arXiv subjects

Ranveer Kumar Singh

Publications and source records attributed to Ranveer Kumar Singh.

At least 19 recordsLinked to original sources

arXiv2026

A Comment On Topological Degeneracy In Gauged WZW Models

Given a Lie group $G$, a level $k$, and a Lie subgroup $H$ one can construct 2d conformal field theories by either 1.) gauging a nonanomalous $H$ symmetry of the WZW model constructed from $(G,k)$ or 2.) using an algebraic procedure known as the GKO coset construction. The two models are closely related, but not precisely the same: The gauged WZW model is identified with the corresponding GKO model coupled to a 2d topological field theory. The topological theory is characterized by a commutative Frobenius algebra derived from the endomorphisms of an algebra object in a modular tensor category constructed from $(G,H,k)$. The partition function on the torus of the two models differ by a factor of the dimension of this algebra of endomorphisms. Concrete examples are constructed and some applications to string theory and 2d Yang-Mills coupled to nonanomalous matter are briefly discussed. This paper is a summary of a longer companion paper.

hep-th↗

arXiv2026

Generating Function of single-centered Black Hole Index in CHL Models

We present the construction of the generating function of single-centered black hole index in general $\mathbb{Z}_N$ CHL models. This is done by subtracting from the index of quarter BPS dyons, described by a meromorphic Siegel modular form, the generating function for the index of two-centered black holes. We use black hole bound state metamorphosis in CHL models for the construction of the generating function of two-centered black hole index. We prove the convergence of the generating function for the cases $N=2,3$.

hep-th↗

arXiv2026

Macdonald Index From Refined Kontsevich-Soibelman Operator

We propose a refinement of the Kontsevich-Soibelman operator for a class of ``special'' 4d $\mathcal{N}=2$ superconformal field theories characterized by the following conditions: (1) their Coulomb branch admits a source/sink chamber, i.e., a chamber in which the BPS quiver consists of only source and sink nodes, (2) The nodes with valency greater than 2 of the BPS quiver in a source/sink chamber are either all sources or all sinks. We present strong evidence that the trace of this refined operator is related to the Macdonald index of the theory. In particular, we conjecture closed form expressions for the Macdonald indices of the $(A_1,\mathfrak{g})$ Argyres-Douglas theories for any simply-laced Lie algebra $\mathfrak{g}$.

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arXiv2025

Beauty And The Beast Part 2: Apprehending The Missing Supercurrent

The Moonshine module is a $c=24$ conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in \cite{Dixon:1988qd} that there exists a spin lift of the Moonshine CFT with superconformal symmetry. Reference \cite{Dixon:1988qd} did not provide an explicit construction of a superconformal current. The present paper fills that gap. In fact, we will construct several superconformal currents in a spin lift of the Moonshine CFT using techniques developed in \cite{Harvey:2020jvu}. In particular, our construction relies on error correcting codes.

hep-th↗

arXiv2025

Generating Function of Single Centered Black Hole Index from the Igusa Cusp Form

We introduce manifestly duality invariant generating function of the index of single centered black holes in the heterotic string theory compactified on a six dimensional torus. This function is obtained by subtracting, from the inverse of the Igusa cusp form, the generating function of the index of two centered black holes constructed from the Dedekind eta function. We also study the analytic properties of this function in the Siegel upper half plane.

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arXiv2025

Mock Modularity Of Twisted Index In CHL Models

We study the twisted partition function of quarter BPS states in CHL models and show that for a large class of single-centered black holes, the degeneracy of microstates is given by the Fourier coefficients of mock Jacobi forms. Our analysis is a continuation of the programme initiated by Dabholkar, Murthy and Zagier (DMZ) for $1/4$-BPS dyons in $\mathcal{N} = 4$ string theory and further extended by Bhand, Sen and Singh (BSS) to quarter BPS states in CHL models. We also present the multiplicative lift construction of the partition function and comment on the additive lift of the same.

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arXiv2025

Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra

In this paper, we relate the MacDonald index of a 4d $\mathcal{N}=2$ SCFT with the Hilbert series of the arc space of the Zhu algebra of the corresponding Schur VOA. Using this, we conjecture a simple formula for the MacDonald index of $(A_1,D_{2n+1})$ Argyres-Douglas theory. We perform checks of the formula against the known Schur limits and RG flows. To match the Schur limit, we prove new $q$-series identities.

hep-th↗

arXiv2025

Mock Modularity In CHL Models

Dabholkar, Murthy and Zagier (DMZ) proved that there is a canonical decomposition of a meromorphic Jacobi form of integral index for $\mathrm{SL}(2, \mathbb{Z})$ with poles on torsion points into polar and finite parts, and showed that the finite part is a mock Jacobi form. In this paper we generalize the results of DMZ to meromorphic Jacobi forms of rational index for congruence subgroups of $\mathrm{SL}(2, \mathbb{Z})$. As an application, we establish that a large class of single-centered black hole degeneracies in CHL models are given by the Fourier coefficients of mock Jacobi forms. In this process we refine the result of DMZ regarding the set of charges for which the single-centered black hole degeneracies are given by a mock modular form. In particular, in the case studied by DMZ, we present examples of charges for which the single-centered degeneracies are not captured by the mock modular form of the expected index.

