Papers

We analyze finite-temperature effects in the perturbative Large Volume Scenario (LVS), examining the dynamics of thermalized Kähler moduli and the stability of thermally induced vacua. We determine the maximum decompactification temperature $T_{\max}$, showing its dependence on winding-loop corrections in the effective theory. Moduli stabilization arises from perturbative logarithmic loop corrections to the Kähler potential, with higher-derivative $F^4$ terms used to test vacuum robustness. We derive cosmological implications, including bounds on reheating, and show that the model favors high scale inflationary scenarios with the heavy modulus decaying before dominating the energy density of the universe. We also analyze thermal metastability, demonstrating that the recovery of the $T=0$ vacuum is sensitive to the post-inflationary thermal history, potentially yielding either an AdS vacuum, a metastable phase, or a stable dS configuration. We conclude by briefly discussing the relevance of finite-temperature effects for entropy-assisted tunneling and the broader string landscape.

Domain wall networks have attracted renewed interest, particularly in relation to the dynamics of network collapse. Accurately describing this process is challenging and typically requires large scale numerical simulations. Here we adopt a complementary approach by studying the collapse of individual closed domain walls, extending previous thin wall analyses and comparing them with adaptive mesh refinement field theory simulations. Firstly, we show that collapsing domain walls generically develop worldvolume singularities of two types: cuspidal edge singularities, consisting of one dimensional singular edges that propagate along the wall surface at the speed of light for a finite time, and cuspidal vertex singularities, which are spike like and instantaneous events where the wall moves momentarily at the speed of light. Both types of features arise generically from smooth initial conditions, and their formation and evolution follow the universal patterns of singularity theory. We show that these structures are captured both by the Nambu-Goto equations and by an eikonal like approximation valid in the relativistic regime. Furthermore, we demonstrate that the same singular structures are reproduced qualitatively in full field theory simulations, establishing that they are not artifacts of the thin wall approximation but robust features of realistic domain wall dynamics. Naturally, such focusing effects in the field theory simulations result in localized regions of high energy density. We briefly discuss possible phenomenological implications.

We derive analytical approximations to describe the ultra-high-frequency secondary peak of the stochastic gravitational wave background generated by cosmic strings that is sourced by loops created in the friction-dominated era. We show that these approximations provide a very good description of the contribution of the friction-era loops over the relevant frequency range and for a broad range of cosmic string parameters, thus enabling a fast and accurate characterization of this signature. We also use these approximations to uncover the full parameter range in which this ultra-high-frequency peak should be distinguishable on the stochastic gravitational wave background spectrum and show that it should be present in a broader range of high-energy physics scenarios than originally reported in~\cite{Mukovnikov:2024zed}.

We develop a complete theoretical framework for open quantum systems coupled to scale-invariant environments. We show that such environments are universally described by unparticle baths characterized by a single scaling dimension $d_{\mathcal{U}}$. This work provides the proof of the uniqueness theorem, the formalism of the resulting non-Markovian dynamics, and applications to several physical systems. From the uniqueness theorem, we derive the non-Markovian memory kernels, the exact noise kernel including vacuum and thermal contributions, and a fractional generalization of the Caldeira-Leggett master equation for arbitrary $d_{\mathcal{U}}$. The scaling dimension governs a rich phase structure, including a thermalization transition at $d_{\mathcal{U}}=3/2$, the Ohmic boundary at $d_{\mathcal{U}}=2$, and a decoherence transition at $d_{\mathcal{U}}=5/2$ in the thermal regime, beyond which long-time quantum coherence is protected. Three realizations are studied. For the quantum Ising model at criticality, coupling to the energy operator in $(1+1)$ dimensions gives $d_{\mathcal{U}}=3/2$, producing $1/f$ noise, while the $(2+1)$D case yields $d_{\mathcal{U}}\approx1.413$ from the conformal bootstrap. In inflationary cosmology, massless scalar and graviton baths in de Sitter spacetime give $d_{\mathcal{U}}=2$, predicting linear decoherence growth consistent with the quantum-to-classical transition. For high-energy astrophysical neutrinos, the decoherence rate $\Gamma_{\mathrm{decoh}}\propto \mathcal{B}(E,T_{\mathcal{U}})L^{5-2d_{\mathcal{U}}}$ provides an observable signature of the scaling dimension. We also compare the framework with Caldeira-Leggett and Lindblad approaches, analyze the validity regimes, and discuss experimental implications for trapped-ion simulators, neutrino telescopes, and superconducting qubits.

