arXiv subjects

Abhijit Gadde

Publications and source records attributed to Abhijit Gadde.

At least 19 recordsLinked to original sources

arXiv2026

From Z to all: cyclic sum rules for thermal CFT partition functions

The high-temperature expansion of twisted $S^{d-1}\times S^1$ partition functions of CFT$_d$, $d = 2κ$, has recently been shown to obey an infinite tower of universal constraints. We determine these constraints explicitly and demonstrate that they can be packaged into a single equation involving a large conformal diffeomorphism isomorphic to $\mathbb{Z}_{κ+1}$, which cyclically permutes the thermal circle and the rotation angles. Our equation asserts that the $\mathbb{Z}_{κ+1}$-invariant part of $\ln Z/β$ is a constant fixed by the a-anomaly. Our derivation assumes CP-invariance and locality of the thermal effective action, whose structure we constrain using an algebraic formalism starting from embedding space.

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arXiv2026

Hironaka decompositions in supersymmetric theories: an exploration

We ask when tree-level supersymmetric cohomology admits a Hironaka decomposition: a unique expansion in finitely many secondary operators with polynomial coefficients in algebraically independent bosonic primaries. Such a decomposition organizes the cohomology into towers with a common set of unrestricted dressings. For diagonal models with $N$ labels, $d\geq1$ bosonic species and $f$ fermionic species, we construct this decomposition and obtain $(N!)^{d-1}2^{fN}$ secondaries. We also prove that the scalar-branch ring of ABJM theory admits a Hironaka decomposition at every rank and positive integer Chern--Simons level, and construct explicit bases for the $SU(2)\times SU(2)$ Klebanov--Witten scalar ring. We also do the same for the Higgs branches of two class-S theories. However, not all supersymmetric cohomologies admit a Hironaka decomposition. In the Wess--Zumino model with $W=x^2y^2$, every positive-degree scalar annihilates the nonzero class $xy$, while $x^n$ is in cohomology for every $n\geq 1$. These two properties rule out a Hironaka decomposition over scalar primaries.

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arXiv2026

Rényi multi-entropy of graph states and the $n -> 1$ limit

Rényi multi-entropy extends the Rényi entropy to pure states of more than two parties. It is defined by a replica contraction at integer replica number $n$, and the multi-entropy is its $n\to1$ limit. In holography this limit is conjectured to compute the area of a minimal soap-film web in the bulk. Understanding multi-entropy for general states, however, is harder. Unlike the bipartite case, the replica contraction is not a moment of a density matrix, and the continuation to $n=1$ has to be found by other means. We study this problem for qubit graph states. We show that at every odd $n$ the contraction equals $2^{-k/2}$, where $k$ is a sum of ranks of matrices over a finite field, one row and one column per qubit. We define a class of graphs that we call collision-controlled, for which the rank sum is a polynomial in $n$. This class includes graphs without even cycles and all complete bipartite graphs. The natural polynomial $n \to 1$ continuation is a finite sum over partitions of the parties. While the Rényi multi-entropy is non-increasing under single-qubit Pauli measurements at every odd integer $n>1$, the continuation to $n=1$ is not. A $Z$ measurement on one qubit of an odd ring with $2r + 1 \geq 7$ qubits raises it from $(r+1)\log 2$ to $(2r-1) \log 2$. Thus the continuation is not an entanglement monotone.

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arXiv2026

Monotones from multi-invariants: the Coxeter classification

Multi-invariants are multiplicative polynomial invariants of multipartite pure states under local unitaries. They yield entanglement monotones when their contraction graphs satisfy edge-convexity. We classify all connected edge-convex multi-invariants. Up to duplication of entire edge-colour families, their contraction graphs are precisely the standard edge-labelled Cayley graphs of finite Coxeter systems. Necessity follows by identifying edge-reflecting graphs with Coxeter Cayley graphs. For sufficiency, we prove vertex-convexity of parabolic quotients and lift their matrices by induction. This covers all classical and exceptional families. For the largest quotients, $E_8/D_7$ and $H_4/A_3$, wall symmetry reduces the matrices to exact positivity tests over $\mathbb Q$ and $\mathbb Q(\sqrt5)$.

