Papers

We study the effect of boundary deformations on the von Neumann entropy of subregions in two-dimensional boundary conformal field theories (BCFTs) at zero and finite temperature. The deformations considered are infinitesimal global conformal transformations that move the boundary and can equivalently be viewed as the leading-order effect of certain BCFT perturbations with the boundary displacement operator. We demonstrate that at large central charge the von Neumann entropy in the presence of a deformed boundary is reproduced by the island entropy of the same interval in an undeformed BCFT acting as a bath and coupled to a gravitating spacetime. Here, the BCFT is joined to an AdS$_2$ region governed by Jackiw-Teitelboim (JT) gravity via transparent boundary conditions. The boundary condition for the dilaton field is set by the boundary deformation in the BCFT computation. Our analysis relies on mild assumptions about the spectrum and OPE coefficients of the BCFT. Notably, these conditions are consistent with an exponentially large number of light operators and are therefore weaker than those required for holographic BCFTs. This is possible since the BCFT result is not reproduced by a gravitational computation in three dimensions with an O(1) number of matter fields, but instead by a computation in two dimensions and with an O(c) number of light fields.

We show how one can use the convexity of non-commutative $L^p$ norms to bound the relative entropy between a faithful state on a von Neumann algebra and an arbitrary excitation thereof. Our results hold for general von Neumann algebras, including the local algebras of type III that are ubiquitous in quantum field theory, and do not require knowledge of the relative modular operator. As an application of our results, we prove that for the chiral current on a light ray, the relative entropy between the vacuum and a dense set of single-particle states is uniformly bounded.

Using the Bogoliubov-Parasiuk theorem we derive differential equations for the sum of leading UV divergences of the Kähler potential in the general $\mathcal{N}=1$ supersymmetric chiral theory. The obtained equations recover the limit of the renormalizable Wess-Zumino theory and also allow one to consider non-renormalizable chiral interactions. Some implications of the obtained equations are shown.

We study the large-$N$ limit of $U(N)$ and $SU(N)$ unitary matrix models inspired by QCD. The model is analyzed in two cases: $\mu = 0$, where the potential is real, and finite $\mu$, where it becomes complex. The complex action drives the eigenvalues into the complex plane, leading to $\langle U \rangle \neq \langle U^{-1} \rangle$. In the ungapped phase, we obtain analytic expressions for the spectral density, Wilson loops, and free energy, which reproduce the low-temperature behaviour of QCD. In contrast, the gapped phase involves a nontrivial resolvent and is solved partially analytically and numerically. At $\mu=0$, the model exhibits a $3^{rd}$ order phase transition, while at finite $\mu$, it shows a continuous phase transition of at least second order.

In this paper, we fill some gap in the existing literature on higher spins by presenting an explicit solution to the on-shell constraints for a frame-like, gauge invariant description of massive, higher spin fields in d=4. We begin with the massive spin 2 and massive spin 5/2 as simple illustrations, and then consider arbitrary integer and half-integer spin. We also show that our results allow us to find explicit solutions to the so-called unfolded equations that determine all higher-order derivatives of the physical field that are non-zero on-shell.

We have considered the Yukawa theory at two loop in the inflationary de Sitter spacetime, for a massless minimally coupled scalar and a massless fermion. The one loop computation for the same has been investigated in detail in the earlier literatures. The chief motivation behind this study is the fact that at one loop, the scalar self energy contains only fermions, which are conformally invariant. At two loop, there are two diagrams, each containing one internal scalar line, thereby breaking the conformal invariance. This should result in the appearance of infrared secular logarithms in the scalar self energy. The renormalisation of this two loop self energy has been performed. We next compute the loop corrected coincident two point correlation function, $\langle \phi^2\rangle$, due to the self energies. The expectation value has been taken with respect to the initial Bunch-Davies vacuum. We argue that the late time secular contribution from the local or UV self energy must dominate the non-local or IR ones in the present case, from the point of view of the powers of these large logarithms of the scale factor. This corresponds to the fact that fermion lines do not show any IR secular effect. The leading behaviour of $\langle \phi^2\rangle$ at one and two loop are respectively found to be $\ln^3 a$ and $\ln^4 a$. These are hybrids of UV and IR logarithms, where the latter originate from the massless and minimal two external scalar lines. A resummed expression for $\langle \phi^2\rangle$ has also been computed. The same is found to be bounded and decreasing monotonically with the increasing magnitude of the Yukawa coupling. Accordingly, the dynamically generated scalar mass increases with the increasing coupling.

