Exact WKB and the quantum Seiberg-Witten curve for 4d N = 2 pure SU(3) Yang-Mills. Abelianization

Yan, F.

doi:10.1007/jhep03(2022)164

Cited by 10 publications

(12 citation statements)

References 92 publications

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“…[11]), is an important tool in understanding the correspondences between 4d N = 2 gauge theories and quantum mechanical systems. In this paper and [16], we aim to generalize such analysis to higher rank theories, using 4d N = 2 pure SU (3) SYM as a concrete example.…”

Section: Different Methods To Compute Resummed Quantum Periodsmentioning

confidence: 99%

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Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization

Yan¹

2020

Preprint

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We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU (3) Yang-Mills, in the language of abelianization. The relevant differential equation is a third-order equation on CP 1 with two irregular singularities. Exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,C)-connections. In particular, in the weak coupling region we encounter coordinates of higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series; we perform numerical analysis supporting this conjecture.

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Section: Different Methods To Compute Resummed Quantum Periodsmentioning

confidence: 99%

“…In this paper we focus on the method described in §1.2.1, namely we compute Borel resummed quantum periods via abelianization. In the followup [16], we intend to investigate the TBA method described in §1.2.2 and the instanton calculus method described in §1.2.3.…”

Section: The Su (3) Equationmentioning

confidence: 99%

Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization

Yan¹

2020

Preprint

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“…[8][9][10][11][12][13][14][15]. Some recent papers which discuss quantum periods and their relation to four dimensional N = 2 theories are [7,[16][17][18][19][20][21][22][23][24][25][26][27][28]. 1 In the exact WKB terminology these quantities are also called Voros symbols.…”

Section: Quantum Periodsmentioning

confidence: 99%

“…Various comparisons of this sort have been made before in the literature; for example see [31] for comparisons between methods 1, 3, 4 in the pure SU (2) theory, and [18,30,32] for methods 2, 3 in Argyres-Douglas theories (note method 4 is not available in Argyres-Douglas theories at the moment, since it relies on the Lagrangian description of the theory). See also [22] for computations in the pure SU (3) theory using method 2 and comparisons to the WKB series.…”

Section: Computing the Quantum Periodsmentioning

confidence: 99%

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Exact WKB methods in $SU(2)$ $N_f=1$

Grassi,

Hao,

Neitzke

2021

Preprint

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We study in detail the Schrödinger equation corresponding to the four dimensional SU (2) 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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WKB analysis of the linear problem for modified affine Toda field equations

Ito,

Zhu

2023

J. High Energ. Phys.

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We study the WKB analysis of the solutions to the linear problem for a modified affine Toda field equation, which is equivalent to the higher-order ordinary differential equation (ODE) studied in the ODE/IM correspondence. After gauge transformation, we diagonalize the flat connection of the linear problem to reduce the latter to a set of independent first-order linear differential equations. We explicitly perform this procedure for classical affine Lie algebras with lower ranks. In particular, we study the WKB solutions of the $$ {D}_r^{(1)} $$ D r 1 - and $$ {D}_{r+1}^{(2)} $$ D r + 1 2 -type linear problems, which correspond to the higher-order ODEs with the pseudo-differential operator. The diagonalized connection is obtained from the Riccati equations of the adjoint linear problem and related to the conserved currents of the integrable hierarchy constructed by Drinfeld and Sokolov up to total derivatives.

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Exact WKB and the quantum Seiberg-Witten curve for 4d N = 2 pure SU(3) Yang-Mills. Abelianization

Cited by 10 publications

References 92 publications

Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization

Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization

Exact WKB methods in $SU(2)$ $N_f=1$

WKB analysis of the linear problem for modified affine Toda field equations

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