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arXiv2026

From Multipartite Entanglement to TQFT

At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional manifold $M$ -- in the ground state of a $(d-1)+1$-dimensional gapped theory and the partition function of the low energy TQFT on $M$. Under certain assumptions, the conjecture implies that for $d=3$, the ground state wavefunction can determine the modular tensor category description of the low energy TQFT. We verify our conjecture for general (2+1)-dimensional Levin-Wen string-net models.

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arXiv2026

On genuine multipartite entanglement signals

We give a general construction of genuinely multipartite entanglement signals from families of lower-partite symmetric local-unitary invariants satisfying a natural compatibility condition. Möbius inversion on the partition lattice plays a key role in this construction. We show that many examples of multipartite entanglement signals considered in the literature fit naturally into this framework. We also explain how the genuinely multipartite signal can be extracted from a general, not necessarily symmetric, multi-invariant.

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arXiv2026

Multi-partite entanglement monotones

If we want to transform the quantum state of a system to another using local measurement processes, what is the probability of success? This probability is bounded by quantifying entanglement in both the states. In this paper, we construct a family of local unitary invariants of multipartite states that are monotonic under local operations and classical communication on average. These monotones are constructed from local unitary invariant polynomials of the state and its conjugate, and hence are easy to compute for pure states. Using these measures we bound the success probability of transforming a given state into another state using local quantum operations and classical communication.

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arXiv2026

Multi-invariants in stabilizer states

Multipartite entanglement is a natural generalization of bipartite entanglement, but is relatively poorly understood. In this paper, we develop tools to calculate a class of multipartite entanglement measures - known as multi-invariants - for stabilizer states. We give an efficient numerical algorithm that computes multi-invariants for stabilizer states. For tripartite stabilizer states, we also obtain an explicit formula for any multi-invariant using the GHZ-extraction theorem. We then present a counting argument that calculates any Coxeter multi-invariant of a q-partite stabilizer state. We conjecture a closed form expression for the same. We uncover hints of an interesting connection between multi-invariants, stabilizer states and topology. We show how our formulas are further simplified for a restricted class of stabilizer states that appear as ground states of interesting models like the toric code and the X-cube model.

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arXiv2025

Probing Non-Graviton Spectra in $\mathcal{N}=4$ SYM via BMN truncation and S-Duality

The one-loop cohomology of N=4 SYM is conjectured to be isomorphic to the exact cohomology. As a result, its truncations are expected to be subrings of the exact cohomology. We study the superconformal index restricted over one such truncation known as the BMN truncation. We present a systematic algorithm to compute the BMN index using the method of residues. We compute the BMN index for SU(N) SYM for N = 2,...,6 in closed form. It is expressed as a rational function of the fugacity. A term of the type (1-x) in the denominator indicates the presence of a bosonic generator counted with fugacity x. We find a rich and universal set of such terms in the denominator showing an interesting bosonic Fock space in the spectrum of protected operators. This Fock space cannot be explained as coming from the non-interacting supersymmetric graviton gas far away from the black hole as in the grey-galaxy solutions because the charges of the bosonic generators are not compatible with those of the supersymmetric gravitons. This suggests a novel microstructure within the supersymmetric black hole itself. We also examine the indices of S-dual pairs SO(2N+1) and Sp(N) SYM. Although their full 1/16-BPS indices coincide, we find discrepancies in their BMN-sector indices. As the BMN indices restricted to the graviton sector are expected to be the same, this mismatch allows us to identify non-graviton cohomologies. We explicitly find one of them in the SO(7) theory that is responsible for the mismatch of the BMN index. We also show that indices restricted to other one-loop cohomology truncations, in general, do not match under S-duality. If the conjecture of exactness of one-loop cohomology is correct, this suggests the presence of new cohomology subrings that match under S-duality with the letter-based truncations of the one-loop cohomology. This offers a way to check the one-loop exactness conjecture.

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arXiv2025

Multi-invariants and Bulk Replica Symmetry

In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants, multi-invariants, with a given replica symmetry that acts freely and transitively on the replicas. We look for a subclass of measures such that the dual bulk geometry also preserves replica symmetry. We obtain the most general solution to this problem if we require the bulk to preserve replica symmetry for general configurations of the regions. Orbifolding the bulk solution with the replica symmetry gives us a bulk geometry with a network of conical singularities. Our approach makes it clear that there are infinitely many infinitely large families of multi-invariants such that each family evaluates identically on the holographic state. Geometrically, these are equalities involving volumes of handlebodies, possibly of different genus, at particular points in the moduli space. In certain cases, we check our bulk computation with an explicit calculation in CFT. Finally we comment on the generalization to higher dimension.