We investigate certain Liouville integrable systems constructed earlier via reduction of the quasi-Hamiltonian double of $\mathrm{SU}(n)$. These systems live on compact connected symplectic manifolds of dimension $2(n-1)$ and can be interpreted as compactified trigonometric Ruijsenaars–Schneider systems. Depending on the value of a parameter $0<y< \pi$, they arise in two drastically different forms: in type (i) these are toric systems, while in the type (ii) cases they possess globally continuous action variables that generate a Hamiltonian torus action (only) on a dense open subset of the phase space. The principal goal of the paper is to study those fibers of the action map (alias the $\mathbb{T}^{n-1}$ momentum map) which are contained in the complement of the domain of the densely defined torus action occurring in the type (ii) cases. We demonstrate that all such `singular fibers' are smooth connected isotropic submanifolds. We also work out a model of the fibers as quotient spaces of certain subgroups of $\mathrm{SU}(n)$ with respect to an action of another subgroup. The general results are exemplified by determining the vertices of the polytope filled by the action variables in the simplest type (ii) cases that appear for any $n\geq 4$ with $\pi/(n-1) <y < \pi/(n-2)$, and proving that the fibers over the `singular vertices' are diffeomorphic to $S^3 \simeq \mathrm{SU}(2)$ in these cases. In this way, our findings enrich the set of examples of Liouville integrable systems with spherical singularities.

We investigate the leading gravitational eikonal in nonlocal $D$ dimensional theories of gravity. We analyze the simplest cases of $2\rightarrow2$ massless and massive scalar scattering at tree level, studying the effects of nonlocal form factors in the gravitational sector. We give an interpretation of our results in terms of geodesic motion in effective generalized Aichelburg-Sexl geometries for the massless case, and in smeared linearized Schwarzschild metrics for the massive case in the probe limit. Combining our results for the geometries at linearized level with general requirements about the behaviour of the solutions in the core, we propose a nonlinear completion of the geometries. The resulting spacetimes describe singularity-free, asymptotically flat deformations of the Schwarzschild solution with a de Sitter core. We also analyze the main geometric and thermodynamic features of these solutions.

We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a spindle $\mathbb{WCP}_{[n_1,n_2]}^1$. Starting from the spindle solutions of five-dimensional STU gauged supergravity, we construct theories on a spindle which preserve supersymmetry via either the twist or anti-twist mechanism and admit two Killing spinors of opposite R-charge. While the study of field theories on anti-twisted spindles has already been undertaken in some detail, the advantage of our approach allows for the derivation of analogous results in the twist case. We apply the technique of supersymmetric localisation to compute the exact partition function for a theory consisting of an abelian vector multiplet and a charged chiral multiplet in the presence of a Fayet-Iliopoulos term. We compare and contrast the results for the twisted and anti-twisted spindle and find a general formula which encompasses the partition function for both cases simultaneously.

