Quantum periods for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> SU(2) SQCD around the superconformal point

Ito, Katsushi; Okubo, Takafumi

doi:10.1016/j.nuclphysb.2018.07.007

Cited by 15 publications

(14 citation statements)

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“…With the conjectured relation (4.7), we find that the partition functions Z ǫ 1 ,ǫ 2 (A 1 ,A 3 ) and Z ǫ 1 ,ǫ 2 (A 1 ,D 4 ) are invariant under (ǫ 1 , ǫ 2 ) → (−ǫ 1 , −ǫ 2 ) with masses and the vev of Coulomb branch operators fixed. This invariance is consistent with quantum periods of Argyres-Douglas theories recently evaluated in [22,23,73]. The quantum periods are a I ≡ A I λ and a D I ≡ B I λ deformed by the Ω-background (ǫ 1 , ǫ 2 ) = ( , 0), where A I and B I are canonical 1-cycles of the Seiberg-Witten curve, and λ is the Ω-deformed Seiberg-Witten 1-form.…”

Section: Conclusion and Discussionsupporting

confidence: 85%

“…a D = ∂F /∂a. As shown in [22,23], the -expansion of these quantum periods for (A 1 , A r ) and (A 1 , D r ) theories have only even powers of . 34 This means that, at least in the limit of ǫ 2 → 0, the quantity ǫ 1 ǫ 2 log Z ǫ 1 ,ǫ 2 is invariant under (ǫ 1 , ǫ 2 ) → (−ǫ 1 , −ǫ 2 ).…”

Section: Conclusion and Discussionmentioning

confidence: 84%

“…In[22], the (A 1 , A 3 ) and (A 1 , D 4 ) theories are realized at the most singular point on the Coulomb branch of SU(2) gauge theory with two and three flavors, respectively. Its generalization to the whole (A 1 , A r ) and (A 1 , D r ) theories was carefully studied in[23].…”

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confidence: 99%

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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: Conclusion and Discussionsupporting

confidence: 85%

Section: Conclusion and Discussionmentioning

confidence: 84%

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Argyres-Douglas theories and Liouville irregular states

Nishinaka

Uetoko

2019

J. High Energ. Phys.

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“…• It would be interesting to study the Nekrasov-Shatashvili limit [37] of the Ω-deformed (A 3 , A 3 ) theory. In this limit, combining the results of [38][39][40][41] with our formula, one can evaluate the deformed prepotential of the (A 3 , A 3 ) theory including both the perturbative and instanton parts.…”

Section: Jhep04(2021)205mentioning

confidence: 99%

Argyres-Douglas theories, S-duality and AGT correspondence

Kimura

Nishinaka

Sugawara

et al. 2021

J. High Energ. Phys.

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We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional $$ \mathcal{N} $$ N = 2 U(2) gauge theories coupled to (A1, D2n) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A1, D2n) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A3, A3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A3, A3) theory.

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“…(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%

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

Cited by 15 publications

References 54 publications

Argyres-Douglas theories and Liouville irregular states

Argyres-Douglas theories and Liouville irregular states

Argyres-Douglas theories, S-duality and AGT correspondence

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

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