Papers

Colour-kinematics duality is, even at tree level, not manifest from the standard Lagrangian of Yang-Mills theory in that the usual Feynman-diagram expansion does not follow the kinematic Jacobi identities. For a Lagrangian manifesting colour-kinematics duality, the kinematic Jacobi identities of the Feynman-diagram expansion follow from the existence of a second-order differential operator $\mathsf{b}$ acting on the algebra of colour-stripped fields that forms part of the data of a BV$^\square$-algebra. We argue that the existence of differential operators of order greater than two implies weaker but nontrivial fragments of kinematic Jacobi identities. We further show that a superspace formulation of the first-order Yang-Mills action in the Batalin-Vilkovisky formalism admits a differential operator of order six in every spacetime dimension. Therefore, the Feynman-diagram expansion of tree and loop scattering amplitudes of the first-order formulation of Yang-Mills theory automatically enjoy a weak form of colour-kinematics duality.

Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic $\bar{Q}Q$ systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature $T$ and the $\bar{Q}Q$ energy gaps ($\Delta E$) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for $T\gtrsim \Delta E$ to the quantum optical (QO) regime for $\Delta E\gtrsim T$. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the $Q\bar{Q}$ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.

We characterize the gravitational radiation present in the general Plebański-Demiański type~D solution with cosmological constant $\Lambda$ of any sign. We show that radiation escapes towards infinity if and only if the acceleration parameter is non-zero. We calculate the Cotton-York tensor and the boundary stress-energy tensor at infinity for negative $\Lambda$, and for positive $\Lambda$ the $D$ tensor that complements initial or final data at $\mathscr{J}$. In addition, we recast a recent parametrization of this family of metrics into a new form by a simple homothety, correctly identifying $\Lambda$, and study the existence and regularity of the possible axes of symmetry, searching for a relation between deficit angles and radiation. We also identify the branch of general non-radiating solutions with non-vanishing Cotton-York tensor at $ \mathscr{J} $.

We investigate the sensitivity of IndIGO-D, a proposed space-based decihertz gravitational-wave interferometer, to different classes of ultralight dark matter. IndIGO-D will probe the $\sim0.01$–$10~\mathrm{Hz}$ frequency band between those accessible to current ground- and future space-based gravitational-wave interferometers, providing access to ultralight dark-matter masses beyond the reach of existing instruments. We consider two complementary signatures: interferometric displacements induced by coherently oscillating scalar (dilaton), vector (dark-photon, $U(1)_B$ and $U(1)_{B-L}$ gauge groups), and tensor fields with masses $m_{\rm DM}\sim10^{-17}$–$10^{-14}~\mathrm{eV}$; and changes in laser polarization induced by pseudoscalar axion dark matter at higher masses, around $m_a\sim10^{-12}~\mathrm{eV}$. For the dilatons, dark photons and tensors, we compute the expected sensitivities using two pipelines – cross-correlation and BSD excess-power – assuming L-shaped and triangular interferometer layouts and three representative noise power spectral densities (S1, S2, S3), each for two years of continuous observation. We find that the projected sensitivities agree to within a factor of order unity across the search pipelines and interferometer geometries. In particular, we show that IndIGO-D could open previously unconstrained coupling parameter space for vector and tensor dark matter across $m_{\rm DM}\sim10^{-16}$–$10^{-14}~\mathrm{eV}$, bridging the sensitivity of space- and ground-based experiments. For axion dark matter, we demonstrate that a complementary detection for laser light polarization shifts, limited primarily by photon shot noise, could probe the axion-photon coupling $g_{a\gamma}$ at masses around $m_a\sim10^{-12}~\mathrm{eV}$ at a level potentially better than that of other future experiments without degrading sensitivity to gravitational waves.

