A-D-ESingularity and the Seiberg-Witten Theory

Ito, Katsushi

doi:10.1143/ptps.135.94

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…These singular points are called the superconformal points. For A r type SW curve (1), they are given by [28] u 2 = · · · = u r = 0, u r+1 = ±Λ r+1 .…”

Section: Quantum Sw Curve Of a R -Type Ad Theoriesmentioning

confidence: 99%

“…In this section, we study the quantum SW curve for N = 2 super Yang-Mills theory with A r -type gauge group and its scaling limit around the superconformal point [19,21]. The SW curve for A r type gauge group is defined by [25,26,27,28]…”

Section: Introductionmentioning

confidence: 99%

“…We can express the above equations by linear combination of ∂ ũi p0 by using the Picard-Fuchs equations satisfied by p0 [28].…”

Section: Introductionmentioning

confidence: 99%

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

2019

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We study the quantum Seiberg-Witten (SW) curves for (A 1 , G)-type Argyres-Douglas (AD) theory by taking the scaling limit of the quantum SW curve of N = 2 gauge theory with gauge group G. For G = A r , the quantum SW curve of the AD theory is consistent with the scaling limit of the curve of the gauge theory. For G = D r , we need the quantum correction to the SW curve of the AD theory, which depends on the quantization condition of the original SW curve. We also study the universality of the quantum SW curves for (A 1 , A 3 ) and (A 1 , D 4 )-type AD theories.

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“…These singular points are called the superconformal points. For A r type SW curve (1), they are given by [28] u 2 = · · · = u r = 0, u r+1 = ±Λ r+1 .…”

Section: Quantum Sw Curve Of a R -Type Ad Theoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2019

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“…The SW curve for the gauge group G of a Lie algebra g is obtained as the spectral curve of the periodic Toda lattice associated with the dual of its affine Lie algebra ĝ∨ and a representation R of g [30]. After the degeneration of the curve, the SW curve becomes (see [31] for a review)…”

Section: Quantum Sw Curve For the Argyres-douglas Theorymentioning

confidence: 99%

ODE/IM correspondence and the Argyres-Douglas theory

Ito

Shu

2017

J. High Energ. Phys.

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We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral curve. We show that the models for the A 2N -type theories are non-unitary coset models (A 1 ) 1 × (A 1 ) L /(A 1 ) L+1 at the fractional level L = 2 2N +1 −2, which appear in the study of the 4d/2d correspondence of N = 2 superconformal field theories. Based on the WKB analysis, we clarify the relation between the Y-functions and the quantum periods and study the exact Bohr-Sommerfeld quantization condition for the quantum periods. We also discuss the quantum spectral curves for the D and E type theories.

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“…Such spectral curves are time independent since they describe the spectrum of L, and they play an essential role in solving the dynamical system. Roughly speaking, the family of Riemann surfaces C g necessary for the SeibergWitten data is given by the spectral curve (24) for the periodic Toda chain, whose Lax pair is defined in terms of the affine Lie algebra g (1) with the parameter z playing the role of the loop variable. Due to a physical requirement however, we should not consider the affine algebra g (1) but its dual (g (1) ) ∨ which is obtained by replacing roots with coroots.…”

Section: The Seiberg-witten Family Of Riemann Surfacesmentioning

confidence: 99%