arXiv subjects

Abhishek Chowdhury

Publications and source records attributed to Abhishek Chowdhury.

At least 19 recordsLinked to original sources

arXiv2026

Hidden kinetic correlations control collective phases of entropy-conditioned histories

Visible dynamics and mean dissipation need not determine the collective phases of rare histories. We construct local Markov models with identical ordinary visible path distributions, stationary states, mean entropy production, mean jump activity and driving affinities, yet different phases when histories are weighted by their full entropy production. Visible configurations modulate hidden driven cycles, whose exact elimination turns kinetic correlations into interactions. A positive spectral reduction separates hidden relaxation from collective modes. Periodic binary models retain opposite phases with entropy variances matched at every observation time. For conserved particles, a pair matches the first two joint cumulants of entropy and hidden activity at every observation time, yet selects segregation or a fluctuating state with suppressed long-wavelength density noise. Bound-state transport and fermionic evolution determine their contrasting dynamics. At a clean Ising critical midpoint, the entropy source couples quadratically to the thermal perturbation, making the fourth cumulant the first to detect the critical susceptibility. Its rate per site grows logarithmically, with an exact cutoff set by system size and observation time. For two quenched disorder ensembles, exact sample-response formulas and numerical evidence support a finite fourth-cumulant density despite very slow relaxation; a weak-disorder continuum response admits a controlled Borel sum. A common positive hidden eigenvector characterizes autonomous selected dynamics. When this condition fails, a finite network develops visible memory while preserving its ordinary visible process and mean diagnostics. These results identify kinetic information missed by aggregate thermodynamic observations.

cond-mat.stat-mech↗

arXiv2026

Protected domains and the cost of cooperation on weighted networks

Contacts that protect a cooperative group can also make its founding sites difficult for newborn mutants to reach. We study this tension in a donation game with benefit $b$ and cost $c$ on finite weighted networks. Reciprocal contacts determine averaged payoffs and route copying from sources selected globally with a payoff-dependent bias. We compare takeover probabilities of a cooperator and a defector, each introduced singly into a population of the opposite type. Exact linear response about neutral drift and elimination of fast configurations identify protected domains as collective competitors. Under uniform introduction, the sharp weak-selection threshold infima are $b/c=3$ on the four-cycle, $7$ on the five-site path and $1$ on every fixed path with at least six sites. Introduction through newborn offspring eliminates this advantage on the five-site path. On six sites it preserves the infimum one but raises the minimum contact contrast, the largest weight divided by the smallest, needed for threshold $1+ε$ from $656ε^{-2}$ to $4050ε^{-3}$ at leading order. Global polynomial bounds force every six-site design approaching threshold one into the domain hierarchy. Algebraic relations among contact ratios control optimization over all positive weights and establish exact reflection symmetry of the optimizer at sufficiently large contrast. For uniform introduction, the geometry determines absorption and fixation times and tolerance to contact errors. Nonlinear selection narrows the favorable window, making the fixation-probability difference small near the minimum contrast. A sharp variance-time bound quantifies the observation cost when the site- and type-specific terminal fixation probabilities are independently unknown. The same contacts govern collective persistence, access by mutation and the time to resolve the invasion advantage.

cond-mat.stat-mech↗

arXiv2026

Krylov Complexity of Time-Dependent Optical Hamiltonians

State Krylov complexity becomes experimentally concrete in driven optics because its chain can be interrogated through excitation counting, parity, return probability, and phase. Its meaning, however, is fixed jointly by the control history, the prepared state, and the reference used to follow explicit time dependence. We disentangle these ingredients for oscillator, $SU(2)$, $SU(1,1)$, and three-level Hamiltonians and determine when preparation dependence preserves exact solvability. A fixed group displacement of an extremal state can be absorbed into transformed controls, giving an undo-and-count readout for arbitrary drives. A polynomial preparation instead Christoffel-transforms the spectral measure of a fixed operator; an affine moving frame then transports its complete seed-adapted chain even when laboratory Hamiltonians at different times do not commute. We also resolve seed dependence in stroboscopic dynamics and driven three-level geometry. A periodically forced mode started from any finite Fock state has cyclic dimension equal to the denominator of a nonzero-displacement rational rotation and infinite dimension for an irrational rotation. At a half turn its complexity becomes a Laguerre survival deficit and a magnitude-sensitive Wigner readout. In a driven $V$ atom, bright-state geometry interferes with excited-manifold dynamics and controls bright-dark decoupling. Preparation therefore changes not only the initial state but also the chain and the optical observable that realizes its complexity.