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

We numerically investigate whether the center-symmetric confined phase of large-$N$ $SU(N)$ gauge theory with one adjoint Dirac fermion persists under spatial compactification on $\mathbb{R}^3 \times S^1$. To this end, we employ a partially reduced twisted Eguchi-Kawai (TEK) model on a $1^3 \times L_4$ lattice with an adjoint Wilson fermion, and measure both the Polyakov loop around $S^1$ and order parameters for volume independence in the reduced directions. For $N=36$, $L_4=2$, $b=0.30\text{-}0.46$, and $\kappa=0.03\text{-}0.16$, we find that, with periodic boundary conditions, the Polyakov loop remains near zero in the light-fermion regime as the circle size is reduced. For the modified twist, the volume-independence order parameters are also consistent with zero in the explored region, supporting the validity of the partially reduced description. These results provide numerical evidence, within the reduced-model setup and parameter range studied, for an adiabatic-continuity scenario in which the confined phase is smoothly connected between large and small circles. By contrast, with antiperiodic boundary conditions, the Polyakov loop exhibits a clear deconfinement transition. We also discuss how this scenario is compatible with the anomaly constraints of the underlying four-dimensional theory. The symmetric twist is examined as a useful comparison, although its volume-independence properties appear less robust at the present value of $N$.

We extend the Hodge atoms framework of Katzarkov–Kontsevich–Pantev–Yu to one-parameter conifold degenerations of Calabi–Yau threefolds. For a degeneration $\pi\colon X \to \Delta$ whose central fiber $X_0$ has $r$ ordinary double points, we construct a canonical rigid-flexible decomposition of the Hodge atoms of the nearby smooth fiber attached to the corrected degeneration object. The rigid atom $A(\IC^H_{X_0})$ is preserved across the degeneration, while the flexible atoms $A(i_{k*}\QQ^H_{\{p_k\}}(-1))$ are rank-one contributions, one for each vanishing cycle. The total degeneration atom $A(P^H)$ is the atom of the corrected mixed Hodge module $P^H\in\MHM(X_0)$ and fits into an exact sequence of atoms whose non-split structure is controlled by the intersection matrix $(\langle\delta_i,\delta_j\rangle)$. The technical core is the Stokes–Extension Identification, which identifies the Stokes matrix of the Dubrovin connection at the conifold locus with the matrix of the variation morphism $\varF\colon\varphi_\pi(F) \to \psi_\pi(F)$ under mixed Hodge module realization.

We investigate the holographic Schwinger effect in a confining background with a step dilaton profile, which induces a sharp transition between ultraviolet and infrared regimes and provides a qualitatively distinct realization of confinement. Within this framework, the quark–antiquark potential is extracted from the classical configuration of a fundamental string, allowing for a direct analysis of vacuum instability and pair production. In the absence of a magnetic field, the step dilaton leads to a significantly sharper suppression of the potential barrier as the electric field increases, implying an enhanced sensitivity of the critical electric field compared to smooth soft-wall models and demonstrating that the abrupt geometric transition qualitatively enhances the onset of vacuum decay. Incorporating an external magnetic field through the Dirac–Born–Infeld action, we find a nontrivial and amplified deformation of the potential barrier, resulting in a pronounced shift of the critical electric field that depends on both the magnitude and orientation of the magnetic field. Overall, the step dilaton background exhibits a substantially stronger response of the Schwinger effect to external electromagnetic fields than conventional soft-wall models, providing a novel mechanism for controlling pair production and highlighting the crucial role of dilaton structure in non-perturbative dynamics of holographic QCD.

We derive strict quantitative conditions under which a collective quantum system of N~370 spins exhibits classically forbidden temporal correlations in a spinor Bose-Einstein condensate (BEC). The Lipkin-Meshkov-Glick (LMG) model near its Z_2-breaking quantum critical point supports a mesoscopic superposition a|P> + b|R> of two macroscopic ordered phases (|P>: m_z ~ +m_*; |R>: m_z ~ -m_*) at the Goldilocks crossover N ~ N_c, where the tunnel splitting equals k_B T and macroscopic susceptibility chi ~ N coexists with finite quantum coherence. We establish two quantum-discriminating predictions. P4 (Landau-Zener crossover, proposed discriminator): quantum tunnelling drives P_error -> 0 exponentially with quench time, while the classically non-ergodic system remains kinetically frozen at P_error -> 1 - a parametrically large, computable separation that rests on a specific kinetic foil. P5 (Leggett–Garg inequality violation, strictly model-independent): K_3 > 1 is forbidden by macrorealism for all classical models satisfying non-invasive measurability. A five-level Lindblad simulation yields K_3 ~ 1.32 and dephasing threshold gamma_phi < 0.289 s^{-1} at the BEC target (gamma_phi = 0.05 s^{-1}, N = 370, Gamma/J = 0.95) - a margin of 8.8x above the optimal measurement interval, well within current experimental reach. The threshold has a precise physical origin in the emergent collective Z_2 symmetry: exact parity eliminates the dominant dephasing cross-term and renders the LGI correlator immune to T_1 population mixing without requiring ground-state preparation (2.35x improvement over the naive mean-field estimate); constructive dynamical phase alignment of higher odd-parity states at the benchmark parameters contributes a further 2.47x. All results are reproducible from the provided self-tested Python code.

