinetic scalar perturbation: the scalar field initially vanishes, while its conjugate momentum provides a small seed for the instability. We evolve the coupled gravitational, electromagnetic, and scalar sectors and monitor the apparent horizons, the emitted radiation, and the scalar field on the horizons. Our simulations show that the nonminimal electromagnetic-scalar coupling can dynamically trigger the growth of scalar hair even when the individual black holes are initially scalar-free. The subsequent evolution depends on the coupling parameter $\alpha_0$ and on the charge-to-mass ratio of the remnant. For weak coupling, or when charge cancellation suppresses the electromagnetic source after the merger, the scalar field is radiated away or absorbed by the final horizon, and the system dynamically descalarizes. For sufficiently strong coupling and nonzero remnant charge, the scalar field remains finite, and the final black hole approaches a scalarized configuration. For binaries with equal charge-to-mass ratios, $q_1=q_2=0.1$, our simulations identify a transition region between $1900<\alpha_0<2000$, that separates descalarized and scalarized remnants. The coalescence also excites scalar radiation whose time profile is qualitatively correlated with the dominant gravitational-wave mode during the nonlinear stage of the collision. These results provide a binary realization of scalarization/descalarization transitions in EMS theory and show that the fate of scalar hair is controlled by the interplay between the scalar coupling and the charge content of the remnant.

If one extends the AdS/CFT extrapolate dictionary to large but finite $N$, we are expected to obtain non-perturbative violations of bulk micro-causality. Previously this was achieved by implementing a late boundary time cut-off, while smearing the boundary operator via the HKLL kernel. By performing explicit bulk reconstructions in the backgrounds of near-horizon modified AdS$_2$ and BTZ black holes, we recover the same non-locality estimates as above. For these black hole mimickers, the near-horizon modification is controlled by a throat parameter which sets the scale of this non-locality. In three bulk dimensions, probe dynamics also exhibits a dip-ramp-plateau structure in their spectral form factor when averaged over the throat parameter. Such structure has also been found recently in the background with a stretched horizon or a brick wall.

Asymptotically safe quantum gravity is an approach to quantum gravity. It is based on the premise that quantum field theory can describe the quantum nature of gravity in our universe. At its core lies quantum scale symmetry. This review provides an introduction to the key ideas of the approach and surveys the current status of the field. Over the last years, the field has taken large strides towards an increasingly realistic setting: First, compelling evidence for quantum scale symmetry exists in four-dimensional, Euclidean, pure gravity, establishing the Reuter fixed point robustly. Second, matter fields, including the Standard Model as well as beyond-Standard-Model-candidates, have been studied in depth, with increasingly conclusive evidence for quantum scale symmetry. Most recently, the final gap to a realistic description of quantum gravity is being closed, because Lorentzian spacetime signature can now be accounted for. As a consequence of quantum scale symmetry in the ultraviolet, the approach is highly predictive at all scales. This review discusses the physics of asymptotic safety across all scales. Predictive power for particle physics, black holes and cosmology provides a clear pathway to confronting quantum gravity with current and near-future observations. The review closes by discussing the connection to other approaches to quantum gravity. It advocates the perspective that such connections between approaches may lead us to an understanding of universal physical features of quantum gravity.

We present a cosmological reassessment of light sterile-neutrino scenarios, examining whether current observations exclude sterile neutrinos as a class or primarily constrain the fully thermalized case. We consider three distinct realizations: (i) a fully thermalized sterile species (FTS), (ii) a different-temperature sterile-neutrino thermal relic (DTS) relative to the active neutrino background and (iii) a Dodelson–Widrow-like (DW) sterile neutrino with reduced phase-space normalization. Constraints are derived within both $\Lambda$CDM and the CPL dynamical dark-energy framework using combinations of Planck-CMB data, DESI DR2 BAO measurements, and the PantheonPlus and Union3 Type Ia supernova samples. For baseline data combinations without a local $H_0$ prior, the FTS scenario is strongly disfavored in both cosmological models. Adding the local $H_0^{\rm DN}$ prior allows $\Lambda$CDM+FTS to accommodate the high local $H_0$ value and become statistically competitive with standard $\Lambda$CDM once SNIa data are included, although the sterile-neutrino mass remains consistent with zero. By contrast, partially populated sterile-neutrino scenarios remain viable: the DW realization is broadly compatible with current observations, while the DTS scenario yields the least cosmological pressure among the cases considered. Overall, cosmological data mainly require a strongly suppressed effective sterile abundance, leading to tight constraints on \textbf{$m_s^{\rm eff}$} while allowing substantially weaker bounds on the physical sterile mass. We conclude that current observations do not generically exclude sterile neutrinos, but rather place strong pressure on fully thermalized or highly populated scenarios, highlighting the importance of production history and phase-space distribution when interpreting cosmological constraints.