The Axion Weak Gravity Conjecture provides one of the most effective quantum gravity tools for constraining particle physics and cosmology, but it has long been thought of as a slightly fuzzy statement: given an axion with decay constant $f$ there should exist an instanton of charge $n$ and action $S$ with $fS/|n|$ at most an order-one number in Planck units. Recent work related to axion wormholes motivated a specific order-one coefficient, $\frac{fS}{|n|} \leq \frac{\pi}{2 \kappa_d} \sqrt{\frac{d-1}{d-2}}$. In this work, we verify this bound in various axion sectors across the string landscape using three complementary approaches. In the process, we derive even tighter bounds on instantons in such sectors. For example, we argue that supersymmetric instantons in 4d satisfy the stronger bound of $\frac{fS}{|n|}\leq \frac 1{\kappa_4}\sqrt{\frac{7}{2}}$.

We prove a no-go theorem for the mass-radius relation of localized and stable field configurations, known as solitons. Defining the mass-radius index by $\Gamma \equiv \frac{{\rm{d}}\ln M}{{\rm{d}}\ln R}$, for real scalar field theories in $d$ spatial dimensions, we show that typical non-topological, non-relativistic, and spherically symmetric solitons cannot have $\Gamma$ in the range $[0, d]$. The forces considered originate from gradient energy, self-interaction, and gravitation, with the typicality assumption excluding the fine-tuned region of the parameter space where all three forces have comparable strength. Importantly, the theorem works for an arbitrary self-interaction that, in the relativistic theory, is allowed to be non-power-law in the field, be non-analytic around the classical vacuum (where the field amplitude vanishes), or to include derivative couplings. Additionally, the theorem makes no assumptions about the explicit form of the soliton's density profile or the behavior of $\Gamma$ as a function of $R$. We also argue that the same exclusion applies to compact objects formed from self-gravitating, non-relativistic, barotropic fluids with arbitrary equations of state. As a consequence for cosmology, it is worth noting that observations favor a core in the centers of dark matter halos with $\Gamma \simeq 1.7$, which (for $d=3$) lies approximately in the middle of the excluded range. Therefore, proposals such as ultra-light or fluid-like dark matter models are essentially ruled out as natural explanations for halo cores, provided other astrophysical effects are negligible.

We develop a bottom-up open effective field theory (EFT) for non-Abelian gauge theories within the Schwinger–Keldysh formalism. Instead of integrating out the environment completely and starting from a nonlocal influence functional, we retain the slow environmental response variables explicitly and construct a local system-environment EFT. The environmental sector is described by a dynamical color-frame variable, Stückelberg-like field, and an associated color-current sector, which gives the nontrivial interactions and dissipation between the system and the environment. The resulting construction provides a gauge-covariant Markov embedding of nonlocal and non-Markovian color response. After integrating out the retained environmental variables with retarded boundary conditions, the reduced system theory acquires nonlocal dissipative kernels and stochastic sources. We show that the hard thermal loop response arises naturally as a particular realization of the retained environmental response. Our framework provides a local open-EFT description of color transport, memory effects, and fluctuation-dissipation structure in non-Abelian plasmas, and offers a systematic starting point for dissipative Yang–Mills EFTs with dynamical environments.

