Papers

We systematically develop a framework for equilibrium thermodynamics in terms of thermodynamic representations, which are choices of thermodynamic potential and independent variables, one from each conjugate pair. In each representation, equations of state arise from first derivatives of the potential and response functions from its second derivatives. We apply this framework to ideal gases and to Schwarzschild black holes in a spherical cavity in various representations, interpreting the cavity area and its conjugate surface pressure as the thermodynamic volume and pressure of a holographically dual system. For this quasi-local Schwarzschild black hole, stability depends on the thermodynamic representation, or equivalently on which variables are held fixed under equilibrium perturbations. The large black hole branch is thermally stable at fixed volume but mechanically unstable under isothermal compression, while the system is mechanically stable under adiabatic compression everywhere. At fixed pressure, the black hole is thermally unstable throughout the physical state space. We also find that the thermal expansion coefficient is negative everywhere and show that isenthalpic expansion always cools the black hole. More broadly, the framework provides a systematic route to deriving equations of state and response functions for a wide class of black hole systems using quasi-local gravitational thermodynamics.

We investigate the thermal partition and one-point functions of the three-dimensional conformal field theory dual to a massive interacting scalar field in AdS$_4$. Using thermal inversion formulas, we determine the asymptotic behaviour of the spectral density and OPE coefficients involving heavy operators at fixed spin. We first analyse these CFT data for the generalised free field, corresponding to the non-interacting bulk theory. Then we compute the first-order perturbative corrections induced by the cubic and quartic bulk interactions. The thermal observables considered here probe a sector associated with operators of large dimension and, in the bulk description, a regime dominated by states with large particle number. This regime remains comparatively unexplored even in generalised free field theory. Remarkably, the asymptotic formulas obtained from thermal inversion remain quantitatively accurate far from the asymptotic regime, describing CFT data reliably already at intermediate conformal weights. Our results show that this feature survives the inclusion of bulk interactions and provide new analytic control over heavy-state data in conformal field theories.

We construct Hilbert spaces for the minisuperspace quantum cosmology of a closed Universe in the limit of extreme slow-roll inflation, in which the scalar field is approximated as constant. In this setting, the potential energy in the scalar field is an integration constant depending on initial conditions, equivalent to the cosmological constant as it appears in unimodular gravity. If one fixes the value of this integration constant, the Wheeler-DeWitt equation admits two independent solutions, and a natural inner product picks out one of them (essentially Vilenkin's tunnelling wavefunction) with positive norm. The physical Hilbert space is then one-dimensional, in agreement with some recent discussions of closed universes in quantum gravity. However, if the potential energy is left arbitrary, the theory allows for an infinite-dimensional Hilbert space corresponding to energy eigenstates of an effective Hamiltonian. Requiring that this Hamiltonian be represented as a self-adjoint operator leads to a one-parameter family of boundary conditions at the singularity, generalising the DeWitt criterion of a vanishing wavefunction. The boundary condition always leads to a mixture of Hartle-Hawking (no-boundary) and tunnelling wavefunctions, but a particular choice "almost" singles out the Hartle-Hawking wavefunction, with exponentially suppressed corrections.

We construct a helical generalization of the Sachdev-Ye-Kitaev (SYK) model in $1+1$ dimensions, built from left- and right-moving Majorana fermions with local quartic interactions and random couplings in flavor-chirality space. These interactions organize into a symmetry-controlled hierarchy of quartic chirality sectors. At the most restrictive end of this hierarchy, symmetry forces the quartic structure into a density-density form, which admits an exact solution using bosonization, rendering the theory integrable. Once the full quartic helical interaction space is allowed, including purely chiral, chirality-balanced, and chirality-imbalanced sectors, this symmetry-protected integrable structure is lost. Nevertheless, the large-$N$ infrared limit remains analytically tractable through short-distance selection rules and disorder averaging. Using conformal perturbation theory about the free fixed point, we show that the entire interaction space is marginally irrelevant, and the theory thus becomes free and integrable in the IR.

