arXiv subjects

Palash Singh

Publications and source records attributed to Palash Singh.

8 recordsLinked to original sources

arXiv2025

Fortuity in ABJM

We study $1/12$-BPS and $1/16$-BPS cohomologies and the fortuitous mechanism in ABJM theory. We first establish the existence of fortuitous states in the $N=1$ theory, where the theory is abelian and trace relations are extreme. We then provide explicit constructions of fortuitous states at $N=2$. We find fortuitous states both at weak coupling, in direct parallel to what has been done in $\mathcal{N}=4$ SYM, but we also find additional fortuitous states at $k=2$, which is in the strongly coupled regime. The extra fortuitous states that appear at $k=2$ are in non-trivial monopole sectors. A striking distinction from $\mathcal{N}=4$ SYM is that the fortuitous states appear at much smaller quantum numbers, making them easier to find. Along the way, we formulate a non-renormalization conjecture for cohomologies in ABJM.

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arXiv2025

Generalised 4d Partition Functions and Modular Differential Equations

We prove the equivalence of a class of generalised Schur partition functions $\mathcal Z_G(q;\alpha)$ of 4d $\mathcal N=2$ superconformal gauge theories to contour integral representations of vector-valued modular forms of the type that arise in 2d rational conformal field theories (RCFT). Concretely, we consider the $USp(2N)$ theory with $2N+2$ fundamental hypermultiplets and analytically prove that $\mathcal Z_{USp(2N)}(q;\alpha)$ satisfies an order-$(N+1)$ modular linear differential equation (MLDE) with vanishing Wronskian index, explaining how the parameter $\alpha$ of the former determines the parameters of the latter. Several connections are made to characters of RCFTs including unitary ones. We then propose a two-parameter extension $\mathcal Z_{USp(2N)}(q;\alpha,\beta)$ of the generalised Schur partition function. Finally, we relate the $\alpha=-k$ specialisation to quantum monodromy traces ${\rm Tr}\,M^k$ and formulate a conjecture linking their $k$-dependence to MLDEs.

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arXiv2025

Breaking bad theories of class $\mathcal S$

We study weakly-coupled descriptions/channel decompositions of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ of type $\mathfrak{su}(N)$, from the perspective of the 3d $\mathcal{N}=4$ mirror duals of their circle compactifications. This is a delicate problem when the channel decomposition produces pathological, or bad, 4d configurations that correspond to spheres with non-maximal punctures. The star-shaped quivers, describing the 3d mirrors associated with such bad 4d configurations, are bad 3d $\mathcal{N}=4$ theories. Leveraging recent results regarding 3d bad theories, we identify a new and interesting family of bad theories, which we coin \textit{broken} theories, that naturally arise in this context. Using these broken theories, we develop a systematic and analytic method that determines the generically non-Lagrangian matter sectors and the weakly-coupled gauge groups in such channel decompositions. We understand these weakly-coupled descriptions as emerging dynamically via Higgs mechanisms triggered by operators acquiring vacuum expectation values.

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arXiv2025

Simplifying the Type $A$ Argyres-Douglas Landscape

A well-established organisational principle for Argyres--Douglas-type $\mathcal{N}=2$ superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on $\mathbb{CP}^1$. The dictionary between Hitchin system data and various features of the corresponding SCFT has been studied extensively, but the overall structure of the resulting space of SCFTs still appears quite complicated. In this work, we systematically delineate a variety of simplifications that arise within this class of constructions due to several large classes of isomorphisms between SCFTs associated with inequivalent Hitchin system data (and their exactly marginal gaugings). We restrict to the most studied class of theories, namely the type $A$ theories without outer automorphism twists.

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arXiv2021

Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms

We investigate the unflavoured Schur indices of class $\mathcal S$ theories of modest rank, and in the case of $\mathcal{N}=4$ super Yang-Mills theory with special unitary gauge group of somewhat more general rank, with an eye towards their modular properties. We find closed form expressions for many of these theories in terms of quasimodular forms of level one or two, with the curious feature that in general they are sums of quasimodular forms of different weights. For type $\mathfrak{a}_1$ theories, the index can be fixed by taking a simple Ansatz for the family of quasimodular forms appearing in the expansion of this type and demanding that the result be sufficiently regular as $q\to0$. For higher rank cases, an equally simple construction is lacking, but we nevertheless find that these indices can be expressed in terms of mixed-weight quasimodular forms.

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arXiv2021

Poincaré Series, 3d Gravity and Averages of Rational CFT

We investigate the Poincaré approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary examples for which the Poincare series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU($N$)$_1$ and SU(3)$_k$, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions -- the latter corresponding to analogues of 3-manifold "wormholes" -- such that the expected average is correctly reproduced.

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arXiv2020

Rational CFT With Three Characters: The Quasi-Character Approach

Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two characters. These in turn generate all possible admissible characters, of arbitrary Wronskian index, in order two. Here we initiate a study of the three-character case. We conjecture several infinite families of quasi-characters and show in examples that their linear combinations an generate admissible characters with arbitrarily large Wronskian index. The structure is completely different from the order two case, and the novel coset construction of arXiv:1602.01022 plays a key role in discovering the appropriate families. Using even unimodular lattices, we construct some explicit three-character CFT corresponding to the new admissible characters.

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arXiv2019

Contour Integrals and the Modular S-Matrix

We investigate a conjecture to describe the characters of large families of RCFT's in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular S-matrix for arbitrary numbers of characters as a sum over paths. Thereafter we focus on the case of 2, 3 and 4 characters, where agreement between the critical exponents of the integrals and the characters implies that the conjecture is true. In these cases, we compute the modular S-matrix explicitly, verify that it agrees with expectations for known theories, and use it to compute degeneracies and multiplicities of primaries. We also compute S in an 8-character example to provide additional evidence for the original conjecture. On the way we note that the Verlinde formula provides interesting constraints on the critical exponents of RCFT in this context.

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