Real critical systems, such as uniaxial ferromagnets in the 3d Ising universality class, are constrained by boundaries and subject to random couplings. We consider the Wilson-Fisher fixed point in $4-\epsilon$ dimensions subject to a random magnetic field localized on a two-dimensional surface, which becomes co-dimension 1 in the physical $\epsilon\to1$ limit. Using the replica method for the disordered field, we find that the ordinary boundary condition is stable under disorder but also discover a non-trivial “dirty" boundary condition which can be reached by tuning the disorder strength or the local temperature. We also investigate the logarithmic structure of the defect spectrum and how it emerges via the replica formalism.

We study if there is an opportunity to describe quantum particles in the vicinity of three types of cosmological singularities, big bang-big crunch, big rip and big brake. Writing down the Dirac equation for spinors, and choosing a convenient parametrization for basis functions of the spinor field, we show that the corresponding second-order differential equation has two independent solutions which are non-singular in the case of all three types of singularities. That permits us to construct the Fock space for the spinor particles and to interprete this fact as their opportunity to cross these cosmological singularities. We show also that this is impossible to do for scalar particles and changing the parametrization does not help. Thus, fermions look more resilient to the passage of the cosmological singularities than bosons.

Classical A-polynomials $A(\ell,m)$ define constraints on coordinates $\ell$ and $m$ in $SL(2,\mathbb{C})$ (a complexification of $SU(2)$) character varieties associated to knot complements $S^3\setminus K$. Quantum A-polynomials $\hat A(\hat \ell,\hat m)$ are difference operators annihilating Jones polynomials believed to represent wave functions of 3d Chern-Simons theory with gauge group $SU(2)$ on a toroidal pipe surrounding the knot $K$ strand – a boundary of the knot complement. We suggest a construction of classical shaded A-polynomials $A_a(\ell_b,m_c)$ associated to Lie groups $SU(N)$, assuming that color $N$ adds some extra "depth" and "shade" to the classical notion of A-polynomials. We exploit a formalism of Clebsch-Gordan (CG) chords, where indices $a$, $b$, $c$ run over $1,\ldots,N-1$. CG chords have a natural interpretation in terms of 2d CFTs of WZW type, or in terms of quantum group $U_q(\mathfrak{su}_N)$. In the case of $\mathfrak{su}_2$, CG chords could be associated to Reeb chords in a knot contact homology (KCH) framework. KCH suggests its own analogue of A-polynomials, known as augmentation polynomials. The CG chord formalism can be easily extended to arbitrary $\mathfrak{su}_N$ allowing us to generalize the construction of A(ugmentation)-polynomials to arbitrary $\mathfrak{su}_N$ and arbitrary representations as well. We primarily aim at classical A-polynomials by considering a double scaling limit in which $q=e^{\hbar}$, $\hbar\to 0$ and the representations are huge: highest weight vector components $w_i\to \infty$ while combinations $\hbar w_i\sim m_i$ remain finite. We expect the presented techniques will be helpful in deriving quantum A-polynomials for arbitrary Lie (super)algebras $\mathfrak{g}$. We discuss explicit examples of A-polynomials for knots $3_1$, $4_1$ and $5_1$ for $\mathfrak{g}=\mathfrak{su}_3$.

We scrutinize properties of electrical charges bounded to visible and dark matter sectors, in the vicinity of a magnetic poles of both sectors. It turns out that the considered system has an angular momentum despite the charges are at rest. On the other hand, investigation the behavior of electric charges of visible and hidden sectors held at rest outside a magnetically charged black hole, discloses that even if the electric charge are regarded as perturbations on a spherically symmetric magnetic static black hole in dark photon theory, at large distances it looks like a stationary axisymmetric magnetically charged black hole.

We propose a hybrid inflation model where a pseudo-Nambu-Goldstone boson inflaton couples to $N$ waterfall scalar fields respecting a $Z_N$ symmetry. We identify the phases for the inflation and the consequent waterfall transition, concretely, in $Z_2$, $Z_3$ and $Z_4$ cases. From the Coleman-Weinberg potential for the inflaton, we show that the quadratically divergent corrections coming from the waterfall sector are cancelled due to the $Z_N$ symmetry, while the logarithmically divergent corrections are absent only for $N>2$, ensuring the radiative stability of the inflaton potential. We show the parameter space for a successful inflation with the loop-corrected inflaton potential in each model and compare the results between different discrete symmetries. We further analyze the vacuum structure of the models and the reheating process due to the $Z_N$-invariant Higgs-portal couplings for the waterfall fields. We find that the maximum temperature can be smaller than the mass of the waterfall field condensate such that the $Z_N$ symmetry is not restored after reheating and there is no domain wall problem in the models. We also comment on the possibility of multi-component dark matter from the $Z_N$ partners of the waterfall field condensate.