The classical dimer model on bipartite lattices hosts a Coulomb phase, characterized by algebraic correlations and topological order. Its long-wavelength properties can be described by the fluctuations of a vector field with zero divergence, which, in two dimensions, is equivalent to a continuum height model. We show how this field theory can be derived constructively for both square and honeycomb lattices, starting from an exact representation of the dimer model in terms of Grassmann integrals. Taking the continuum limit gives a massless Dirac fermion in two-dimensional Euclidean space, which, using bosonization in the path integral representation, maps exactly to the well-known height field theory, incorporating the relationship between its boundary discontinuity (or "tilt") and the flux. By including source terms coupling to the flux density and the local valence-bond-solid order parameter, which we show are the only ones required to describe the asymptotic long-distance correlations, we derive expressions for the dimer observables in terms of the height.

We develop a geometric framework for non-supersymmetric effective gauge theories based on their nonlinear supersymmetrizations. We construct supersymmetric embeddings for most operators up to dimension six from constrained chiral and vector superfields, and formulate vector bundles using the superfields to systematically organize the operators under field redefinitions in the gauge sector. This formalism manifests a complex geometry underlying gauge operators and accommodates redefinitions across different spins.

Many string compactifications down to four non-compact space-time dimensions with N=8, N=6 and N=4 supersymmetry have BPS black holes carrying pure D-brane charges and preserving four supersymmetries. The string coupling does not flow in these backgrounds and can be set to any arbitrary value. Therefore the supersymmetric index of these black holes must be independent of the string coupling. On the other hand, explicit computation of one loop correction to the index from gravitational path integral is sensitive to the choice of ultraviolet cut-off. We show that if the cut-off scale is chosen to be the string scale in accordance with the rules of string theory, then the dependence of the index on the string coupling disappears in accordance with the expectation from supersymmetry. Similar results are obtained for type II string theories compactified on Calabi-Yau manifolds with zero Euler number. For non-zero Euler number we encounter a puzzle that we discuss but do not fully resolve.

Renormalisation is traditionally understood to be a Wilsonian memoryless process in which ultraviolet (UV) degrees of freedom gradually decouple, leaving an autonomous infrared (IR) description. However this need not be the case: in UV/IR mixed theories correlations between widely separated scales can persist. In this work I recast UV/IR mixing as a Hilbert-space phenomenon, realised as correlations across renormalisation scales. This formulation is implemented using the Born-Reciprocal Tensor Network (BRTN), a new configuration of tensor network that is globally symmetric under phase-space reciprocity. On this network I prepare the vacuum and reproduce the expected radiative corrections. The resulting renormalisation geometry exhibits memory, with a bridge linking reciprocal representations of IR physics, whose cross-bridge entanglement provides a precise criterion for the viability of an effective description. I analyse when this criterion is met, and show that there is a large-volume limit, with the fundamental scale held fixed, in which the obstruction to a local description scales away: Wilsonian behaviour is restored and renormalisation forgets. The BRTN therefore provides a concrete and calculable platform for UV/IR mixing.

Charged massive spin-3/2 fields have long been regarded as problematic, because their coupling to electromagnetism generically leads to loss of hyperbolicity, acausal propagation and loss of unitarity. At the same time, fractionally charged supermassive gravitinos play a central role in a recent proposal of two of the present authors, where they are the only fermionic degrees of freedom beyond the Standard Model and provide novel dark matter candidates. We address this apparent tension by revisiting the result of Deser and Waldron, who showed that the inclusion of gravity can compensate the electromagnetic source of the inconsistency. For a minimally coupled Rarita-Schwinger field in an Einstein-Maxwell background, consistency requires a lower bound on the mass in terms of the charge and the cosmological constant. What is usually a severe obstruction to low-energy charged spin-3/2 phenomenology becomes an independent indication that such particles must lie close to the Planck scale, as argued by two of the present authors on other grounds. We rederive the inequality from the solvability of the Rarita-Schwinger constraints and from the characteristic determinant, emphasizing how the Einstein-Maxwell stress tensor compensates the purely electromagnetic pathology. We then reformulate the system using a Stückelberg spinor, showing that the helicity-1/2 sector reproduces the same condition. This formulation is also essential for obtaining a renormalizable propagator. We discuss this propagator and the corresponding ghost system.

