arXiv subjects

Anik Rudra

Publications and source records attributed to Anik Rudra.

12 recordsLinked to original sources

arXiv2026

Hironaka Geometry and Resurgence in Finite-$N$ Matrix Models

We study how finite-$N$ invariant theory organizes the non-perturbative structure of matrix models. For a model of four traceless Hermitian $2\times 2$ matrices, the Hironaka decomposition realizes the gauge-invariant configuration space as an eight-sheeted branched cover of the space of primary invariants. We show that ramification points of this cover naturally generate additional saddle points when the action depends only on the primaries. For an explicit rank-two saddle, we compute its action, one-loop normalization and Picard--Lefschetz connection to the perturbative vacuum. The same saddle controls the leading Borel singularity and large-order growth of perturbation theory, while its first fluctuation correction reproduces the first subleading large-order correction with no fitted parameters. Our results provide a concrete link between finite-$N$ invariant geometry and resurgence in matrix models.

hep-th↗

arXiv2026

A pedagogical introduction to invariant theory and finite-$N$ holography

These lectures provide a pedagogical introduction to the study of finite-$N$ physics of the AdS/CFT correspondence. More specifically we develop the consequences of the trace relations for the space of gauge invariant operators, using powerful methods from invariant theory. Our key conclusions are \begin{itemize} \item that the complete set of trace relations can be solved, leaving a non-redundant set of gauge invariant operators, \item that this non-redundant set can be generated using two types of generators, called primary and secondary invariants, and \item that the primary invariants acquire a natural interpretation as perturbative gravitational degrees of freedom, while the secondary algebra encodes non-perturbative effects of the dual gravitational theory. \end{itemize}

hep-th↗

arXiv2026

Overcrowding and the Finite-$N$ Hilbert Space

Finite-$N$ trace relations reorganize the Hilbert space of gauge-invariant operators beyond the freely generated large-$N$ description. We study this structure using the Hironaka decomposition of the invariant ring of $d$ Hermitian $N\times N$ matrices. We first prove that the primary invariants may always be chosen to be homogeneous single-trace operators. We then show that, for any such choice, a nontrivial secondary invariant must appear by degree $L_{N,d}=2\log_d N+\log_d\log_d N+\mathcal{O}_d(1)$, which is parametrically below the first universal trace identity at degree $N+1$. This is a global overcrowding effect: exponentially many independent short single traces compete for only $1+(d-1)N^2$ algebraically independent coordinates. The overcrowding scale matches the fastest scrambling times expected for fast scramblers. We argue that this agreement of scales is not accidental: overcrowding provides a microscopic algebraic picture of scrambling in matrix models. Low-rank examples show that secondary invariants can distinguish configurations with identical primary data and, for suitable dynamics, label semiclassical sectors connected by instantons. These results identify the Hironaka decomposition as a natural framework for organizing perturbative and intrinsically finite-$N$ information in collective descriptions of gauge theories.

hep-th↗

arXiv2026

Bulk Reconstruction in Bilocal Holography

Bilocal holography provides a constructive approach to the higher-spin gravity theories dual to vector-model conformal field theories. Its central advantage is that it is completely gauge fixed and formulated entirely in terms of physical degrees of freedom. We derive a remarkably local bulk reconstruction formula and demonstrate its agreement with standard bulk reconstruction, after the same boundary data and gauge-fixed variables have been identified. We further clarify how subregion duality is realized in this framework.

hep-th↗

arXiv2026

Consistent Truncations from Duality Symmetries and Desingularization of Orbifold Uplifts

This paper is an extension of the results presented in \cite{Guarino:2024gke}. We study $ G_S$-invariant subsectors of maximal gauged supergravities and show that such models can provide consistent truncations even when $G_S$ is not a symmetry of the original supergravity. We show that this construction is key to building pure supergravities around a supersymmetric AdS$_D$ solution. We illustrate this construction by building a consistent $\mathcal{N}=4$ subsector of the $D=4$ $\mathcal{N}=8$ $[\mathrm{SO}(6)\times \mathrm{SO}(1,1)]\ltimes \mathbb{R}^{12}$ gauged supergravity. We use this result to build the uplift of the multicharge spindle solutions in type IIB and we define a simple criterion for assessing the regularity of the uplift. We show that the type IIB uplift of the spindle is always non-regular, admitting eight codimension-six orbifold singularities. We apply the same criterion to other spindle uplifts, recovering known results and making predictions on the regularity of spindles on (quasi-)regular SE$_7$ manifolds.

hep-th↗

arXiv2025

Collective Theory at Finite-$N$: Reduction of the Emergent Hilbert Space

Continuing the formulation of finite $N$ Hilbert spaces in emergent theories we study in this work $S_{N}$ symmetric collective models. For the case of $N$ bosons in $d$ dimensions, which map to matrix models with commuting matrices, we describe a complete algorithm and give a detailed case study reproducing the expected primaries and determining secondary invariants at each bidegree (a Hironaka decomposition). The method is based on null spaces (of the full collective theory) which are seen to yield all the independent trace relations, reducing the construction to linear algebra. As a stringent check, of our algorithm, we have verified that the system of invariants generates a subset of gauge invariant operators with no redundancies. This results in a reduction of the Hilbert space, in particular the gauge invariant secondary invariants realize an emergent Fock space with finite-$N$ occupation-numbers.