We study the Lorentzian Wetterich Renormalization Group (RG) flow equation for interacting quantum fields on curved backgrounds within the framework of perturbative Algebraic Quantum Field Theory (pAQFT). Specifically, we consider two classes of models: two mutually interacting scalar fields on globally hyperbolic spacetimes without boundary and, under the further assumption that the underlying background is spin, self-interacting Dirac fields. In both cases, we derive the corresponding RG flow equations within a Local Potential Approximation and compute the beta functions for the relevant couplings. For the scalar model, we also discuss an asymmetric interaction potential which is formally reminiscent of the Martin-Siggia-Rose description of a stochastic dynamics, thereby indicating a possible connection between Lorentzian algebraic RG methods [DDP+24] and stochastic field-theoretic models, [Duc25]. In addition, we address the local well-posedness of the resulting flow equations. Adapting the strategy detailed in [DP23] and based on the the Nash-Moser theorem, we prove local existence and uniqueness of solutions for both the scalar and the Dirac models.

Building on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and highlight the emergent nature of gravity, we demonstrate its robustness in a broader context. Using the same entropy density, we show that the Brown-York tensor is associated with a tangential projection of the entropy-functional polymomentum, thereby providing a common construction applicable to both timelike and null hypersurfaces. This perspective places the two (null and timelike) cases on the same variational footing and clarifies the structural differences of the null Brown-York tensor, including its generally non-symmetric character, without resorting to separate or ad hoc prescriptions in the formulation. We further extend the analysis to scalar-tensor theories, showing that the entropy-based formulation reproduces the expected equations of motion along with the corresponding BY tensor. Our results provide a coherent variational interpretation of quasi-local gravitational quantities and reveal a common underlying structure linking bulk dynamics and boundary momentum.

We study the entropy of static, spherically symmetric black holes in diffeomorphism-invariant theories with nonminimal matter–curvature couplings, using the covariant phase space formalism. For regular bifurcate Killing horizons, the Iyer–Wald construction gives the standard Wald entropy. If a matter field cannot be smoothly extended to the regular bifurcation surface, however, the entropy-sector horizon surface charge variation can contain finite contributions that are not included in the Wald entropy density. In the representative obtained by directly varying the action, and after ordinary non-gravitational boundary terms have been separated into the work sector, we decompose the entropy entering the first law of black hole thermodynamics as \(\SH=\SW+\Sone+\DeltaS\). Here \(\SW\) is the Wald entropy, \(\Sone\) is the non-Wald part of the entropy-sector Noether charge, and \(\DeltaS\) is the remaining integrable part of the entropy-sector horizon surface charge variation. Applying this criterion to Kalb–Ramond, bumblebee, and extended Gauss–Bonnet black holes, we find that the regular Kalb–Ramond branch has \(\SH=\SW\), the bumblebee branches yield either \(\Sone=0\) with \(\DeltaS\neq0\) or a cancellation between \(\Sone\) and \(\DeltaS\), and the Weyl-vector extended Gauss–Bonnet examples require both corrections. This provides a direct test of whether the Wald density is sufficient or whether the full horizon surface charge variation is required.