We investigate the fluid interpretation, Hawking–Ellis classification, and energy conditions of the proper kinetic gravity braiding contribution to the stress tensor of minimally coupled scalar fields for timelike, spacelike, and open-region null scalar gradients. Using a $2+1+1$ decomposition adapted to the gradient, we derive the associated effective fluid variables. Unlike k-essence, braiding generates heat fluxes and pressure anisotropies: radial and tangential heat fluxes for timelike gradients, and a radial heat flux plus mixed radial–tangential anisotropies for spacelike gradients. These quantities depend only on the normal fundamental scalars and the two-dimensional accelerations, despite the larger set of variables appearing at intermediate stages. For open-region null gradients, the proper-braiding stress tensor has null-dust form. We obtain the complete Hawking–Ellis classification: the timelike sector is Type I for positive discriminant, Type II on the nontrivial discriminant hypersurface, and Type IV for negative discriminant; the spacelike sector has the same generic branches and additional Type II and Type III degeneracies when the squared radial heat flux equals the squared mixed anisotropy. The open-region null sector is Type II for nonzero null-dust density and vanishes in the zero-density case. Finally, the standard energy conditions further restrict the Type I and generic Type II sectors. The null energy condition excludes Types III and IV and, for spacelike gradients, every nonzero radial heat flux or mixed anisotropy. Thus admissible spacelike proper braiding is diagonal, whereas in the timelike sector the energy conditions bound the total heat flux.

In the late 1980s, Baulieu and Grossman demonstrated that the supersymmetric formulation of Langevin stochastic differential equations (SDEs), proposed earlier by Parisi and Sourlas, belongs to the family of Witten-type topological field theories (TFTs). From a certain angle, this finding may appear puzzling: TFTs have no local degrees of freedom, whereas SDEs do exhibit local fluctuations. In this paper, we address this apparent contradiction in the context of the supersymmetric theory of stochastic dynamics (STS), a generalization of the Parisi-Sourlas-Baulieu-Grossman approach to SDEs of arbitrary form. We further discuss how, within STS, dynamical chaos can be identified with the spontaneous breakdown of the corresponding topological supersymmetry, while 1/f noise can be understood as a consequence of the Goldstone theorem. The butterfly effect, in turn, calls for an effective field-theoretic description that may itself possess a hidden topological structure, as we speculate on the basis of the Ginzburg-Landau approach and insights from AdS/CFT duality.

We investigate the quasinormal modes (QNMs) and greybody factors of dilaton-Euler-Heisenberg (dEH) de Sitter (dS) black holes in string-inspired Euler-Heisenberg gravity. Since the axial gravitational and electromagnetic perturbations decouple, we treat them independently. By applying the asymptotic iteration method (AIM) alongside a sixth-order WKB approximation, we compute the quasinormal frequencies and find excellent agreement between the two approaches. We also find that the QNM spectra depend sensitively on the magnetic charge $Q_{\text{m}}$, cosmological constant $\Lambda$, and nonlinear coupling $\epsilon$, with a notable topological anomaly appearing in the electromagnetic frequency trajectories. Additionally, larger values of $Q_{\text{m}}$ or the multipole number $l$ generally suppress wave transmission, while the electromagnetic sector with $\epsilon=1$ exhibits an anomalous response.

We perform a global search for values of the Yukawa matrices and Majorana masses in the Type-I seesaw mechanism. Using flow matching, which is a generative artificial intelligence (generative AI) method, we generate a broad set of solutions reproducing the experimentally measured values of the neutrino mass-squared differences and the mixing angles. Then, a machine learning method known as an autoencoder is applied to uncover non-trivial correlations among physical quantities in the lepton sector. Our analysis reveals new non-linear relations involving neutrino masses and CP phases. These findings may contribute to elucidating the origins of the mass hierarchies and mixing patterns among generation structure.

We construct spinning conformal fields from neural networks and the embedding formalism, computing their two-, three- and four-point functions in examples, building on scalar conformal field techniques introduced in \cite{Halverson:2024axc}. For a particular ensemble of i.i.d. neurons we recover the 4d Maxwell CFT in the infinite-width limit.

We study finite-rate mode selection among competing Landau-unstable modes in a holographic superfluid. The selected mode is not generally the instantaneous fastest-growing one, while time-dependent linear evolution on the driven background reproduces the full dynamics. Protocols with identical present driving conditions can exhibit opposite modal ordering, revealing memory of the preceding drive. This memory is quantitatively captured by the accumulated difference between the QNM growth rates of the competing modes.

