Superspin chains and supersymmetric gauge theories

In this note, we establish several interesting connections between the super- group gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras. In particular, we construct the super-characteristic polynomials of super-Toda lattice and elliptic double Calogero-Moser system by considering certain orbifolded instanton partition functions of their corresponding supergroup gauge theories. We also derive an exotic generalization of 𝔰𝔩(2) XXX spin chain arising from the instanton partition function of SQCD with super- gauge group, and study its Bethe ansatz equation.

Section: Jhep09(2020)104mentioning

confidence: 99%

Quantum integrable systems from supergroup gauge theories

Chen¹,

Kimura²,

Lee³

2020

“…We have thus obtained partition functions of 3d quiver theories corresponding to Dynkin diagrams of superalgebras. These theories should be 3d uplifts of 2d theories recently studied in [58] (see also earlier work [59]).…”

Section: Jhep08(2021)149mentioning

confidence: 87%

“…Indeed, the characteristic feature of the 2d theories considered in [58] is that they are obtained by gluing together two linear quiver gauge theories of A n−1 and A m−1 type, corresponding to two bosonic subalgebras of the superalgebra gl(n|m). Both parts are N = (4, 4) theories softly broken to N = (2, 2) by introducing the twisted mass for adjoint multiplets at each node of the quiver.…”

Section: Jhep08(2021)149mentioning

confidence: 99%

See 1 more Smart Citation

Higgsed network calculus

Zenkevich

2021

We introduce a formalism for describing holomorphic blocks of 3d quiver gauge theories using networks of Ding-Iohara-Miki algebra intertwiners. Our approach is very direct and gives an explicit identification of the blocks with Dotsenko-Fateev type integrals for q-deformed quiver W-algebras. We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.

“…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

Self Cite

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.