It is known that the Minkowski vacuum appears as a thermal medium to an accelerated observer due to the renowned Unruh effect. More recently, it has been shown that at least for lower-spin fields this medium also exhibits a non-zero "entanglement" shear viscosity, which saturates the fundamental Kovtun-Son-Starinets (KSS) bound. We test the universality of this result for higher spins by computing the entanglement viscosity for spin-3/2 fields within the Rarita-Schwinger-Adler (RSA) theory. Strikingly, we obtain a negative viscosity. However, computing the entropy density using the modular Hamiltonian expansion method, we find it is also negative, and the viscosity to entropy ratio saturates the KSS bound. To clarify the origin of the negativity, we use another approach of Zubarev density operator, which gives positive entropy. We also show that RSA theory has many features of a conformal field theory.

We study a string-motivated theoretical prior on the quintessential dark energy model with exponential potential, \( V(\phi) = V_0 e^{-\lambda \phi} \), allowing for non-zero spatial curvature. First, we formulate the corresponding dynamical system and investigate its cosmological evolution numerically, illustrating the phase-space behaviour and the influence of curvature on the background dynamics. In open universes (\( \Omega_k > 0 \)), it has been suggested that a curvature-related fixed point may support accelerated expansion even for relatively steep potentials compatible with swampland considerations. Next, we explicitly impose swampland-motivated priors on the slope parameter $\lambda$, restricting it to values consistent with the de Sitter conjecture that excludes the (curved) $\Lambda$CDM limit. Furthermore, we restrict our considerations to the range of field excursion that is consistent with the swampland distance conjecture. Our primary interest is the possibility that such theoretically-motivated priors may shift values of cosmological parameters inferred by observational data, compared with the standard analysis based on theory-agnostic priors such as a sufficiently wide flat prior. We examine this possibility using a combination of Planck CMB data, DESI BAO measurements, and recent Type Ia supernova samples, performing a Bayesian inference of the model parameters. Our analysis indicates that the swampland-motivated prior mildly shifts the values of $\Omega_k$.

Global fits of Beyond the Standard Model (BSM) physics often involve a two-way interplay between theory and experiment. Theoretical models provide guidance for experimental searches, while experimental results, in turn, constrain theoretical frameworks. A crucial aspect of this feedback loop is the direct inclusion of measurements and exclusion limits “online” global fits, i.e. during the parameter scans aspects of the global fits. However, incorporating the Large Hadron Collider (LHC) limits into such analyses has been computationally prohibitive, often due to time taken per parameter point exceeding the scales acceptable for global fit frameworks. In this study, we show that LHC limits can be incorporated “online” global fits by leveraging approximations derived from symbolic regression techniques. We utilize a dataset of ATLAS constraints from searches for electroweakino productions to derive a mathematical expression capable of classifying the phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameter space as allowed or excluded. This is subsequently incorporated for making a global fit of the pMSSM to data, including the LHC Run-2 limits.

Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear weak gravity equations and presented a thorough analysis with no ambiguity left. A bit later, we generalised it to linear cosmological perturbations and discussed the strong coupling issues that appear already at this level. Recently, there were claims that some dynamical modes had been missed in our work. However, the authors of the new claims did not look at the equations of motion and analysed the quadratic Lagrangian densities instead. In this paper, I take one of the most elementary cases, namely the vector modes in New GR of Type 3, and show what was their mistake that had led them to claiming that those were dynamical. The main message: Do not substitute constraint equations into a Lagrangian.

We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton states. These states are squeezed, coherent states plus perturbative corrections. We will describe multi-loop corrections to states and their masses. An inner product suitable for non-normalizable momentum eigenstates will be introduced and applied to kink-meson scattering. We will also discuss domain wall solitons.

We introduce the concept of integrable observables and propose them as alternatives to the standard Witten's psi classes (a.k.a. descendants in $2D$ quantum gravity) to be coupled with cohomological field theories and their generalisations. The main property of integrable observables is that they retain the integrability properties. We present three examples of integrable observables. The first two recover the Dubrovin-Zhang and double ramification hierarchies, while revealing new structural features in this framework. The third, a new example, builds on recently established properties of the so-called $\mathbb{\Pi}$-class, extending them and placing this class naturally within the theory of integrable systems. Notably, our integrable observables framework yields a proof that the new $\mathbb{\Pi}$-hierarchies are Miura equivalent both to the Dubrovin-Zhang hierarchies and to the double ramification hierarchies. A new very short proof of Witten's conjecture is also provided.

