arXiv subjects

Anirudh Deb

Publications and source records attributed to Anirudh Deb.

8 recordsLinked to original sources

arXiv2026

Higgsless Lagrangian SCFTs and Strongly Finite VOAs

Vertex operator algebras (VOAs) are well studied in both mathematics and physics. The best understood class is that of strongly rational VOAs, whose representation category is maximally well behaved: indeed, it is a modular tensor category. At the next level of complexity are strongly finite but non-rational VOAs. Their representation category is not semisimple (it is ``logarithmic''), but maintains nice structural properties. Only a few families of examples in this class are known, a fact that may have hindered the development of a comprehensive mathematical theory. The SCFT/VOA correspondence provides a natural way to generate more examples: strongly finite but non-rational VOAs are expected to arise from four-dimensional ${\cal N}=2$ Lagrangian superconformal field theories (SCFTs) that do not admit a Higgs branch moduli space of vacua. We tackle the combinatorial task of classifying all such ``Higgsless'' Lagrangian SCFTs. To our surprise, this set turns out to be rather sparse. Free vector multiplets and their discrete gaugings are immediate examples. The interacting Higgsless theories comprise one infinite sequence of SO/USp quivers and three sporadic examples. We construct and study the novel VOAs associated to two of the sporadic examples, and confirm that they are indeed strongly finite and logarithmic.

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arXiv2026

On non-relativistic integrable models and 4d SCFTs

We elaborate on the relation between the generalized Schur index of $N=2$ SCFTs in four dimensions and the non-relativistic limit of the elliptic Ruijsenaars-Schneider model. In particular we discuss explicitly how to express generalized Schur indices of theories of class $S$ in terms of elliptic Jack functions. For example, in the $A_1$ case the indices are given naturally in terms of eigenfunctions of the Lam\'{e} equation. We use the expression in terms of eigenfunctions to further check the recent observation that the generalized Schur indices of different theories in the Deligne-Cvitanovi\'{c} series can be mapped onto each other. This mapping implies non trivial identities on unrefined sums of eigenfunctions of non-relativistic elliptic Calogero-Moser models associated to different root systems. We claim then that the non-relativistic limits of various integrable models give rise naturally to generalized Schur-like limits of classes of $N=1$ SCFTs. As an example we discuss the relation of the Inozemtsev model, the non relativistic limit of the van Diejen model, and compactifications of the rank $Q$ E-string theory. We argue that in general the ``Schur index'' of $N=1$ $4d$ SCFTs can be understood as being related to the free fermionic limit of a non-relativistic integrable model.

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arXiv2025

Generalized Schur limit, modular differential equations and quantum monodromy traces

We explore some aspects of the generalized Schur limit, defined in arXiv:2506.13764. Based on several examples, we conjecture that the generalized Schur limit as a function of $\alpha$ solves a modular linear differential equation of fixed order, with coefficients depending on $\alpha$. We also observe in examples that for Argyres-Douglas theories of type $(A_1,G)$ with $G=A_n,D_n$, the generalized Schur limit for certain negative integer values of $\alpha$, coincides with the trace of higher powers of the quantum monodromy operator. This hints at a more general correspondence between the wall-crossing invariant traces on the Coulomb branch and the generalized Schur limit, which is related to the Higgs branch.

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arXiv2025

Aspects of holographic entanglement using physics-informed-neural-networks

We implement physics-informed-neural-networks (PINNs) to compute holographic entanglement entropy and entanglement wedge cross section. This technique allows us to compute these quantities for arbitrary shapes of the subregions in any asymptotically AdS metric. We test our computations against some known results and further demonstrate the utility of PINNs in examples, where it is not straightforward to perform such computations.

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arXiv2025

Generalized Schur partition functions and RG flows

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion with coefficients depending on a continuous parameter $\alpha$. The Schur index is a special case with $\alpha=1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformations of the SCFT. In particular, two SCFTs residing in different corners of the same Coulomb branch, satisfying certain restrictive conditions, have the same partition function with a non-trivial map of the parameters, $\hat {\cal Z}_1(q,\alpha_1)=\hat {\cal Z}_2(q,\alpha_2(\alpha_1))$. For example, we show that the Schur index of all the SCFTs in the Deligne-Cvitanovi\'c series is given by special values of $\alpha$ of the partition function of the SU(2) $N_f=4$ ${\cal N}=2$ SQCD.

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arXiv2025

The Nilpotency Index for 4d $\mathcal{N}=2$ SCFTs

A well-developed classification program for 4d $\mathcal{N}=2$ super conformal field theories (SCFTs) leverages Seiberg-Witten geometry on the Coulomb branch of vacua; theories are arranged by increasing $\mathfrak{rank}$, the complex dimension of their Coulomb branch. An alternative organizational scheme focusses on the associated vertex operator algebra (VOA), which is more closely related to the Higgs branch. From the VOA perspective, a natural way to arrange theories is by their ``index of nilpotency'', the smallest integer $\mathfrak{n}$ such that $T^\mathfrak{n} = 0$ in the $C_2$ algebra, where $T$ is the VOA stress tensor. It follows from the Higgs branch reconstruction conjecture that $\mathfrak{n} < \infty$ for any 4d ${\cal N}=2$ SCFT. Extrapolating from several examples, we conjecture that $\mathfrak{n}$ is an RG monotone, $\mathfrak{n}_{\rm IR} \leq \mathfrak{n}_{\rm UV}$. What's more, we find in all cases that $\mathfrak{rank} \leq \mathfrak{n}-1$. Theory ordering by $\mathfrak{n}$ appears thus more refined than ordering by $\mathfrak{rank}$. For example, in the list of $\mathfrak{rank}=1$ theories, the Kodaira SCFTs and $SU(2)$ ${\cal N}=4$ SYM have $\mathfrak{n} =2$, while all others have $\mathfrak{n} >2$.

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arXiv2024

Free field realizations for rank-one SCFTs

In this paper, we construct the associated vertex operator algebras for all $\mathcal{N}=2$ superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly suitable framework for this task. The elementary building blocks of the construction are dictated by the low energy degrees of freedom on the Higgs branch, which are well understood for rank-one theories. We further analyze the interplay between Higgs and Coulomb data on the moduli space of vacua, which tightly constrain the overall structure of the free field realizations. Our results suggest a plausible bottom-up classification scheme for low-rank SCFTs incorporating vertex algebra techniques.

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arXiv2024

$\mathcal{N}=5$ SCFTs and quaternionic reflection groups

It was previously noted that for 3d SCFTs with $\mathcal{N}\geq 6$ the moduli space has the form of $\mathbb{C}^{4r}/\Gamma$, where $\Gamma$ is a complex reflection group, at least following suitable gauging of finite symmetries. Here we argue that this observation can be extended also to 3d SCFTs with $\mathcal{N}\geq 5$ SUSY, where $\Gamma$ is now a quaternionic reflection group. To do this, we study the moduli space of the known 3d $\mathcal{N}=5$ SCFTs. For Lagrangian cases, the results for the moduli space are further checked using the superconformal index.

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