On the Nekrasov partition function of gauged Argyres-Douglas theories

We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of Dp(SU(N)) theories. The same set of theories that we study can also be realized from 6d $$ \mathcal{N} $$ N = (1, 0) compactification on a torus. The main example in this class is the (A2, D4) theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of $$ \mathcal{N} $$ N = 4 super Yang-Mills with gauge algebra 𝔰𝔲(2). We extend this result to infinitely many other Argyres-Douglas theories in the same family, including those with central charges a = c whose conformal manifold is one dimensional, and those with a ≠ c whose conformal manifold has dimension larger than one. Our result is supported by examining certain special cases that can be realized in terms of theories of class 𝒮.

Section: Discussionmentioning

confidence: 99%

Comments on Non-invertible Symmetries in Argyres-Douglas Theories

Carta

Giacomelli

Mekareeya

et al. 2023

“…Then it was shown that the corresponding gauge counterparts in case of r = 2 and r = 3 are just the AD theories denoted by H 1 and H 2 respectively. Such relationships were subject of further detailed investigation in [14][15][16][17][18][19][20][21][22]. In a parallel development it was shown in [23] that H 1 and H 2 partition functions are closely related to third and forth Painlevé τ -functions provided Ω-background parameters are subject to condition ϵ 1 = −ϵ 2 .…”

Section: Introductionmentioning

confidence: 98%

A note on rank 5/2 Liouville irregular block, Painlevé I and the $$ \mathcal{H} $$0 Argyres-Douglas theory

Poghosyan,

Poghossian

2023

We study 4d type $$ \mathcal{H} $$ H 0 Argyres-Douglas theory in Ω-background by constructing Liouville irregular state of rank 5/2. The results are compared with generalized Holomorphic anomaly approach, which provides order by order expansion in Ω-background parameters ϵ1,2. Another crucial test of our results provides comparison with respect to Painlevé I τ-function, which was expected to be hold in self-dual case ϵ1 = −ϵ2. We also discuss Nekrasov-Shatashvili limit ϵ1 = 0, accessible either by means of deformed Seiberg-Witten curve, or WKB methods.

Quasinormal modes of C-metric from SCFTs

Lei,

Shu,

Zhang

et al. 2024

We study the quasinormal modes (QNM) of the charged C-metric, which physically stands for a charged accelerating black hole, with the help of Nekrasov’s partition function of 4d $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in [1] can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov’s partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d $$ \mathcal{N} $$ N = 2 SCFTs, one can solve both the radial and the angular parts of the scalar perturbation equation respectively. The same algorithm can be applied to the de Sitter (dS) black holes to calculate both the dS modes and the photon-sphere modes.