Black-hole entropy and multi-horizon area-product relations represent two apparently distinct manifestations of universality, arising respectively from microscopic statistics and classical geometry. We show that these structures are unexpectedly connected. Extending a minimum-assumptions statistical discretization to multiple Killing horizons, with distinct horizon sectors treated as statistically independent, we derive a general area-product rule. In particular, while the leading Bekenstein-Hawking entropy probes the sum of the horizon areas, the logarithmic correction probes their product. Consequently, whenever the classical area product is mass independent, the logarithmic entropy automatically inherits this universality. We demonstrate this for Reissner-Nordström and, under an area-based extension to rotating horizons, Kerr-Newman black holes. However, Reissner-Nordström-de Sitter provides a crucial three-horizon counterexample, for which the area-product rule survives while mass independence is generically lost for the physical horizons. Thus, statistical area-product selection and classical universality are distinct properties. Our results uncover a structural connection between microscopic entropy counting and classical multi-horizon geometry that is invisible at the level of the leading area law, suggesting that logarithmic corrections encode distinctive information about the global horizon structure.

We study a mirror Standard Model world which contains a high scale duplicate of the Standard Model, and includes a singlet mirror scalar extension coupled to the mirror Higgs particle. Among the interactions of the mirror Higgs to the mirror singlet scalar, we include dimension-six non-renormalizable operators. We examine the electroweak phase transition of this mirror singlet extended world and we show that the phase transition is a strong first order phase transition, the bubble collision of which can be detectable by LISA, the BBO and the DECIGO gravitational wave experiments. We also provide a rough estimate of the abundance of the mirror singlet and we show that the whole dark matter in the Universe may be comprised by mirror particles and atoms.

Can the characteristic monodromy of string scattering be derived from S-matrix consistency alone, without assuming a worldsheet? We show that finite-particle consistency fixes it to a sharply defined extent. In a massless doubly ordered identity model, two exact six-point residues generate a scalar pentagon and the odd Fay identity, forcing every analytic four-point null kernel to satisfy $q''=\kappa q$ and leaving only the linear, trigonometric, and hyperbolic branches. This converts finite-multiplicity factorization into an all-orders constraint normally associated with worldsheet geometry. For a crossing-symmetric target in the opposite KLT module, positive unsubtracted dispersion with nonzero heavy spectral weight selects the trigonometric branch, and moment determinacy fixes the Veneziano germ up to scale. A two-scale counterexample proves that module entrance is an independent input. Our result therefore identifies both a finite-to-infinite rigidity mechanism for string scattering and the precise missing principle needed for a first-principles derivation.

Hawking radiation away from stationarity is governed, at the ray tracing level, by the retarded time evolution of the null mapping. We consider an extracted massless conformal channel whose outgoing directions are labelled on a fixed reference horizon slice. Balanced uniformisation, after fixing a nondegenerate balanced branch, defines an induced antipodal involution on this slice. We prove that creation and erasure of centred antipodal odd structure in the channel labelled peeling field enforce a lower bound on the time integrated spatial norm of the conformal channel defect. The forcing scale depends only on the largest intermediate mismatch and the intrinsic Jacobian distortion of the induced antipode, while greybody filtering, angular and frequency mixing, mass effects, spin dependence, and residual propagation or extraction corrections enter through a remainder whose integrated norm must be controlled independently. Round sphere odd scalar harmonics provide analytic calibrations, with the compact dipole pulse saturating the geometric and temporal estimates. A time-averaged form identifies a transient conformal channel scale proportional to the antipodal peeling amplitude divided by the episode duration.

We revisit the twelve-dimensional anomaly polynomial that has long been known to govern M5-brane worldvolume theories, together with its more recently proposed D3-brane counterpart. We show that these constructions naturally fit into the framework of equivariant integration, allowing the anomaly inflow formulas to be rewritten entirely in terms of equivariant volumes. In particular, we use the fact that the Bott–Cattaneo formula for the integral of powers of the global angular form on $S^{2k}$ emerges from the equivariant Euler-class integration of $\mathbb{C}^k$, with two copies glued antipodally at the north and south poles of the sphere. Building on this perspective, we generalize the anomaly construction to include both electrically and magnetically charged branes, thereby incorporating M2-branes as well as a dual formulation of D3-branes. This provides a unified framework encompassing a number of classical results together with several recent developments, and offers a natural interpretation of the recently proposed M2/M5 duality, arxiv:2604.06343, in terms of an AGT-like correspondence. Remarkably, it also leads to a direct reinterpretation of constant-map contributions in topological string theory as manifestations of M-theory anomalies.

