Quantum integrable systems from supergroup gauge theories

Chen, Heng‐Yu; Kimura, Taro; Lee, Norton

doi:10.1007/jhep09(2020)104

Cited by 14 publications

(13 citation statements)

References 50 publications

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“…This is equivalent to modifying the real moment map to 2) such that k + instantons are generated by I(N) and k − instantons are generated by J † (N). This situation is similar to the instanton partition function of the supergroup gauge theory [83,84]. Such a modification breaks the U(k) symmetry of the real moment map down to U(k + ) × U(k − ).…”

Section: Jhep03(2021)093supporting

confidence: 52%

Quantum spin systems and supersymmetric gauge theories. Part I

Lee

Nekrasov

2021

J. High Energ. Phys.

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The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the N site $$ \mathfrak{sl} $$ sl 2X X X spin chain (for infinite dimensional complex spin representations), as well as the SLN Gaudin system, which reduces, in a limiting case, to that of the N-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.

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Section: Jhep03(2021)093supporting

confidence: 52%

Quantum spin systems and supersymmetric gauge theories. Part I

Lee

Nekrasov

2021

J. High Energ. Phys.

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“…state computes the (time-extended) instanton partition function of a β-deformation of the 5d N = 1 U(N|M) supergroup gauge theory, with the exact supergroup structure emerging only at the unrefined point β = 1 (p = 1), where the magnitude squared of the coupling constants is the same and the signs are opposite. This is the type of deformation considered in [114] in the context of many-body integrable systems associated to supergroups, and further elaborated in [16] from the viewpoint of the gauge/Bethe correspondence and Seiberg-Witten integrable systems. Our analysis can be generalized to include matter (e.g.…”

Section: 21)mentioning

confidence: 99%

Intersecting defects and supergroup gauge theory

Kimura

Nieri²

2021

J. Phys. A: Math. Theor.

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We consider 5d supersymmetric gauge theories with unitary groups in the Ωbackground and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin along a circle. The intersecting defects arise upon implementing the most generic Higgsing (geometric transition) to the parent higher dimensional theory, and they are described by pairs of 3d supersymmetric gauge theories with unitary groups interacting through 1d matter at the intersection. We explore the relations between instanton and generalized vortex calculus, pointing out a duality between intersecting defects subject to the Ω-background and a deformation of supergroup gauge theories, the exact supergroup point being achieved in the self-dual or unrefined limit. Embedding our setup into refined topological strings and in the simplest case when the parent 5d theory is Abelian, we are able to identify the supergroup theory dual to the intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side of the correspondence, finding an interesting large rank duality with super-instanton counting.

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“…Finally, it was shown in [42] that the classical XXX sl 2 spin chain arises in the Seiberg-Witten geometry of the four-dimensional N = 2 theory [21,59], as well as a relation between the XXX sl 2 spin chain coordinate systems and the defect gauge theory parameters, with more general sl 2 -representations which are neither highest-weight nor lowest-weight. The extension to the supergroup gauge theories is also discussed in [65][66][67].…”

Section: Jhep10(2021)120 7 XXX Sl 2 Spin Chainmentioning

confidence: 99%

Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

Jeong

Lee

Nekrasov

2021

J. High Energ. Phys.

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We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the $$ {\hat{\mathfrak{sl}}}_N $$ sl ̂ N current algebra with one of the vertex operators corresponding to the N-dimensional $$ {\mathfrak{sl}}_N $$ sl N representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the $$ {XXX}_{{\mathfrak{sl}}_2} $$ XXX sl 2 spin chain of N Heisenberg-Weyl modules over Y ($$ {\mathfrak{sl}}_2 $$ sl 2 ). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

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Quantum integrable systems from supergroup gauge theories

Cited by 14 publications

References 50 publications

Quantum spin systems and supersymmetric gauge theories. Part I

Quantum spin systems and supersymmetric gauge theories. Part I

Intersecting defects and supergroup gauge theory

Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

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