In this work, we investigate non-interacting holographic dark energy (HDE) with the Hubble radius as the infrared cutoff in Einstein-Cartan gravity. We derive the Einstein-Cartan equations from the action principle and obtain Friedmann-like equations by introducing a torsion scalar. Considering a Weyssenhoff spin fluid, we determine the scaling behavior of the torsion scalar as $\Phi \sim a^{-3}$ without introducing an ad hoc ansatz, resolving the ansatz problem of previous torsion scalar scenarios. In the absence of interactions between dark matter and dark energy, the torsion scalar shifts the equation of state for holographic dark energy toward negative values from the dust-like value obtained in HDE without torsion, making cosmic acceleration possible. In particular, the resulting equation of state can approach $\omega_X \simeq -1$ and cross the phantom divide within the weak torsion regime $|\Phi/H| < 1$. The model predicts a dynamical equation of state in which cosmic acceleration gradually weakens, potentially consistent with recent DESI observations. In spacetimes with torsion, the cosmic distance duality relation between the luminosity distance $d_L$ and the angular diameter distance $d_A$ is modified as $d_L = d_A (1+z)^2 (1+\eta)$. In the presence of the torsion scalar, we show that the standard relation between redshift and the scale factor is preserved, while the deviation parameter arising from torsion effects is determined as $\eta \sim \int_{t_S}^{t_O} dt a^{-3}$, where $t_S$ and $t_O$ denote the emission time at the source and the observation time at the observer, respectively. Overall, our results support the feasibility of the model and provide a theoretical framework for preparing likelihood analyses.

We establish a correspondence between two independent entropic probes – the variation of Rényi mutual information (RMI) across the electroweak symmetry breaking (EWSB) transition and the stabilizer Rényi entropy (SRE) – in tree-level $2\to 2$ elastic scatterings. After angular averaging, the RMI (helicity basis) and the SRE (fixed beam basis) exhibit identical dependence on $\sin^2\theta_W$ within each neutral-current channel. We trace this correspondence to a common physical origin that it's the Yukawa mass insertion acts as a $-\mathrm{i}Y$ quantum gate in chirality space. Minimizing entropies across all processes yields $\sin^2\theta_W$ values matching purely axial vector-like couplings in $Z$ boson exchanged channel.

In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to the two-body problem. While we demonstrated that it reproduces perturbation theory, via the Post-Minkowskian (PM) expansion, and its computational efficiency in reproducing the 1PN Post-Newtonian action, its derivation was heuristic. In this work, we place this flow equation on a firm formal foundation. In particular, we demonstrate that a Legendre transform maps the classical analogue of the Polchinski equation precisely to our classical RG equation. This establishes a duality between equivalent, exact RG equations for the gravitational effective action. The result, combined with the successful applications in arXiv:2510.27676, solidifies the classical RG framework as a powerful and rigorous new approach to the general relativistic two-body problem and gravitational wave physics.

We further develop the proposal in Phys.\ Rev.\ Lett.\ 136 071501 that interprets stochastic inflation as an open quantum system, by constructing the open effective field theory for the reduced density matrix of long wavelength modes. We clarify that this open effective field theory enjoys two renormalization group flows: the conventional Wilsonian channel, and a stochastic channel arising from the openness that has no counterpart in ordinary Wilsonian effective field theory. Focusing on the stochastic channel in the hard cutoff scheme, we identify both Gaussian and non-Gaussian diffusion as effective operators in the influence functional, and show that they are required by matching onto correlators and form factors of the perturbative full theory through a method-of-region in time. Beyond Gaussian order, the matching data are no longer local Wilson coefficients but nonlocal and non-Markovian Wilson kernels. We then obtain the bare Hamiltonian density of this open effective field theory and derive its nonlocal functional master equations, including the Fokker-Planck equation for the diagonal density matrix and the Klein-Kramers equation for the Wigner functional, with their zero-modess simplifications discussed. Finally, we take a first step toward a continuum version of this open effective field theory, replacing the hard cutoff by an analytic regulator in the stochastic channel, and demonstrate stochastic renormalization using a massive scalar as an example.