We apply a convenient parametrization of all Plebanski-Demianski black holes of algebraic type D with the Kerr rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $\Lambda$, recently found by Astorino. This represents a complete class of exact solutions to the Einstein-Maxwell-$\Lambda$ equations such that the (non-null) electromagnetic field is aligned with both the (geodesic, shear-free, double) principal null directions of the Weyl tensor. We derive a novel appropriate metric form and the corresponding canonical frames naturally adapted to both the de~Sitter-like ($\Lambda>0$) and the anti-de~Sitter-like ($\Lambda<0$) conformal infinity, and we demonstrate that these geometric objects are useful for investigation of radiation properties. In particular, using the Fernandez-Alvarez-Senovilla criterion, it confirms that the gravitational radiation is present if, and only if, these black holes are accelerating.

We compute the leading order modification to the quark-antiquark-$W$-boson vertex in the presence of a constant and uniform magnetic field, specifically for the case where the quark and antiquark are the $u$ and $\bar{d}$, respectively. We find the selection rules for transitions where the $u$, $\bar{d}$, and $W$-boson occupy arbitrary Landau levels. We show that, for the particular case where the initial particles each occupy the lowest Landau level, the $W^+$ is also produced in the lowest Landau level with a single polarization aligned with the magnetic field. We also illustrate the general findings by computing the case of transitions between low lying Landau levels and show the correspondence between the polarization vectors for the $W$-boson and the polarization states for the quark and the antiquark.

This thesis studies 4D F-theory compactifications with fluxes and their connection to particle physics, accompanied with a review of F-theory. First, we develop a general formalism for gauge symmetry breaking with fluxes. Vertical and remainder fluxes can be used to break a rigid gauge group, with the former simultaneously inducing chiral matter, even when the unbroken gauge group has no complex representations. We show that it is fairly likely to have three generations of chiral matter. We focus on the realization of the Standard Model gauge groups and chiral matter by breaking rigid $E_7,E_6$ gauge groups with an intermediate SU(5) gauge group, and provide examples of explicit constructions. Then, the phenomenological aspects of rigid $E_7$ models are studied in detail. We find that many other Standard-Model like features are naturally compatible with the $E_7$ models. For example, dimension-4 and dimension-5 proton decay are ubiquitously suppressed. Many of these features are due to the group-theoretic structure of $E_7$ and its F-theory geometry. In particular, a set of approximate global symmetries descends from the $E_7$ group, leading to exponential suppression of undesired couplings. These features suggest a new set of grand unified theories based on the $E_7$ group and its string theory construction. Finally, we study constructions of abelian gauge symmetries with exotic charges. By breaking a rigid nonabelian group to a U(1) gauge group using vertical flux, very large charges can arise in the massless or light spectrum. We give an explicit construction in 4D F-theory in which the vector-like matter carries charges as large as 657, which is much larger than the previously known bounds in F-theory. We heuristically argue that this result may provide an upper bound on charges for light fields under decoupled U(1) gauge groups in the F-theory landscape.

This work develops the deterministic, discrete proper-time framework introduced in our previous work, Eur.\ Phys.\ J.\ C 86 (2026) 829, in which quantum field theory emerges as an effective infrared description characterized by a running Planck constant. There, the effective quantization scale was inferred from the microscopic multiplicity unresolved by coarse-graining. Here, we provide its dynamical and operatorial realization and extend the construction to fermionic degrees of freedom. First, consistency under changes of macroscopic resolution leads to the structure of the Renormalization Group Equation, while the running Planck constant governs the crossover toward the deterministic regime. Second, we represent the reversible microscopic dynamics through finite-difference translations in field-configuration space. After coarse-graining, the resulting operator-valued canonical commutation relations reproduce the same quantization scale previously obtained from statistical microstate counting, thereby linking microscopic evolution to the emergent canonical algebra. Third, representing the same update within a Grassmann algebra yields the corresponding canonical anticommutation relations. The bosonic and fermionic sectors thus inherit a common effective Planck constant without introducing an independent fermionic update or quantization scale. Finally, we discuss possible implications for high-energy loop amplitudes and effective Hawking radiation.