We investigate non-relativistic limits of four-dimensional maximally supersymmetric Yang-Mills theory (4d MSYM) and their relation to the nonperturbative $\operatorname{SL}(2;\mathbb Z)$ S-duality of the relativistic theory. We construct a general family of non-relativistic limits using a Type IIB brane set-up with a D3-brane and $(p,q)$-strings and show that the resulting theories are topological deformations of supersymmetric Galilean Yang-Mills theory or quantum mechanics on the moduli space of BPS monopoles. The deformations of the Galilean Yang-Mills theory are the familiar $\theta$-term and a coupling to the monopole charge, while in the moduli space theory the only deformation is a $\theta$-term. This family of theories fit together into a three-dimensional moduli space with nontrivial topology, on which $\operatorname{PSL}(2;\mathbb Z)$-valued dualities act in a richer and more complex way than in the relativistic parent theory. In the Abelian case, we establish the duality directly using the path integral, while in the non-Abelian case we support our claim by matching the one-particle spectrum as well as the Galilean spacetime symmetries and electric/magnetic invertible one-form symmetries.

We establish the calculus structure on Hochschild invariants of open-closed homotopy algebras. We further define the Getzler-Gauss-Manin connection and show that it is flat up to chain homotopy on the open-closed periodic cyclic chain complex.

We consider the classification of toric self-dual Einstein gravitational instantons with negative cosmological constant. As is well known, any Killing vector field on a self-dual Einstein manifold defines a local conformal Kähler structure. We prove that if the conformal Kähler structure associated to one of the torus Killing fields is global and extends to an ALE manifold with no additional fixed points, then the corresponding self-dual Einstein instanton is precisely given by the infinite class of multipole solutions constructed by Calderbank, Pedersen and Singer.

This dissertation investigates a supercooled phase transition (PT) in the early Universe. Using high-temperature dimensional reduction (DR), we compute the NLO thermal bubble nucleation rate. By explicitly evaluating fluctuation determinants, we provide a state-of-the-art description of thermal bubble nucleation. As a case study, we consider the SU(2)cSM, an extension of the conformal Standard Model with an additional SU(2)$_X$ gauge sector and scalar field that acquires a vev through radiative symmetry breaking. This symmetry breaking proceeds via a supercooled first-order phase transition. The first part of the thesis introduces the theoretical framework, including effective actions, RG improvements, finite-temperature quantum field theory, effective field theory techniques, and thermal bubble nucleation. The second part applies these methods to the SU(2)cSM. We establish a consistent power-counting scheme, construct the leading-order effective potential, analyse symmetry breaking and parameter space, derive an RG-improved potential, and incorporate thermal corrections. We then apply high-temperature DR to a classically scale-invariant model for the first time, derive the corresponding three-dimensional EFT, and compute the NLO nucleation rate. A detailed numerical evaluation of fluctuation determinants enables a comparison of different approximation schemes and their limitations. Finally, we present the phenomenological implications. We determine phase transition parameters, perform parameter scans, and predict the resulting gravitational wave signals. We find that the supercooled phase transition in the SU(2)cSM produces a strong signal detectable by LISA throughout the parameter space considered, making the model experimentally testable. We also demonstrate that higher-order corrections can significantly affect both phase transition dynamics and gravitational wave predictions.