Precision Higgs physics offers a sensitive window into physics beyond the Standard Model. In parallel, neutrino-oscillation experiments have established the existence of nonzero neutrino masses, thus implying the presence of new physics. Motivated by these facts, we investigate the one-loop contributions of light and heavy Majorana neutrinos to the $ZZh$ vertex within a variant of the type-I seesaw mechanism in which light-neutrino masses vanish at tree level and are then generated radiatively. We analyze the $CP$-conserving and $CP$-violating anomalous couplings which characterize the $ZZh$ vertex and study their phenomenological implications in two relevant kinematic scenarios at future lepton colliders: Higgsstrahlung production and Higgs production via neutral-current vector-boson fusion. We find that $CP$-conserving effects can reach magnitudes of order $10^{-3}$, potentially within projected future experimental sensitivities, whereas $CP$-violating contributions are strongly suppressed, lying well beyond such projections.

Optimal transport and Wasserstein distance are prominent tools to quantify the space of probability distributions. From a novel viewpoint of manifold hypothesis in machine learning being a possible guide for the holographic principle, we study how holographic spacetime can emerge from quantum systems in general as a Wasserstein space through optimal transport. We employ the simplest example of a single quantum harmonic oscillator and demonstrate that, among various definitions of distance, the manifold hypothesis selects the 1-Wasserstein distance of optimal transport between Husimi Q-representations of states, and it gives rise to an emergent space. Furthermore, the Lindblad time evolution of the harmonic oscillator coupled to a bath, of the form of a Fokker-Planck equation, provides a time trajectory in the Wasserstein space, yielding an emergent Wasserstein spacetime that shares properties with black hole spacetimes and their event horizons. The methodology is applied to a Lindbladian subsystem of SYK model, revealing that the Wasserstein space is consistent with the AdS${}_2$ black hole geometry of the standard holographic dictionary. We remark that, in our examples, the 1-Wasserstein distance is identified as a generalized Krylov complexity, and argue that optimal transport with the manifold hypothesis can yield general emergent spacetimes, positioning the holographic principle on a broader basis.

The motivation behind the present work is to adopt methodology from field theory and high-energy physics to crystallography. In particular, we establish a relationship between the electromagnetic sector of the Standard-Model Extension (SME) for Lorentz invariance violation and optical media. At an effective level, electromagnetic properties associated with different crystal structures are demonstrated to be parametrized in the SME. Crystallographic and magnetic point groups provide the mathematical tools to show this correspondence. Birefringent and magnetoelectric media merit a dedicated study. Intriguing effects, which have not been described systematically in the modern literature, are rediscovered for the latter and expressed in SME language. With the setting developed at our disposal, materials with specific symmetries such as birefringent or multiferroic crystals serve as condensed-matter analogs for SME effects. It enables us to propose materials with unusual optical properties, which have not been thoroughly looked at in recent times.