Gravitational waves (GWs) from first order phase transitions (FOPTs) are conventionally sourced by bubble collisions, sound waves, and plasma turbulence. We propose a novel microscopic GW source arising from graviton bremsstrahlung during the decay of the scalar field driving the FOPT. In the presence of Yukawa interactions with light fermions, the scalar decay is inevitably accompanied by graviton emission due to the universal coupling of gravity to the energy-momentum tensor. We show that these gravitons generate an additional stochastic GW background during the phase-transition epoch, complementing the conventional FOPT signal. The resulting GW spectrum can exhibit a characteristic multi-peaked structure. Unlike scenarios in which different GW components originate from distinct cosmological epochs, all contributions considered here emerge from the dynamics of the same FOPT, offering a unique probe of both its microscopic particle dynamics and macroscopic plasma evolution.

We study a generalization of a two-matrix model proposed by J. Hoppe in '89. At strong coupling and large $N$, we unveil an emergent area preserving diffeomorphism symmetry of this model, which allows us to completely solve it at leading order. The solution for all $n$-point connected correlators takes the form of a Witten diagram-like expansion in an emergent two-dimensional dual spacetime. We conclude with speculations about the quantization of this dual model and comment on its extensions to higher dimensions and relations to holography more broadly.

In the landscape of compactifications of type IIB string theory on O3/O7 orientifolds of Calabi–Yau threefolds, we identify regions of the axion potential in specific geometries that support small-field inflation, under the assumption that the overall Calabi–Yau volume can be stabilized at certain tuned values. At the tuned volume multiple critical points of the axion potential merge in a “catastrophe”, creating a region with small gradient and small Hessian determinant — necessary conditions for slow-roll inflation. We describe an algorithm that identifies several explicit examples of these catastrophes that have small field range $f / M_{\rm Pl} \ll 1 $ yet inflate for thousands of efolds. Some examples correctly reproduce the observed spectral tilt but not the amplitude of scalar perturbations, while others reproduce the observed amplitude but with a tilt that is slightly too red. All our examples have negligible tensor perturbations and no significant non-Gaussianity generated during the slow-roll phase. Our results demonstrate that string theory axions can be the source of cosmic inflation without alignment or large field ranges, provided that the Kähler moduli can be stabilized at special values of the volume.

At a black-hole exceptional point (EP), two quasinormal modes coalesce and their separate residues become ill-conditioned. Rather than postulating a near-degenerate modal fit, we derive the response constructively from the complex-scaled Regge–Wheeler–Zerilli resolvent, treating the modes as one isolated rank-two Riesz cluster. Its zeroth and first contour moments determine an exact pair resolvent on both sides of, and at, the EP, without labeling the individual modes or constructing a normalized Jordan chain. At a second-order EP, these moments determine the simple- and double-pole Laurent operators. Although the modal decomposition is singular, fixed-real-frequency transmission and the greybody factor remain real-analytic through the EP, provided that the cluster remains isolated, the complementary resolvent is regular, and no pole reaches the physical axis. Source–observer matrix elements of the Laurent operators define finite, normalization-independent amplitudes and fix both the constant and linear-in-time terms in the causal ringdown. Their equality with the coefficients from the Jost double-zero expansion shows that they are operator-defined coefficients of the specified physical response, rather than fitting parameters. Thus two cluster moments provide mode-label-free data from which both scattering and driven responses follow.

