Quantum Seiberg-Witten curve and universality in Argyres-Douglas theories

Ito, Katsushi; Koizumi, Saki; Okubo, Takafumi

doi:10.1016/j.physletb.2019.03.024

Cited by 16 publications

(23 citation statements)

References 44 publications

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“…This is then identified via (2.14) with the partition function of the (A 1 , D 4 ) theory, i.e., [15]. 23 Since the expression obtained in [15] is for the case Q = 0, we will focus on the Q → 0 limit of (3.24) in the rest of this sub-section. Note that Q = 0 corresponds to ǫ 1 + ǫ 2 = 0 in four dimensions.…”

Section: Irregular Conformal Blockmentioning

confidence: 99%

“…This partition function was reproduced in [26] as the irregular conformal block with an irregular singular point of rank 3 2 and a regular singular point. On the other hand, from the class S construction of the (A 1 , A 3 ) theory, the same partition function is expected to be obtained as the one-point function of an irregular vertex 2 Another important progress in the study of the partition functions of AD theories has been made through the E-string theory on T 2 [21] and quantum periods in the Nekrasov-Shatashvili limit [22,23]. 3 See also [27] for closely related results related to asymptotically free gauge theories.…”

Section: Introductionmentioning

confidence: 98%

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Argyres-Douglas theories and Liouville irregular states

Nishinaka

Uetoko

2019

J. High Energ. Phys.

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We study irregular states of rank-two and three in Liouville theory, based on an ansatz proposed by D. Gaiotto and J. Teschner. Using these irregular states, we evaluate asymptotic expansions of irregular conformal blocks corresponding to the partition functions of (A 1 , A 3 ) and (A 1 , D 4 ) Argyres-Douglas theories for general Ω-background parameters. In the limit of vanishing Liouville charge, our result reproduces strong coupling expansions of the partition functions recently obtained via the Painlevé/gauge correspondence. This suggests that the irregular conformal block for one irregular singularity of rank 3 on sphere is also related to Painlevé II. We also find that our partition functions are invariant under the action of the Weyl group of flavor symmetries once four and two-dimensional parameters are correctly identified. We finally propose a generalization of this parameter identification to general irregular states of integer rank.

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Section: Irregular Conformal Blockmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Argyres-Douglas theories and Liouville irregular states

Nishinaka

Uetoko

2019

J. High Energ. Phys.

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“…super Yang-Mills theory [32] whose SW curve is obtained from the SU(2N) with massless N f = 4 hypermultiplets [42]. Now we focus on the type B scaling of N f = 2n theory.…”

Section: Quantum Sw Periods and The Scaling Limitmentioning

confidence: 99%

“…We can also check the scaling limit of p 4 reduces to that of the AD theory with the same Q 2 (ξ). The existence of corrections to the potential depends on the flavor symmetry which are kept manifestly in the quantum SW curve [32].…”

Section: Quantum Sw Periods and The Scaling Limitmentioning

confidence: 99%

“…(See also [27,28,29,30] for its relation to CFT. )In the previous papers [31,32], we have studied the quantum SW curves for the AD theories associated with N = 2 SU(2) SQCD, the (A 1 , A r )-type and (A 1 , D r )-type AD theories. We have calculated the quantum corrections to the SW periods up to the fourth order in the deformation parameter and confirmed that they are consistent with the scaling limit of the quantum periods of the UV theories.…”

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confidence: 99%

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Quantum Seiberg-Witten periods for N=2 SU(N) SQCD around the superconformal point

Ito¹,

Koizumi²,

Okubo³

2020

Nuclear Physics B

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We study the quantum Seiberg-Witten periods of N = 2 superconformal field theories which are obtained by taking the scaling limit of N = 2 SU (N c ) SQCD around the superconformal fixed point. The quantum Seiberg-Witten curves of these superconformal field theories are shown to be classified into the Schrödinger type and the SQCD type, which depend on flavor symmetry at the fixed point. We study the quantum periods and compute the differential operators which relate the quantum periods to the classical ones up to the fourth-order in the deformation parameter. IntroductionThe low-energy description of N = 2 supersymmetric gauge theories has singularities in the strong coupling region [1,2]. In particular, there appears an IR fixed point at a locus of the Coulomb branch, where mutually non-local BPS particles become massless [3,4,5].The dynamics around the fixed point is described by an interacting N = 2 superconformal field theory called the Argyres-Douglas (AD) theory.One can study the BPS spectrum of the AD theory from the Seiberg-Witten (SW) curve, which is obtained by degeneration of the SW curve of the UV gauge theory. It is also realized from the compactification of the six-dimensional N = (2, 0) superconformal field theory on a punctured Riemann surface [6,7,8] and classified in [9,10,11,12].One can also study the SW theories in the Nekrasov-Shatashvili (NS) limit of the Omega-background [13]. The Omega background deforms four dimensional spacetime by the two-dimensional torus action [14]. The NS limit is defined by the limit where one of the deformation parameters goes to zero. In this limit, the deformed theory is reformulated by the quantum SW curve [15], which is a differential equation obtained by the quantization of the symplectic structure based on the SW differential. The deformation parameter plays a role of the Planck constant.The WKB analysis of the quantum SW curve determines the deformed SW periods [16,17,18]. In the weak coupling region, the quantum corrections to the SW periods agree with those obtained from the NS limit of the Nekrasov partition function [15,19,20,21].In the strong coupling region such as the massless monopole/dyon point, the quantum SW periods for the SU(2) SQCD with N f ≤ 4 have been studied in [22,23,24]. The relation to the topological strings have been studied in [25,26]. (See also [27,28,29,30] for its relation to CFT.)In the previous papers [31,32], we have studied the quantum SW curves for the AD theories associated with N = 2 SU(2) SQCD, the (A 1 , A r )-type and (A 1 , D r )-type AD theories. We have calculated the quantum corrections to the SW periods up to the fourth order in the deformation parameter and confirmed that they are consistent with the scaling limit of the quantum periods of the UV theories. Recently the exact WKB periods for the quantum SW curve of (A 1 , A r )-type AD theory are shown to be determined by the

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Exact WKB methods in SU(2) Nf = 1

Grassi

Hao

Neitzke

2022

J. High Energ. Phys.

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We study in detail the Schrödinger equation corresponding to the four dimensional SU(2) $$ \mathcal{N} $$ N = 2 SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schrödinger operator using the TS/ST correspondence and Zamolodchikov’s TBA, again finding good agreement. In addition, we explore two aspects of the relationship between singularities of the Borel transformed WKB series and BPS states: BPS states of the 4d theory are related to singularities in the Borel transformed WKB series for the quantum periods, and BPS states of a coupled 2d+4d system are related to singularities in the Borel transformed WKB series for local solutions of the Schrödinger equation.

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Quantum Seiberg-Witten curve and universality in Argyres-Douglas theories

Cited by 16 publications

References 44 publications

Argyres-Douglas theories and Liouville irregular states

Argyres-Douglas theories and Liouville irregular states

Quantum Seiberg-Witten periods for N=2 SU(N) SQCD around the superconformal point

Exact WKB methods in SU(2) Nf = 1

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