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arXiv2025

Analysis of s-t symmetric classical S-matrices

We analyze the complex analytic properties of Classical (tree-level) S-matrices for four scalar particles with s-t crossing symmetry, involving an infinite number of exchanges. Under suitable analytic conditions, we demonstrate that such S-matrices exhibit a spectrum of poles that is equally spaced. We extend this result to S-matrices with accumulating poles, proving that under analogous conditions, their pole spectrum coincides with that of the Coon S-matrix. The boundedness of the S-matrix in the Regge limit is not essential for our results. While studying S-matrices that do not meet the conditions of our theorems, we encounter functions that have novel non-isolated singularities akin to what is called the natural boundary.

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arXiv2023

Monotonicity conjecture for multi-party entanglement I

In this paper, we conjecture a monotonicity property that we call monotonicity under coarse-graining for a class of multi-partite entanglement measures. We check these properties by computing the measures for various types of states using different methods.

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arXiv2023

Towards classification of holographic multi-partite entanglement measures

In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in arXiv:2206.09723 . We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in $2d$ CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.

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arXiv2023

Bound on the central charge of CFTs in large dimension

In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions $D$. Specifically, we work with the four-point function of identical scalars $ϕ$ with scaling dimension $Δ_ϕ$, and use a certain class of analytic functionals to show that the OPE coefficient squared $c^2_{ϕϕT^{μν}}$ must be exponentially small in $D$. For this to hold, we need to make a mild assumption about the nature of the spectrum below $2Δ_ϕ$. Our argument is robust and can be applied to any OPE coefficient squared $c^2_{ϕϕO}$ with $Δ_O< 2Δ_ϕ$. This suggests that conformal field theories in large dimensions (if they exist) must be exponentially close to generalized free field theories.

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arXiv2023

A new multi-partite entanglement measure and its holographic dual

In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate "soap-film" anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the sub-leading corrections in G_N.

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arXiv2022

A Scattering Amplitude for Massive Particles in AdS

In this paper, we propose a conformally covariant momentum space representation of CFT correlation functions. We call it the AdS S-matrix. This representation has the property that it reduces to the S-matrix in the flat space limit. The flat space limit in question is taken by keeping all the particle masses fixed as the operator conformal dimensions go to infinity along with the AdS radius $\mathtt{R}$. We give Feynman-like rules to compute the AdS S-matrix in $1/ \mathtt{R}$ perturbation theory. Moreover, we relate it to the Mellin space representation of the conformal correlators in $1/ \mathtt{R}$ perturbation theory.

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arXiv2020

Classification of four-point local gluon S-matrices

In this paper, we classify four-point local gluon S-matrices in arbitrary dimensions. This is along the same lines as \cite{Chowdhury:2019kaq} where four-point local photon S-matrices and graviton S-matrices were classified. We do the classification explicitly for gauge groups $SO(N)$ and $SU(N)$ for all $N$ but our method is easily generalizable to other Lie groups. The construction involves combining not-necessarily-permutation-symmetric four-point S-matrices of photons and those of adjoint scalars into permutation symmetric four-point gluon S-matrix. We explicitly list both the components of the construction, i.e permutation symmetric as well as non-symmetric four point S-matrices, for both the photons as well as the adjoint scalars for arbitrary dimensions and for gauge groups $SO(N)$ and $SU(N)$ for all $N$. In this paper, we explicitly list the local Lagrangians that generate the local gluon S-matrices for $D\geq 9$ and present the relevant counting for lower dimensions. Local Lagrangians for gluon S-matrices in lower dimensions can be written down following the same method. We also express the Yang-Mills four gluon S-matrix with gluon exchange in terms of our basis structures.

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arXiv2020

Lectures on the Superconformal Index

In these lectures, we give a pedagogical introduction to the superconformal index. This is the writeup of the lectures given at the Winter School "YRISW 2020" and is to appear in a special issue of JPhysA. The lectures are at a basic level and are geared towards a beginning graduate student interested in working with the superconformal index.

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