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arXiv2024

Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions

A consistent action for heterotic and type II superstring field theory was recently proposed by Sen. We give an algebraic formulation of this action in terms of certain twisted $L_\infty$-algebra. We further show that Sen's Wilsonian effective superstring field action can be obtained using homotopy transfer and the effective theory also possesses the algebraic structure of a twisted $L_\infty$-algebra.

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arXiv2024

Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The example of $\mathcal{N}=2^*$ theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional $\mathcal{N}=2$ theories and argue that the topological partition functions depend on (a): the diffeomorphism type of the spacetime, (b): the characteristic classes of background gerbe connections and (c): a "generalized spin-c structure," a concept we introduce and define. The main ideas are illustrated with both Lagrangian theories and class $\mathcal{S}$ theories. In the case of class $\mathcal{S}$ theories of $A_1$ type, we note that the different $S$-duality orbits of a theory associated with a fixed UV curve $C_{g,n}$ can have different topological data.

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arXiv2024

Rationality of Lorentzian Lattice CFTs And The Associated Modular Tensor Category

We classify the irreducible modules of a rational Lorentzian lattice vertex operator algebra (LLVOA) based on an even, self-dual Lorentzian lattice $Λ\subset\mathbb{R}^{m,n}$ of signature $(m,n)$. We show that the set of isomorphism classes of irreducible modules of the LLVOA are in one-to-one correspondence with the equivalence classes $Λ_0^\circ/Λ_0$ for a certain subset $Λ_0^\circ\subset\mathbb{R}^{m,n}$ and a full rank sublattice $Λ_0\subsetΛ$. We also classify the intertwining operators between the modules and calculate the fusion rules. We then describe the standard construction of modular tensor category (MTC) associated to rational LLCFTs. We explicitly construct the modular data and braiding and fusing matrices for the MTC. As a concrete example, we show that the LLCFT based on a certain even, self-dual Lorentzian lattice of signature $(m, n)$, with $m$ even, realizes the $D(m \bmod 8)$ level 1 Kac-Moody MTC.

hep-th↗

arXiv2024

Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs

Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature $(m,n)$ assuming the validity of a technical result about automorphisms of the lattice. We finally show that Narain conformal field theories in physics are examples of non-chiral VOA. Our formalism helps us to identify the chiral algebra of Narain CFTs in terms of a particular sublattice and give us the decomposition of its partition function into sum of characters.

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arXiv2023

Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism

It is known that $\mathcal{N}=8$ supergravity is dual to $\mathcal{N}=4$ super Yang-Mills (SYM) via the double copy relation. Using the explicit relation between scattering amplitudes in the two theories, we calculate the soft and collinear limits in $\mathcal{N}=8$ supergravity from know results in $\mathcal{N}=4$ SYM. In our application of double copy, a particular self-duality condition is chosen for scalars that allows us to constrain and determine the R-symmetry indices of the supergravity states in the collinear limit.

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arXiv2022

Asymptotic Symmetry algebra of $\mathcal{N}=8$ Supergravity

The asymptotic symmetry algebra of $\mathcal{N}=1$ supergravity was recently constructed using the well-known $2$D celestial CFT (CCFT) technique in ArXiv: 2007.03785. In this paper, we extend the construction to the maximally supersymmetric four dimensional $\mathcal{N}=8$ supergravity theory in asymptotically flat spacetime and construct the extended asymptotic symmetry algebra, which we call $\mathcal{N}=8$ $\mathfrak{sbms}_4$. We use the celestial CFT technique to find the appropriate currents for extensions of $\mathcal{N}=8$ super-Poincaré and $\mathrm{SU}(8)_R$ R-symmetry current algebra on the celestial sphere $\mathcal{CS}^2$. We generalise the definition of shadow transformations and show that there is \textit{no} infinite dimensional extension of the global $\mathrm{SU}(8)_R$ algebra in the theory.

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arXiv2022

Demonstration of a general fault-tolerant quantum error detection code for (2n+1)-qubit entangled state on IBM 16-qubit quantum computer

Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error detection codes have been proposed and realized for lower number of qubit systems. Here we present an error detection code for a (2n+1)-qubit entangled state using two syndrome qubits and simulate it on IBM's 16-qubit quantum computer for a 13-qubit entangled system. The code is able to detect an arbitrary quantum error in any one of the first 2n qubits of the (2n+1)-qubit entangled state and detects any bit-flip error on the last qubit of the (2n+1)-qubit entangled state via measurements on a pair of ancillary error syndrome qubits. The protocol presented here paves the way for designing error detection codes for the general higher number of entangled qubit systems.

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arXiv2022

Zagier's weight $3/2$ mock modular form

Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the discriminant $(-n)$. In the modern framework, these results show that the generating function of $H(n)$ is a mock modular form of weight 3/2 with the theta function being the shadow. In this expository paper, we provide a detailed proof of Zagier's result.

math.NT↗

arXiv2022

An Analogue of Weil's Converse Theorem for Harmonic Maass Forms of Polynomial Growth

We construct a family of harmonic Maass forms of polynomial growth of any level corresponding to any cusp whose shadows are Eisenstein series of integral weight. We further consider Dirichlet series attached to a harmonic Maass form of polynomial growth, study its analytic properties, and prove an analogue of Weil's converse theorem.

math.NT↗

arXiv2022

Maass lifts of half-integral weight Eisenstein series and theta powers

In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of $Θ^k, k \in \{ 3, 5, 7\}$ under the shadow operator, where $Θ$ is the classical Jacobi theta function.

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