Classical critical collapse provides a dynamical route from smooth initial data to a naked singularity, representing a sharper violation of predictability than ordinary black hole singularities. We argue that this distinction is erased by quantum backreaction. Building on the semiclassical interior analysis, where quantum self-energy of the collapsing matter generates a universal growing mode and a finite mass gap, we study the exterior naked singularity region that determines global visibility in the Einstein-scalar system. We analyze controlled exterior models in both $2+1$ and $3+1$ dimensions. In the former, smooth matching and physical boundary conditions analytically select a vacuum polarization state, whose backreaction cloaks the classically naked region by a quantum trapped branch. In the latter, numerical horizon tracing shows that near a quantum-shifted threshold the exterior develops finite-mass marginally trapped surfaces rather than a zero-mass naked endpoint. These results suggest a global quantum picture in which the Choptuik naked singularity shares the fate of an ordinary black hole singularity: quantum effects push the putative Cauchy horizon behind a quantum-generated horizon, thereby reducing the loss of predictability to the standard black hole evaporation problem.

Determining whether the neutrino is a Dirac or Majorana fermion remains a fundamental open question. Conventional searches rely on neutrinoless double beta decay, but this electron-only channel suffers from blind spots. We propose a new, complementary probe to overcome this limitation. A heavy neutral lepton (HNL) triggers a high-energy shift in how the active neutrino flavors ($\nu_e$, $\nu_\mu$, $\nu_\tau$) mix – but only if the neutrinos are Majorana. For GeV-scale HNLs, the upcoming beam-dump experiment SHiP can discover the HNL and measure how it mixes with the active flavors. Separately, the scattering of TeV–PeV astrophysical neutrinos can resolve the HNL, revealing a shift in the proportions of each flavor arriving at Earth that could be detected by neutrino telescopes, regardless of the unknown flavor composition at the astrophysical neutrino sources. Because this flavor shift is most sensitive to the muon and tau sectors, it bypasses the blind spots of neutrinoless double beta decay. A correlated signal at SHiP and next-generation neutrino telescopes would prove that neutrinos are Majorana; its absence would point to them being Dirac.

We find exact solutions of a Liouville-type scalar field theory on $D$-dimensional de Sitter and anti-de Sitter backgrounds, treating the geometry as nondynamical. Using the embedding-space formalism with an auxiliary null vector, we derive first-order (Bäcklund-like) equations whose integrability yields the solution of the Liouville equation for the scalar field. This method produces two classes of analytic solutions, whose physical properties are different for de Sitter and anti-de Sitter spacetimes.

We present a dynamical mechanism for the erasure of inflationary isocurvature perturbations of the non-compact QCD axion. The key ingredient is an early-time runaway exponential potential, which drives the axion onto the well-known scaling cosmological attractor after inflation. Once on the attractor, the axion tracks the dominant component of the Universe, radiation, and isocurvature modes are erased even if the field is effectively massless during inflation. When the QCD potential turns on, the axion carries nonzero velocity, and kinetic misalignment can become operative. The exponential potential induces residual CP violation, potentially accessible to future electric dipole moment searches. This mechanism requires that the axion be effectively non-compact over the field range relevant for its post-inflationary evolution.

We consider five-dimensional supergravity coupled to vector multiplets, gauged or ungauged, and propose an efficient method to evaluate the on-shell action of supersymmetric black saddle solutions with toric ${\rm U}(1)^3$ symmetry and general topology, explicitly known or just assumed to exist, including higher-derivative corrections. This is equivalent to equivariant integration of the anomaly polynomial six-form over simplicial cones obtained by decomposing the toric diagram of the solution. The on-shell action is then expressed as a sum over contributions localized at the tip of each cone. We obtain a simple derivation of recently calculated expressions as well as new predictions, both for the on-shell action of the black saddles and the Wald entropy of the related extremal solutions. These may be asymptotically AdS$_5$ or asymptotically flat. As examples, we discuss black holes, black rings and black lenses, including a black hole in the background of a topological soliton.

A covariant reconstruction framework for electromagnetic Kantowski–Sachs (KS) geometries in teleparallel $F(T)$ gravity is developed using the coframe/spin-connection (CSC) formalism and the invariant approach. In a restricted Maxwell-compatible branch, the electromagnetic conservation laws strongly constrain the anisotropic KS scale factors and lead to the scaling $\rho_{\mathrm{em}}\propto A_3^{-4}$. The corresponding symmetric and antisymmetric field equations are derived and used to reconstruct the functional form of $F(T)$ directly from the KS dynamics. Power-law and exponential ansätze generate distinct invariant reconstruction branches associated with electric, magnetic, and transverse electromagnetic sectors. The exponential branch naturally admits reduced teleparallel de Sitter limits and shifted models of the form $F(T)=f(T_0-T)$. The reconstructed branches describe anisotropic cosmological sectors together with local BH-interior-like sectors that may reproduce reduced BH-interior-like or RN–dS-type behaviors at the level of the KS dynamics. These branches are organized through the invariant coframe/spin-connection classification and screened using the necessary leading-order viability conditions $F_T>0$ and $F_{TT}>0$. The local and branch-dependent nature of the construction is emphasized throughout.