hep-th↗

arXiv2025

QNMs of charged black holes in AdS spacetime: a geometrical optics perspective

We investigate the quasinormal modes of the Reissner$-$Nordström anti$-$de Sitter black hole using the Penrose limit, motivated by the geometrical optics approximation. This approach offers a novel framework for approximating quasinormal modes with large real frequencies by associating a plane wave to spacetime regions near null geodesics, providing a geometric interpretation of the geometrical optics approximation. Applying this limit to bound null orbits around black holes allows us to explore the black hole response to perturbations. We analyze the effects of black hole charge and negative cosmological constant on the quasinormal spectrum, finding that increasing charge enhances both the real and imaginary parts of the frequencies, while a decreasing cosmological constant leads to higher real frequencies and longer lived perturbations, with the spectrum stabilizing at larger values of the cosmological constant.

gr-qc↗

arXiv2024

Blackening S-folds

We construct the universal AdS$_{4}$ black hole that asymptotes to the $(φ,χ)$-family of type IIB S-fold backgrounds dual to the conformal manifold of $\mathcal{N}=2$ S-fold CFT's. We present the explicit type IIB embedding of such a universal black hole for two particular asymptotics: the $\,\mathcal{N}=2\,$ S-fold with $\,\textrm{U}(2)\,$ symmetry at $\,(φ,χ)=(0,0)\,$ and the $\,\mathcal{N}=4\,$ S-fold with $\,\textrm{SO}(4)\,$ symmetry at $\,(φ,χ)=(1,0)$. As a byproduct, we also present a novel $1/16$-BPS two-parameter family of $\,\textrm{AdS}_{2} \times \textrm{M}_{8}\,$ S-fold backgrounds with $\,\textrm{M}_{8}=\mathbb{H}^{2} \times \textrm{S}^{5} \times \textrm{S}^{1}$ that features a parametrically-controlled scale separation.

hep-th↗

arXiv2019

Persistence of quantum violation of macrorealism for large spins even under coarsening of measurement times

We investigate quantum violation of macrorealism for multilevel spin systems under the condition of coarsening of measurement times -- i.e., when measurement times have experimental indeterminacy. This is studied together with the effect of coarsening of measurement outcomes for which individual outcomes cannot be unambiguously discriminated. In our treatment, along with different measurement outcomes being clubbed together into two groups in order to model the coarsening of measurement outcomes, importantly, varying degrees of coarsening of measurement time intervals have also been considered. This then reveals that while for a given dimension, the magnitude of quantum violation of macrorealism decreases with the increasing degree of coarsening of measurement times, interestingly, this effect of coarsening of measurement times can be annulled by increasing the dimension of the spin system so that in the limit of large spin, the quantum violation of macrorealism continues to persist. Thus, the result obtained demonstrates that classicality for large spins does not emerge from quantum mechanics in spite of the coarsening of measurement times.

quant-ph↗

arXiv2019

Analytic solutions of the geodesic equation for Reissner-Nordström-(anti-)de Sitter black holes surrounded by different kinds of regular and exotic matter fields

The purpose of this study is the derivation of the equation of motion for particles and light in the spacetime of Reissner-Nordström-(anti-)de Sitter black holes in the background of different kinds of regular and exotic matter fields. The complete analytical solutions of the geodesic equations are given in terms of the elliptic Weierstraß $\wp$-function and the hyperelliptic Kleinian $σ$-function. Finally after analyzing the geodesic motion of test particles and light using parametric diagrams and effective potentials, we present a list of all possible orbits.

gr-qc↗

arXiv2019

A sincere tribute to E.C.G Sudarshan's phenomenal contribution toward quantum theory of optical coherence

The diagonal representation and optical equivalence theorem are the E. C. G. Sudarshan's mid 20th century adventures in non-classical optics. It basically deals with a quantum mechanical description of photons to explain the quantum properties of light. Inspired by Sudarshan's pioneering work we try to explain the every minute mathematical details of his paper "Equivalence of semi-classical and quantum mechanical descriptions of statistical light beams". In this article we are going to go through some of the basics in developing quantum optics, then land up in E.C.G's original work and try to present it as rigorous as possible. We show some of its important applications in various classes of physics problems.

physics.hist-ph↗

arXiv2019

Energy extraction and particle acceleration around a rotating dyonic black hole in $N=2$, $U(1)^2$ gauged supergravity

In the present paper, we explore various gravitational aspects such as energy extraction (via the Penrose process and Superradiance), particle collisions around a $\mathcal{N}=2$, $U(1)^2$ dyonic rotating black hole (BH) in the gauged supergravity model. The impact of the rotation parameter ($a$) and the gauge coupling constant ($g$) on the behaviour of horizon and ergoregion of the BH is studied. It is of interest to note that, compared with the extremal Kerr BH, the gauge coupling constant, under certain constraints, can enhance the maximum efficiency of energy extraction by the Penrose process almost double. Under the same constraints, we can extract approximately 60.75\% of the initial mass energy from the BH which is noticeably higher in contrast to the extremal Kerr BH. The limit of energy extraction in terms of the local speeds of the fragments is also examined with the help of the Wald inequality. We identify an upper limit on the gauge coupling constant up to which the phenomenon of Superradiance is likely to occur. Finally, we computed the center-of-mass energy ($E_{CM}$) of two particles with the same rest masses moving in the equatorial plane of the BH. Our study also aims to sensitize $E_{CM}$ to the rotation parameter and the gauge coupling constant for extremal and nonextremal spacetime as well. Especially, for the extremal case, an infinitely large amount of $E_{CM}$ can be achieved closer to the horizon which allows the BH to serve as a more powerful Planck-energy-scale collider as compared to Kerr and any other generalized BHs in the Kerr family explored so far in general relativity. However, $E_{CM}$ for the nonextremal spacetime is shown to be finite and has an upper bound.

gr-qc↗