quant-ph↗

arXiv2026

Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity

At fixed Hamiltonian $H$, changing the initial state changes the cyclic pair and hence generally the Lanczos basis and spread. For every normalizable polynomial preparation $\lvertψ_Q\rangle=N_Q^{-1/2}Q(H)\lvert K_0\rangle$, we reconstruct its state-Krylov problem exactly from reference cyclic data. The transfer assumes no integrability and applies on finite or infinite cyclic support. Reweighting the reference spectral measure by $\lvert Q\rvert^2$ gives a finite-band connector for every prepared amplitude and a finite-rank Christoffel-Darboux projection for cumulative probabilities and spread, without rerunning ambient-space Lanczos. Fixed-degree seeds preserve the limiting Jacobi coefficients of asymptotically constant chains. Every Charlier number-state jump obeys $K_r(t)\ge K_0(t)$, with strict inequality for $r\ge1$ away from revivals. At every fixed finite $r$, the Hermite endpoint has exact all-level amplitudes, whereas the continuous-$q$-Hermite chord chain of double-scaled SYK has an all-level root-free re-Lanczos reconstruction. Writing $D_r^{\rm H}$ and $D_r^{\mathrm{ch}}(t)$ for the mean absolute Fock and chord displacements, respectively, the bounds are $K_r\ge D_r^{\rm H}$ and $K_r(t)\ge D_r^{\mathrm{ch}}(t)\ge\lvert\overline n_r(t)-r\rvert$. Thus rebuilt spread bounds physical displacement and signed chord drift. At fixed $0\le q<1$ and time, $K_r(t)-D_r^{\mathrm{ch}}(t)\to0$ as $r\to\infty$, with both approaching the same folded-Bessel limit. In Liouville space, the exact unnormalized gap measure family on an open inverse-temperature interval determines the positive transition-resolved measure, assuming the thermal kernel is known and strictly positive and the requisite exponential moments exist. One cyclic solution can therefore be reused across polynomial seeds while separating physical propagation, basis response, and rebuilt spread.

hep-th↗

arXiv2026

Pure D-brane Black Holes: BPS Counting and non-BPS Vacua

In this paper, we present a unified computational framework to analyze the microscopic vacuum structure of 4-charge extremal black holes in Type IIA string theory, applying techniques from computational algebraic geometry and numerical topology to their pure D-brane effective quantum mechanics. We apply this approach to two physically distinct configurations. First, in the supersymmetric sector, we compute the $14^{\text{th}}$ helicity trace index of $\frac{1}{8}$-BPS, $N=8$, D2-D2-D2-D6 configurations dual to D1-D5-P-KK monopole dyonic black holes. Extending previous work to higher charges, we employ a parametric monodromy method to explicitly resolve the vacua for the $(1,1,1,5)$ and $(1,1,1,6)$ configurations, reproducing the degeneracies predicted by the U-dual picture. Second, we apply complementary techniques to a configuration where supersymmetry is explicitly broken at the level of the effective action. The corresponding 4-charge non-BPS extremal pure D-brane system is obtained by replacing the D6-brane with an anti-D6-brane and assigning incompatible R-symmetry rotations to different brane triplets. Analyzing the associated scalar potential using analytical Gröbner bases, we demonstrate the absence of zero-energy classical ground states. To handle the continuous flat directions populating the non-BPS landscape, we implement specific topological regularizations, namely Morse-Bott deformations and gated soft-trapping. These methods allow us to systematically characterize the classical energy landscape, identifying a non-compact Coulomb branch, marginally bound stabilizer submanifolds, and an isolated collection of doubly degenerate low-energy stable states.