The problem of quantum tomography is to estimate an unknown quantum state $\rho$ from a measurement of $n$ copies of $\rho$. One can ask which tomography protocol, i.e.\ which choice of multi-copy measurement, gives the best possible estimate of $\rho$. To do so, we characterize tomography protocols by their rate function, which governs the exponential rate at which a protocol assigns probability to a particular estimate $\sigma$ of the true state $\rho$. This rate function is a quantum mechanical generalization of the classical relative entropy between the true state and its estimate, and depends on the choice of protocol. It is bounded by the quantum relative entropy, and we show that this bound is sharp: for any $\rho$ and $\sigma$ we construct a family of protocols whose rate functions converge to the quantum relative entropy $D(\sigma\|\rho)$. We consider the family of covariant tomography protocols; these are the basis independent state estimation schemes that assume no prior information about $\rho$ and $\sigma$. Keyl described a specific tomography protocol based on Schur sampling, and conjectured that among all covariant tomography protocols it has the largest possible rate function for all $\sigma$ and $\rho$. We prove this conjecture. The resulting rate function is an annealed version of quantum relative entropy, due to the cost of learning the eigenbasis in covariant quantum state tomography.

We have recently shown that a natural way to implement the Wilsonian paradigm in gauge theories is through the introduction of a “spectral cutoff", a cut on the eigenvalues of the covariant Laplacian, pointing out that this provides the route toward the renormalization group (RG) construction. Here we apply this idea to quantum gravity, resorting to two realizations of the spectral running cutoff: “hard" and “smooth". We derive the RG equations for the Newton and cosmological constant and find the RG pattern of the asymptotic safety scenario, with a non-Gaussian UV-attractive fixed point.

Static Love numbers of four-dimensional Schwarzschild black holes vanish in general relativity. We study how the fixed-quadrupole static tidal solution is modified by the parity-even cubic Weyl operator in the gravitational effective field theory. Working perturbatively in $\epsilon_{\rm e}=\lambda_{\rm e}(\Lambda r_s)^{-4}$, we construct the reduced quadratic radial action for static even-parity $\ell=2$ perturbations, order-reduce the higher-derivative equations, and solve the resulting boundary-value problem directly in metric variables. The order-$\epsilon_{\rm e}$ equations reduce to a first-order two-dimensional inhomogeneous system for $X_0$ and $X_K$, with $X_2$ fixed by an algebraic constraint. Horizon regularity leaves one constant, but matching to infinity shows that this freedom only renormalizes the applied tidal branch. After removing this tidal renormalization, the decaying branch is unambiguous. Calibrating the spatial sector at fixed $\ell=2$ against the associated-Legendre branches $P_2^{2}$ and $Q_2^{2}$, we obtain a fixed-quadrupole response amplitude $\Delta(B/A)=-2400\epsilon_{\rm e}$. Equivalently, the scalar fixed-$\ell$ quotient gives $\Delta k_{2,\rm sc}^{\rm fix}=-20\epsilon_{\rm e}$. The second number is a scalar fixed-$\ell$ conversion of the metric branch ratio, not, by itself, the analytically continued, gauge-invariant electric Love number. A comparison with canonical Teukolsky-based Love numbers requires an additional continuation in $\ell$ and a precise map of normalizations. The result should therefore be viewed as a reproducible metric-sector benchmark for the cubic Weyl EFT, complementary to gauge-invariant master-equation approaches.

We derive analytic templates for the scalar and tensor primordial power spectra describing cosmologies that transition from kinetic dominance to slow-roll inflation in the presence of spatial curvature. Our results extend recent works in the literature, allowing us, in particular, to recover the scalar and tensor tilts analytically. We revisit the case of curvature-assisted single-exponential models in light of this framework. In the case of an open universe, the phase space of such models naturally includes cosmologies that start out in a kinetic-dominance regime followed by a parametrically controlled quasi-de Sitter phase. However, they do not fit in the framework of the templates, as their second Hubble slow-roll parameter remains of order one in the quasi-de Sitter regime.

Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.

We produce the dimensional reduction to 10D IIA supergravity (SuGra), via cyclification, of the remarkable result that full 11D SuGra is put on shell just by imposing the duality-symmetric Bianchi identities on C-field super-flux densities over supertorsion-free superspace. Generally, we highlight that when duality-symmetric superspace Bianchi identities are characterized by Whitehead bracket $L_\infty$-algebras $\mathfrak{l}\mathcal{A}$ of a classifying space $\mathcal{A}$, their dimensional reduction is characterized by the cyclic loop space $\mathrm{Cyc}(\mathcal{A})$. We promote this to a general mechanism of dimensional reduction on super-spacetime, compatible with the global (infrared) completion of supergravity theories by flux quantization in non-abelian cohomology with coefficients in $\mathcal{A}$ and $\mathrm{Cyc}(\mathcal{A})$, respectively. In the case of 11D SuGra, the characteristic $L_\infty$-algebra is $\mathfrak{l}S^4$ and hence we obtain that full on-shell 10D IIA SuGra is equivalent to $\mathfrak{l}\mathrm{Cyc}(S^4)$-Bianchi imposed identities on NS/RR super-flux densities over supertorsion-free 10D super-spacetime. This implies that any space which is $\mathbb{R}$-rationally equivalent to $\mathrm{Cyc}(S^4)$ classifies an admissible flux quantization law, which provides a global completion of 10D IIA SuGra that admits oxidation to 11D.

The exact time-space correlation function of the $1D$ Glauber-Ising model, quenched to temperature $T=0$ and on a semi-open lattice of finite size $N$, is obtained. This also allows to deduce the exact empty-interval probability of the dual $1D$ coagulation-diffusion process on a periodic finite ring and to reproduce the long-time decay of the particle concentration. These results are consistent with the generic expectations of dynamical finite-size scaling theory.

Boundary conformal field theory (BCFT) contains universal data that are usually accessed microscopically by imposing spatial boundaries on the lattice. In non-Hermitian many-body systems, however, changing boundary conditions can qualitatively reorganize spectra and eigenstates, and their boundary criticality remains elusive. Here, we introduce a periodic-chain spectroscopy to extract universal boundary quantities, such as the Affleck-Ludwig $g$-factor, directly from non-Hermitian bulk-critical quantum chains, avoiding the need to engineer microscopic open boundaries and circumventing subtle boundary effects in non-Hermitian systems. We illustrate our method with a $\mathcal{PT}$-symmetric Ising realization of the real nonunitary Yang-Lee CFT and reveal a universal negative excited-to-ground ratio, which has no counterpart in unitary critical theories and provides a microscopic signature of nonunitarity. For the genuinely complex fixed points of the non-Hermitian five-state Potts chain, we extract intrinsically complex boundary coefficients, verify the exact Kramers-Wannier duality relation, and select the consistent analytic-continuation branch of the boundary states. Our results establish a route to nonunitary BCFT universal data using only knowledge of the bulk critical system, opening a window into non-Hermitian boundary criticality.

We derive the Lehmann-Symanzik-Zimmermann reduction formalism for a massive spin-2 particle on Minkowski spacetime and extend the formalism to cosmological spacetimes. The reduction formalism allows for a versatile proof that the Goldstone boson equivalence theorem holds in Friedmann-Lemaître-Robertson-Walker space-times. For the de Sitter and the radiation filled universe, we investigate the Goldstone dynamics and perform an analysis of the range of validity provided by the effective kinetic operator.

In this work we present an effective Lifshitz black hole solution with Born-Infeld electrodynamics and explore some of its properties. We discuss the mechanism for capturing the solution, achieved through diffeomorphism invariance breaking, study the emergent causal structure, and analyze aspects of critical behavior and local stability in the associated thermodynamics.

