Spectra of elliptic potentials and supersymmetric gauge theories

He, Wei

doi:10.1007/jhep08(2020)070

Cited by 4 publications

(5 citation statements)

References 53 publications

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“…It is not directly related to gauge theory regarding the Gauge/Bethe correspondence, but it is a special case of a more general elliptic potential that arises in the study of Gauge/Bethe correspondence. [33] The stationary points of the Lamé potential are also the stationary points of the potential u(z) = ∆k 2 sn 2 z + Ωk 4 sn 4 z. The monodromy along 2K (i.e.…”

Section: Ellipsoidal Wave Equationmentioning

confidence: 99%

“…In fact, the complete expansion of eigenvalues ( 28) and ( 34) can be related by a transformation, which is related to the monopole-dyon duality of N = 2 N f = 4 super QCD model. [33] The potential of ellipsoidal wave equation actually has more stationary points z * given by the solutions of 2Ωk 2 sn 2 z * +∆ = 0. Therefore it raises the question if they are associated to other still unknown asymptotic spectral solutions?…”

Section: Ii) the Second Small Energy Asymptotic Solutionmentioning

confidence: 99%

“…How-ever, the detail is more complicated and will be presented elsewhere. [33] Below we only explain a particular feature of the Darboux-Treibich-Verdier potential that makes the problem more complicated.…”

Section: Darboux-treibich-verdier Potentialmentioning

confidence: 99%

“…It needs more space to explain the details about the proper expansion for v(z) in this case, the results would be given in Ref. [33], along with some other related issues. There it would be more transparent that the choice of the integral contours in the Appendix B is unavoidable for elliptic potentials.…”

Section: Darboux-treibich-verdier Potentialmentioning

confidence: 99%

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A New Treatment for Some Periodic Schrödinger Operators I: The Eigenvalue

He¹

2018

Commun. Theor. Phys.

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We study the problem of how the Floquet property manifests for periodic Schrödinger operators which are known to have multiple of asymptotic spectral solutions. The main conclusions are made for elliptic potentials, we demonstrate that for each period of the elliptic function there is a relation about the Floquet exponent and the monodromy of wave function. Among them there are two relations not explained by the classical Floquet theory. These relations produce both old and new asymptotic solutions consistent with results already known. (2010): 35P20, 33E10, 34E10. Mathematics Subject Classification

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Section: Ellipsoidal Wave Equationmentioning

confidence: 99%

Section: Ii) the Second Small Energy Asymptotic Solutionmentioning

confidence: 99%

Section: Darboux-treibich-verdier Potentialmentioning

confidence: 99%

Section: Darboux-treibich-verdier Potentialmentioning

confidence: 99%

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A New Treatment for Some Periodic Schrödinger Operators I: The Eigenvalue

He¹

2018

Commun. Theor. Phys.

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“…In another direction, modular properties of (properly normalized) instanton partition functions under S-duality are studied in [218,219,224,225,573,996,997,[1109][1110][1111][1112][1113][1114][1115][1116][1117][1118][1119][1120] through matrix model and other techniques. Other works and reviews abound [301,629,639,[1121][1122][1123][1124][1125][1126][1127][1128][1129][1130][1131][1132][1133][1134], as well as PhD theses [1135][1136][1137].…”

Section: Discussionmentioning

confidence: 99%

A slow review of the AGT correspondence

Floch¹

2022

J. Phys. A: Math. Theor.

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Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School ‘YRISW 2020’ to appear in a special issue of J. Phys. A. Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD (quantum chromodynamics) to non-Lagrangian theories) obtained by twisted compactification of 6d N = ( 2 , 0 ) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg–Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of a 4d N = 2 S U ( 2 ) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres–Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson–’t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

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Properties of some elliptic Hill’s potentials

He,

2024

Anal.Math.Phys.

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Spectra of elliptic potentials and supersymmetric gauge theories

Cited by 4 publications

References 53 publications

A New Treatment for Some Periodic Schrödinger Operators I: The Eigenvalue

A New Treatment for Some Periodic Schrödinger Operators I: The Eigenvalue

A slow review of the AGT correspondence

Properties of some elliptic Hill’s potentials

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