hep-th↗

arXiv2025

Warp Drives and Martel-Poisson charts

We extend the construction of Alcubierre-Natário class of warp drives to an infinite class of spacetimes with similar properties. This is achieved by utilising the Martel-Poisson charts which closely resembles the Weak Painlevé-Gullstrand form for various background metrics (Mink, AdS, dS). The highlight of this construction is the non-flat intrinsic metric which in three dimensional spacetimes introduce conical singularities at the origin and in higher dimensions generates non-zero Ricci scalar for the spatial hypersurfaces away from the origin. We analyse the expansion/contraction of space and the (NEC) violations associated with these warp drives and find interesting scalings due to the global imprints of the conical defects. Other properties like tilting of light cones, event horizons and several generalisations are also discussed.

gr-qc↗

arXiv2025

Information Scrambling with Higher-Form Fields

The late time behaviour of OTOCs involving generic non-conserved local operators show exponential decay in chaotic many body systems. However, it has been recently observed that for certain holographic theories, the OTOC involving the $U(1)$ conserved current for a gauge field instead varies diffusively at late times. The present work generalizes this observation to conserved currents corresponding to higher-form symmetries that belong to a wider class of symmetries known as generalized symmetries. We started by computing the late time behaviour of OTOCs involving $U(1)$ current operators in five dimensional AdS-Schwarzschild black hole geometry for the 2-form antisymmetric $B$-fields. The bulk solution for the $B$-field exhibits logarithmic divergences near the asymptotic AdS boundary which can be regularized by introducing a double trace deformation in the boundary CFT. Finally, we consider the more general case with antisymmetric $p$-form fields in arbitrary dimensions. In the scattering approach, the boundary OTOC can be written as an inner product between asymptotic 'in' and 'out' states which in our case is equivalent to computing the inner product between two bulk fields with and without a shockwave background. We observe that the late time OTOCs have power law tails which seems to be a universal feature of the higher-form fields with $U(1)$ charge conservation.

hep-th↗

arXiv2024

Counting $\mathcal{N} = 8$ Black Holes as Algebraic Varieties

We calculate the helicity trace index $B_{14}$ for $\mathcal{N} = 8$ pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations with syzygies. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. Unlike other schemes, these methods are almost exact with a very high success rate for finding all solutions. A gauge invariant analysis is also possible using the symbolic Hilbert series. Furthermore, exploiting various exchange symmetries, we show the non-existence of a quartic and(or) higher order terms in the potential which if present would have spoiled the counting. Incorporating recent developments in mathematics, algorithms and multi-threading, we have extended the scope of one of the author's previous works to other charges and presented a new perspective for the microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to $\mathcal{N} = 2$ black hole counting.

hep-th↗

arXiv2023

Loop braid groups and integrable models

Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in physics stems from the fact that they capture anyonic statistics in three dimensions which is otherwise known to only exist for point particles on the plane. Here we explore another direction where the algebraic relations of the loop braid groups can play a role -- quantum integrable models. We show that the {\it symmetric loop braid group} can naturally give rise to solutions of the Yang--Baxter equation, proving the integrability of certain models through the RTT relation. For certain representations of the symmetric loop braid group we obtain integrable deformations of the $XXX$-, $XXZ$- and $XYZ$-spin chains.

math-ph↗

arXiv2022

Non-CSS color codes on 2D lattices : Models and Topological Properties

The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the $\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit. However its short range physics include single qubit Pauli operations that violate either three or six stabilisers as opposed to the toric code where single qubit Pauli operations violate two or four stabilisers. Exploiting this fact we construct several non-CSS versions of the two-dimensional color code falling into two families - those where either three, four or five stabilisers are violated and those which violate exactly four stabilisers for all the three types of single qubit Pauli operations. These models are not equivalent to the original color code by a local unitary transformation. Nevertheless the code spaces of the CSS and non-CSS versions are related by local unitaries which reflects the fact that their long range physics coincide. This also implies that the non-CSS versions host transversal Clifford gates and hence support fault-tolerant computations. As a consequence of the non-CSS structure, the logical operators are of a mixed type which in some cases include all the three Pauli operators making them potentially useful for protection against biased Pauli noise.