Consider level-$k$ $SL(2,R) \times SL(2,R)$ Chern-Simons theory on a semi-infinite solid cylinder, with a Wilson line in the unitary principal continuous series inserted along the time direction at the center of the spatial disc. We argue that at the $\tau=0$ cut, this Euclidean path integral prepares the bulk dual of a heavy Virasoro primary above the BTZ threshold, with Drinfel'd-Sokolov (DS) reduction playing a crucial role in converting the affine module into a Virasoro module. Semi-classically, the DS constraint turns into the DS gauge, familiar from asymptotically AdS$_3$ gravity. Together with boundary gravitons, these primaries provide a bulk construction of BTZ black hole microstates at finite $k$. In the large-$k$ WKB limit, the saddle that controls an $individual$ primary is the BTZ black hole with a $singular$ horizon. We study the (grand-)canonical partition function of the microstates with density of states dictated by modular invariance. The temperature and chemical potential then fix the holonomy saddle to be the Euclidean BTZ black hole with a $smoothly$ contractible thermal cycle. A density of heavy primaries growing as $e^{2\pi\gamma QP}$ would instead lead to a defect (or excess) saddle, except at the Cardy value $\gamma=1$ fixed by modular invariance. After analytic continuation, the eternal Lorentzian black hole with a smooth horizon is therefore not just any thermal ensemble, but the “modular ensemble" of (semi-classically singular) horizonless microstates. We compute the thermal fluctuations in this ensemble, and reproduce the fluctuations in the area of the form expected from semi-classical general relativity. Ensembles of theories do not play a direct role in any of our discussions. We also note that these microstates, unlike fuzzballs, do $not$ break the isometries of the black hole.

We compute the one-loop effects of vector-like fermions (VLFs) on the Higgs-strahlung cross-section, the flagship precision observable of future $e^+e^-$ Higgs factories such as FCC-ee. We consider four benchmark extensions of the Standard Model (SM): two in which a VL quark (VLQ) or VL lepton (VLL) doublet, together with its singlet partners, couples to the Higgs boson through purely internal Yukawa interactions, and two in which a single VL singlet mixes directly with the third-generation charged lepton or neutrino. Working throughout in the on-shell renormalization scheme and imposing perturbativity bounds on the relevant couplings under renormalization-group (RG) running, we compute both the universal self-energy and the non-universal vertex contributions to the Higgs-strahlung amplitude at one loop, together with the oblique parameters $S$ and $T$ and the $H\to\gamma\gamma$ rate as complementary cross-checks. In the two Yukawa-driven scenarios, we find that a sizable fraction of the parameter space still allowed by current LHC searches produces shifts in $\sigma(ZH)$ at or above the per-mille sensitivity envisioned for FCC-ee, offering a radiative probe of these couplings. In the two mixing-driven scenarios, existing electroweak-precision bounds on the relevant mixing angles already preclude an observable effect, although we characterize the underlying loop dynamics in full generality for future reference. These results identify the VL Yukawa couplings, rather than any residual mixing with the SM fermions, as the more promising target for Higgs-strahlung precision measurements at a future $e^+e^-$ collider.

After a historical introduction, the most important classical and quantum entropies are introduced as constructions in classical and quantum probability theory. Classical entropies are studied from large deviation theory, including theorems of Sanov, Cramér, Gärtner-Ellis, and Varadhan, and are illustrated in some applications to both Boltzmannian and Gibbsian statistical physics. Quantum entropies superficially connect to classical entropies at the formula level, but more deeply do so via the crucial role of entropy in statistical hypothesis testing. The classical (relative) Kullback-Leibler entropy, its quantum counterpart introduced by Umegaki, as well as their deformations proposed by Renyi all fit naturally in this context. Quantum entropy faces the new problem of defining and computing the relative entropy of a pair of states on a subsystem, here formalized as a von Neumann algebra. This requires modular (aka Tomita-Takesaki) theory, which provides the framework for the relative quantum entropies introduced by Araki and Uhlmann (these encompass both the Kullback-Leibler and Umegaki entropies as special cases). To (re)define and compute these entropies in terms of density operators and traces, further constructions are needed, namely Haagerup's noncommutative L^p spaces. Von Neumann algebras also provide the setting for the Connes-Stormer-Narnhofer-Thirring entropy, which is a quantum version of the Kolmogorov-Sinai entropy in dynamical systems and ergodic theory, to which we also provide an introduction. This course was originally inspired by, and should be relevant to, black hole thermodynamics, although we discuss neither this application nor the second law. The course tries to be both mathematically rigorous and interesting to theoretical physicists. Prerequisites are undergraduate probability theory, functional analysis, and quantum theory.