We investigate the localization of fermionic fields in a five-dimensional braneworld scenario within the framework of modified teleparallel gravity described by a general $f(T,T_G)$ function. Considering a non-minimal coupling between a Dirac spinor and the torsional invariants, we derive the effective Schrödinger-like equations governing the Kaluza-Klein modes. We showed that the contribution of the teleparallel Gauss-Bonnet term significantly modifies the effective potentials and, consequently, the localization properties. The zero-mode analysis reveals that only one chiral component can be localized on the brane, with the degree of confinement depending on the chosen model. In the massive sector, the spectrum is continuous, but resonant states arise due to the internal structure of the potentials. Additionally, we employ information-theoretic measures, such as Shannon entropy and relative probability, to quantify the localization mechanism. Our results show that the torsional modifications induce a nontrivial redistribution of information, exhibiting stronger localization. These findings highlight the role of higher-order torsional terms in shaping fermionic localization and resonance structures in braneworld scenarios.

We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state, describing the expanding magnetic field, is obtained exactly and compared with the corresponding quantum magnetostatic state. In contrast to the magnetostatic case, the expanding solution exhibits a propagating shockwave-like front separating regions where the magnetic field has already been formed from those that remain causally disconnected from the source. We show that although the expanding field locally approaches the magnetostatic field behind the shockwave-like front, the associated quantum systems remain distinct at all times. In particular, we obtain manifestly different results for the energy, photon number, and their fluctuations in expanding and magnetostatic field configurations. Our results are first derived for a general external current and then illustrated with a specific example.

We show that, contrary to common belief, supersymmetry alone is not sufficient in Model A dynamics to ensure relaxation toward a stationary state satisfying time-reversal invariance (TRI). An additional condition on top of supersymmetry is required for TRI, which we analyze in detail. We explicitly construct a model that is supersymmetric but violates TRI, and argue that, at least perturbatively, TRI nevertheless emerges as an effective large-scale symmetry. Using the functional renormalization group (FRG), we further show that the dynamical effective action, $\Gamma[\varphi,\tilde\varphi]$, contains the derivative of the equilibrium effective action, $\Gamma^{\mathrm{eq}}[\varphi]$, whose renormalization-group flow is identical to that of the equilibrium theory order by order in the derivative expansion. Finally, extending the same line of reasoning, we show that the probability distribution of the total magnetization in the Ising model can be recovered within the Model A framework.

We study the maximal analytic extension of the Schwarzschild-like black hole solution in Lorentz gauge theory. The lapse function is $f(r)=A_0^{-2}-2\m/r$, so the horizon is located at $r_+=2\m A_0^2$ and the non-affinity coefficient of the horizon generator is $\kappa=1/(4\m A_0^4)$. We first analyze the radial null curves in the Schwarzschild-Droste (SD) and ingoing Eddington-Finkelstein (IEF) charts, and then construct the Kruskal-Szekeres (KS) chart adapted to the LGT geometry. The KS extension contains two exterior regions, a black-hole region and a white-hole region. We also present the standard and regular Carter-Penrose (CP) compactifications. The conformal skeleton is Schwarzschild-like, but the physical scale of the horizon, the surface gravity and the constant-radius curves remain controlled by $A_0$. Hence the solution has the same causal topology as Schwarzschild, while it is geometrically inequivalent to it when $A_0\neq1$.

This talk introduces a Cartan-geometric framework for generalised geometries governed by a differential graded Lie algebra. In contrast to ordinary Cartan geometry, the tangent bundle is extended and qu both a global duality group and a local gauge group. This framework provides a systematic construction of generalised connections and their torsion and curvature tensors for generic generalised geometries. We also review the realisation of these algebraic structures on the phase space of branes in M-theory.