Feynman briefly considered a nonlinear theory of gravity in flat spacetime by imposing energy-momentum conservation on the sum of the energy-momentum tensor of matter and that of the gravitational field. He used the symmetrized canonical energy-momentum tensor as the energy-momentum tensor of the gravitational field. He reported that the resulting construction gave an incorrect value for Mercury's perihelion precession and abandoned this route in favor of a variational argument based on dynamical consistency. We reconsider the abandoned route. The key step is to identify the gravitational energy-momentum tensor not with the conventional Belinfante tensor, which becomes symmetric upon use of the field equations, but with its off-shell Belinfante-Rosenfeld tensor, which contains explicit Euler-Lagrange terms. If we apply the law of conservation of energy and momentum to the sum of this tensor and the matter energy-momentum tensor, we obtain Feynman's consistency condition. Thus Feynman's dynamical-consistency argument and the reconstructed energy-momentum argument, although based on different physical assumptions, yield the same identity. The Euler-Lagrange terms are essential to this result.

We investigate the combined effects of a brane intersecting the AdS boundary and background gravitational field on the local characteristics of the electromagnetic vacuum. Two types of boundary conditions on the brane are considered, which are higher-dimensional generalizations of the perfect electric (PEC) and perfect magnetic (PMC) boundary conditions in Maxwell's electrodynamics. The brane-induced contributions to the Wightman functions of the vector potential and field tensor are explicitly extracted. Simple expressions in terms of elementary functions are provided. The behavior of the vacuum expectation values (VEVs) is mimicked by a scalar field with a negative effective mass squared determined by the radius of the AdS spacetime. The expectation values of the electric and magnetic fields squares and of the energy-momentum tensor are investigated as local characteristics of the vacuum state. The brane-induced contributions to these VEVs have opposite signs for the PEC and PMC conditions. For the PMC condition, this contribution is negative for the electric field squared and positive for the magnetic field squared. The VEV of the energy-momentum tensor has a nonzero off-diagonal component. The brane-induced vacuum energy density is positive for PMC condition, whereas the normal and parallel stresses change sign as functions of the distance from the brane. Unlike the problem involving a planar boundary in the Minkowski bulk, the vacuum energy-momentum tensor does not vanish in (3+1)-dimensional AdS spacetime.

We show that the diffusion-based models proposed in Refs.~\cite{Perez2021,Landau2022} within the framework of Unimodular Gravity (UG) to alleviate the $H_0$ tension are incompatible with the second law of thermodynamics. Starting from the Gibbs equation for a pressureless matter fluid, we derive a general thermodynamic admissibility condition for the $\Lambda$CDM$+$diffusion class in UG, demonstrating that the second law requires $\dot{Q} < 0$, independently of the specific form of the diffusion function $Q(t)$. This condition implies that energy must flow from the effective cosmological term $\Lambda_{\rm eff}$ into the matter sector, rather than in the opposite direction. We then establish a no-go theorem: no choice of $Q(t)$ can simultaneously satisfy the second law and generate the growing effective cosmological term $\dot{\Lambda}_{\rm eff} > 0$ required to alleviate the $H_0$ tension. We confirm this result explicitly for the models of Perez, Sudarsky, and Wilson-Ewing~\cite{Perez2021} and Landau et al.~\cite{Landau2022}, noting that the former explicitly identify $\dot{\Lambda}_{\rm eff} > 0$ as a necessary feature of their proposal without addressing its thermodynamic implications. The incompatibility is therefore structural and applies to the entire class of $\Lambda$CDM$+$diffusion models in UG with a pressureless matter component.

The coadjoint orbit action for a multifermion system, as an exact description of its dynamics, is considered. A parametrization of the variables involved is given which facilitates the approximation of this by another coadjoint orbit action suitable for expansions around the Fermi surface, recovering various actions which have been used in previous literature. The presentation of this in terms of functions on phase space with star-products as well as further truncations are briefly considered.

We introduce a refined version of the 3D index for 3-manifolds, building on the construction of the 3D $\mathcal{N}=2$ gauge theory $T[M]$ by Dimofte-Gaiotto-Gukov and Gang-Yonekura. The refined index is a superconformal index of $T[M]$ equipped with additional gradings that capture enhanced flavor symmetries of the effective theory. Our construction is based on a Dehn surgery presentation of $M$ in terms of an ideally triangulated link complement $N$. We derive an explicit infinite-sum formula for the refined index and provide nontrivial checks in representative examples, supporting its invariance under changes of triangulation, Dehn surgery presentation, and other auxiliary data. As a strictly stronger invariant, the refined index enables finer distinctions among 3-manifolds and among distinct IR phases of the associated gauge theories. We also introduce a computational tool, Refined Index Calculator, for its explicit evaluation.