Motivated by the mirror symmetry for circle compactified 4d $N=2$ theories, we propose a geometric framework for studying the representation theory of non-admissible $W$-algebras $W^{k}(\mathfrak g,f)$ at levels $k=-h^\vee+\frac{1}{n}\frac{m}{u}$, using the geometry of generalized affine Springer fibers $Sp_{\nu}(\tilde{g},f)$ with slope $\nu=u/m$. The central proposal is that each non-empty $C^*$-fixed locus, labeled by a double coset $\tilde w\in W_\nu\backslash\tilde{W}/W_f$, gives rise to simple modules whose highest weight is determined by the map $\tilde w\mapsto\tilde w(k\Lambda_0+\tilde\rho)-\tilde\rho$, while the dimension of the fixed variety encodes additional non-semisimple structure (logarithmic modules). We verify this correspondence in numerous examples, including $D_4$, $E_6$, $E_8$, and twisted theories of type $^3D_4$ and $^2A_3$, where our geometric counting reproduces known results for both admissible and non-admissible $W$-algebras.

We study non-minuscule boundary 't Hooft lines in four-dimensional $\mathcal N=4$ $U(N)$ super Yang–Mills theory with the regular Nahm-pole boundary condition. For one-row charges we construct the exact spherical-DAHA operator $\mathbf e_+h_r(Y)\mathbf e_+$, determine its finite shift expansion and discrete Macdonald spectrum, and evaluate the S-dual Neumann Wilson two-line index as a finite-$N$ Macdonald pairing. For the first non-minuscule $U(2)$ coefficient, a local two-minuscule convolution model with Higgs branch $T^*\mathbb P^1$ has two Jeffrey–Kirwan residues, while subtracting the determinant intersection-cohomology summand supplies the additional $-\mathfrak t$ term. The same transverse $A_1$ calculation, dressed by the spectator-root factor, reproduces the first lower $U(3)$ coefficient. The local convolution calculation and its spectator lift provide low-rank checks of the complete DAHA coefficients independent of the inverse recursion, while their boundary-localization interpretation remains conjectural. Assuming an isometric oriented boundary Fourier intertwiner, the DAHA construction is compatible with the expected boundary S-duality relation.

We study heavy quark observables, namely the static interquark potential, the thermal free energy, and the running coupling, in a five dimensional asymptotically anti-de Sitter (AdS) spacetime with broken translational symmetry. The Einstein-Maxwell-axion (EMa) geometry contains two independent scales: the chemical potential $\mu$, which controls finite baryon density, and the translational symmetry breaking parameter $\beta$, which controls momentum relaxation. Using high precision numerical calculations at finite temperature and at zero temperature, we show that both scales weaken color interactions and promote quarkonium dissociation in a strongly coupled quark gluon plasma, although the underlying mechanisms differ. The chemical potential dominates color screening and strongly modifies the heavy quark potential and running coupling, whereas $\beta$ mainly changes the plasma entropy and therefore gives the leading correction to the thermal free energy. At zero temperature, thermal contributions vanish and the renormalized free energy reduces to a static potential modified by the medium, with an approximately Coulombic form. At all temperatures, a finite baryon density suppresses the binding of quark antiquark ($Q\bar{Q}$) pairs much more strongly than momentum relaxation. We extract the color screening length and dissociation scale, and discuss implications for quarkonium production in heavy ion collisions. These results show that static color interactions and thermodynamic observables are controlled by different medium scales, which offers a unified picture of heavy quark probes in dense dissipative plasmas.

This proceedings contribution summarizes the main results of the original paper arXiv:2506.18988. Cascading RG flows are characteristic of $\mathcal{N}=1$ gauge theories realized by D3-branes probing singularities in the presence of fractional branes. A celebrated example is the Klebanov-Strassler model, which exhibits an infinite cascade that ends with confinement. In this work, we explore a related setup where the addition of an orientifold plane modifies the cascade structure: the RG flow now consists of a finite number of steps, originating from a UV fixed point with a finite number of degrees of freedom. We provide a supergravity solution dual to this flow, that reproduces all its salient features.

We construct embeddings of gravitational and electromagnetic waves in the dark bubble scenario using pp-wave geometries in AdS5, motivated by the fact that pp-wave spacetimes often provide exact solutions to the equations of motion. The setup is realised by gluing two AdS5 pp-wave spacetimes across a three-brane. As an application, we analyse localised beams of light and their gravitational backreaction. Imposing suitable mixed boundary conditions in AdS5, we find gravitational corrections consistent with a weakening of 4d gravity at the 5d AdS scale.