We construct an exact solution-generating correspondence between restricted ansatz sectors of quartic biadjoint scalar theory, complexified $SU(2)$ Yang–Mills theory and four-dimensional general relativity with conformally flat metrics and traceless energy-momentum. A factorised biadjoint field, a Corrigan–Fairlie–'t Hooft–Wilczek gauge potential and a conformal metric are generated by a common scalar seed. Their equations of motion reduce to the same equation of motion under the identification of couplings, which retains the nonlinear dynamics on all three legs of the correspondence. The scalar equation captures only the trace of the Einstein equations; deriving the trace-free part of the Einstein equation additionally yields a source relation between Gravity and Yang-Mills. From this, we construct a non-perturbative classical double copy for the restricted ansatz sectors between quartic biadjoint scalar theory, $SU(2)$ Yang–Mills theory and gravity. We illustrate the dictionary of mappable solutions with rational and constant profiles representing $AdS_4$, planar $dS_4$ and Minkowski space, and with Jacobi-elliptic profiles generating a positive-energy recollapsing branch for negative cosmological constant and a negative-energy bouncing branch for positive cosmological constant. Using these results, we provide a new example of the Kerr-Schild double copy.

Perturbations around a spherically symmetric solution of the scalar Dirac-Born-Infeld (DBI) theory obey the equation of motion of a massless scalar field in a curved background with black hole-like properties like finite temperature and an event horizon with zero speed of propagation of information (a black hole analogue). After reviewing some properties of the background geometry for the propagations, we investigate the solutions considering static and dynamic regimes. In the former case we obtain the so-called Love numbers, or more generally scalar polarizability. In the latter case, we employ boundary conditions analogous to the computation of quasi-normal modes, and argue that the background geometry acts as a classical high-pass filter. We therefore provide further evidence that the scalar black hole analogues can be analyzed similarly to a black hole.

We initiate the study of four point functions in the symplectic bi-Grassmannian framework for four dimensional conformal field theories. We derive factorization formulae analogous to those for scattering amplitudes and bootstrap several examples of AdS$_5$ exchange correlation functions involving scalars, photons, fermions, gluons and gravitons. These correlators are rational functions of the minors of the Grassmannian matrices in contrast to their momentum space counterparts which are much more complicated. We then develop the $GL(2,\mathbb{R})$ twistor space formalism, deriving the Penrose transform and the twistorial Grassmannian where we find remarkably simple expressions. We also find an elegant and natural extension to $\mathcal{N}=1$ supersymmetry, deriving the supersymmetric Penrose transform and the super-twistor Grassmannian. Performing a half-Fourier transform from twistor space, we derive the supersymmetric symplectic bi-Grassmannian corresponding to spinor-helicity variables. We test our formalism in the context of AdS$_5$ $\mathcal{N}=1$ super-Yang Mills theory where we impose consistent factorization and input the bootstrapped four-fermion correlator to obtain those involving gluons, scalars and fermions. Finally, we discuss the application to supergravity theories.

We construct the bulk kinematical Poisson structure of general relativity on a caustic-free null segment, prior to imposing the Raychaudhuri and Damour constraints. We first show that shifts of the Ehresmann connection, also known as Carroll boosts, are pure gauge in gravity. This allows the Ehresmann connection to be fixed as a background structure and leads to the prime phase space of null gravitational data. The resulting phase space comprises of a spin-0 pair that includes the area and its conjugate, a spin-1 pair including the null direction and its conjugate, and the spin-2 sector encoded in the unimodular transverse metric. We then construct the brackets through a three-stage Dirac reduction implementing a normalization, horizontality, and shear constraints. We find that the spin-2 bracket is non-local and involves an antisymmetric Green kernel for a first-order transport operator along the null generators. The self-brackets of the spin-0 and spin-1 momenta involve, respectively, the vertical and horizontal derivatives of the transverse metric contracted with the spin-2 propagator. We finally provide an independent derivation of the brackets from the explicit realization of the Hamiltonian vector fields of the symplectic form. These results provide the classical canonical arena for studying the null constraint algebra, observables, and quantization.