We study the hydrodynamics of the Filtered Dark Matter (Filtered DM) scenario during a first-order phase transition (FOPT). In this scenario, the bubble wall is highly reflective of the dark matter (DM) fluid but transparent to radiation, making the hydrodynamic problem fundamentally different from that of the electroweak FOPT. Motivated by this property, we formulate the hydrodynamics of this system as a two-component fluid composed of DM and radiation, and find that the solutions can be classified into detonation-like and deflagration-like branches in the ballistic regime and in the local thermal equilibrium (LTE) regime. In the ballistic regime, the energy–momentum of DM that cannot enter the wall appears as a reflected mode, while in the LTE regime, it relaxes into the energy–momentum of radiation. We find that this difference in the fate of the DM fluid that cannot enter the interior of the wall leads to different hydrodynamic behaviors in the DM and radiation fluids independently and, in particular, results in different existence conditions for solutions in the deflagration-like branch. Based on these results, we further revisit the impact of hydrodynamic effects on the relic abundance of Filtered DM and demonstrate the change in the abundance induced by hydrodynamic effects. In addition, we also discuss the non-conservation of the entropy current from the viewpoint of the two-fluid system, and briefly comment on the similarity between the Filtered DM system and information-thermodynamic systems.

We establish a deformation framework for highly symmetric solutions to the Einstein equations. In this framework, four-dimensional metrics are constructed from three-dimensional {\eta}-Einstein metrics admitting a deformation determined by a single function. Under this deformation, the resulting spacetime solves the Einstein equations with a string-cloud source. Within this framework , a wide range of symmetric spacetimes can be treated in a unified manner. These include FLRW, Kantowski-Sachs, and LRS Bianchi cosmological models (including Taub-NUT-(A)dS solutions), as well as Reissner-Nordström-(A)dS black holes admitting spherical, planar, or hyperbolic symmetry. In the cosmological setting, the deformation leaves the evolution equations for the scale factors unchanged, and hence the expansion history coincides with that of the corresponding undeformed models. For the deformed Reissner-Nordström-(A)dS black holes, the structure of Killing horizons is insensitive to the deformation.

In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a smooth orientable manifold) and an observer-dependent one (which has an inherently discrete causal set structure). The interaction between the two allows us to prove the main result of the paper: relative locality can be obtained in general PQG models, regardless of momentum-space curvature. {We also discuss the treatment of spacetime symmetries in our model, and introduce a direct link between spacetime symmetries and relative locality effects.} Our construction is presented in a coordinate-independent way and is based on fibre bundles where spacetime, rather than momentum-space, is the base manifold. This makes causality manifest even in general models with relative locality. Furthermore, it allows for the application of this formalism to cosmology on general backgrounds, something which is not clearly possible in the canonical approach to relative locality, where momentum-space serves as the base manifold.

In this paper, we study the quasinormal modes of the generalized Joshi-Malafarina-Narayan (JMN) naked singularity spacetime using the exact Wentzel-Kramers-Brillouin (WKB) method. Working in the complex radial plane, we construct the exact WKB momentum function, determine its turning points, and compute the associated Stokes geometry for representative quasinormal mode (QNM) frequencies. We obtained a bow-shaped deformation of Stokes curves on the side of the complex plane containing the central singularity in JMN spacetime. We show analytically that this structure originates from the logarithmic branch-point singularity of the WKB phase at $(r = 0)$, which is absent in Schwarzschild spacetime. This establishes the bow-shaped Stokes topology as a direct signature of the naked singularity in the global analytic structure of the perturbation equation. Our results demonstrate that exact WKB analysis provides a powerful framework for probing the analytic structure of compact objects, and suggest that topological features of Stokes geometry may offer a new avenue for distinguishing black holes from horizonless alternatives.