quant-ph↗

arXiv2020

On Mathieu moonshine and Gromov-Witten invariants

We show that a large number of $CY_3$ manifolds are involved in an intricate way in Mathieu moonshine viz. their Gromov--Witten invariants are related to the expansion coefficients of the twined/ twisted--twined elliptic genera of $K3$. We use the string duality between CHL orbifolds of heterotic string theory on $K3 \times T^2$ and type IIA string theory on $CY_3$ manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality.

hep-th↗

arXiv2019

Dyonic black hole degeneracies in $\mathcal{N} = 4$ string theory from Dabholkar-Harvey degeneracies

The degeneracies of single-centered dyonic $\frac14$-BPS black holes (BH) in Type II string theory on K3$\times T^2$ are known to be coefficients of certain mock Jacobi forms arising from the Igusa cusp form $Φ_{10}$. In this paper we present an exact analytic formula for these BH degeneracies purely in terms of the degeneracies of the perturbative $\frac12$-BPS states of the theory. We use the fact that the degeneracies are completely controlled by the polar coefficients of the mock Jacobi forms, using the Hardy-Ramanujan-Rademacher circle method. Here we present a simple formula for these polar coefficients as a quadratic function of the $\frac12$-BPS degeneracies. We arrive at the formula by using the physical interpretation of polar coefficients as negative discriminant states, and then making use of previous results in the literature to track the decay of such states into pairs of $\frac12$-BPS states in the moduli space. Although there are an infinite number of such decays, we show that only a finite number of them contribute to the formula. The phenomenon of BH bound state metamorphosis (BSM) plays a crucial role in our analysis. We show that the dyonic BSM orbits with $U$-duality invariant $Δ<0$ are in exact correspondence with the solution sets of the Brahmagupta-Pell equation, which implies that they are isomorphic to the group of units in the order $\mathbb{Z}[\sqrt{|Δ|}]$ in the real quadratic field $\mathbb{Q}(\sqrt{|Δ|})$. We check our formula against the known numerical data arising from the Igusa cusp form, for the first 1650 polar coefficients, and find perfect agreement.

hep-th↗

arXiv2019

On interpolating anomalous dimension of twist-two operators with general spins

We study non-perturbative interpolating functions to probe the physics of anomalous dimensions associated with twist-two operators in ${\cal N}=4$ SYM of finite and infinite spin. Compared to previous studies, the novel result of this paper is to introduce single multivariate functions of both coupling $g$ and spin $j$ to approximate such anomalous dimensions. We provide a unified framework to study such operators in interim ranges of the parameters which so far has eluded previous results. Explicitly, we consider twist-two anomalous dimensions in two distinct scenarios using interpolating functions. For the large $N$ case, we stick to simple Padé approximants and its generalizations . For the finite $N$ case, ${\cal N}=4$ SYM is expected to be S-dual invariant, hence the observables are expected be modular invariant. To probe the finite $N$ physics, we take into account the non-planar and instanton contributions by constructing modular invariant interpolating functions to approximate the cusp and twist-two anomalous dimensions. We also consider interpolating functions for the twist-four operators and study level crossing phenomenon between the twist-two and twist-four operators.

hep-th↗

arXiv2019

Scaling limits of dS vacua and the swampland

We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over $α'$ and string loop corrections.

hep-th↗

arXiv2018

Calabi-Yau manifolds and sporadic groups

A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M$_{24}$ was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau $d$-folds for $d>3$ have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.

hep-th↗

arXiv2017

S-duality invariant perturbation theory improved by holography

We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling $τ$. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the $\mathcal{N}=4$ superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points $τ=i$ and $τ=e^{iπ/3}$. It turns out that our interpolating functions have maximum at $τ=e^{iπ/3}$, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.

hep-th↗

arXiv2016

Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory

By relating the functional averages of a generic scalar operator in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. Numerical results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.

hep-lat↗

arXiv2016

Do All BPS Black Hole Microstates Carry Zero Angular Momentum?

From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on $T^6$, represented by four stacks of D-branes wrapped on various cycles of $T^6$. For this system the above conjecture translates to the statement that the moduli space of classical vacua must be a collection of points. Explicit analysis of systems carrying a low number of D-branes supports this conjecture.

hep-th↗