We investigate bubble dynamics in a holographic superfluid undergoing a first-order phase transition with spontaneous $U(1)$ symmetry breaking. Near the nucleation threshold, the system exhibits universal critical behavior governed by a single unstable mode, leading to logarithmic scaling of the time spent near the critical solution. The terminal bubble wall velocity increases with charge density but remains small due to strong dissipation. In multi-bubble collisions, vortex formation depends sensitively on the initial phases and deviates significantly from the geodesic rule. Notably, we identify a regime where three-bubble collisions produce a vortex-antivortex pair that subsequently annihilates, a phenomenon not predicted by the geodesic rule. The lifetime of this pair scales logarithmically with the distance to the critical collision radius. Our results underscore the crucial role of non-equilibrium dynamics in strongly coupled superfluids and provide new insights into topological defect formation during first-order phase transitions.

We present a review of supersymmetry, supergravity, and the non-perturbative dynamics of gauge theories, tracing a path from the supersymmetry algebra to moduli stabilisation and de~Sitter vacua in string theory. Representations of the supersymmetry algebra, the superspace formalism, and basic models including the Wess–Zumino model and $\mathcal{N}=1$ supersymmetric Yang–Mills theory are discussed. The non-perturbative dynamics of $\mathcal{N}=2$ gauge theories is analysed through the Seiberg–Witten solution: the curve, prepotential, Picard–Fuchs system, BPS spectrum, and confinement via monopole condensation. The transition to $\mathcal{N}=1$ supergravity is carried out in three steps, showing how the Kähler potential $K$ and superpotential $W$ determine all five Lagrangian sectors and how the scalar potential acquires its exponential prefactor and gravitationally induced negative contribution. String theory applications include D-brane gauge theories, the AdS/CFT correspondence, geometric engineering of the Seiberg–Witten solution, and reduction of $\mathcal{N}=4$ to $\mathcal{N}=1$ supersymmetry. The KKLT moduli stabilisation mechanism is analysed in detail, including $\alpha'^3$ corrections to the Kähler potential. Three regimes of the scalar potential are identified – classical KKLT, corrected KKLT with a shifted AdS minimum, and a runaway regime – and the critical parameter $\hat{\xi}_c$ separating controlled de~Sitter vacua from decompactification is determined. The tension with the de~Sitter swampland conjecture is discussed.

In this thesis, we have used a linearized quantum gravity setting to investigate the effects of gravitons on matter systems. Based on the graviton-matter interaction, we have then proposed detector models that may be able to pick up graviton-induced signatures in a matter of a few years. We start with the simple model of a two-particle model detector system interacting with quantized gravitational fluctuations while the detector degrees of freedom obey the generalized uncertainty principle (GUP). For the first part we have hinted at the existence of quantum gravity induced memory effect as well as obtained a quantum gravity modified uncertainty relation. For the next part of the thesis, we have mainly focused on the phenomenological aspects of a linearized quantum gravity theory. For the initial phenomenological model, we have considered the same two-particle model detector system interacting with gravitational fluctuations where the entire set-up is placed inside a harmonic trap potential and looked at the stimulated absorption and spontaneous emission scenario for gravitons. In order to inspect a more involved phenomenological aspect, instead of the standard matter-detector system, we make use of a relativistic scalar Bose-Einstein condensate (BEC) and investigated the response of the BEC based model towards incoming gravitons and proposed a graviton detector based on graviton mediated decoherence from entangled BECs.

A "mysterious" relation between the number variance and the variance of the $L$-th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited and proven to be asymptotically exact for the $\beta=2$ Dyson symmetry class. Central to the proof is a previously unknown sum rule for the level spacing auto-covariances. Its derivation hinges on our previous work on the power spectrum description of eigenvalue fluctuations in random matrix theory. Analytical results for $\beta=2$ are complemented by conjectural extensions to the $\beta=1$ and $\beta=4$ symmetry classes. Our findings are corroborated by a comprehensive numerical analysis.