TY - JOUR

T1 - Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

AU - Jeong, Saebyeok

AU - Lee, Norton

AU - Nekrasov, Nikita

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/10

Y1 - 2021/10

N2 - We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional 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 sl̂ N current algebra with one of the vertex operators corresponding to the N-dimensional slN representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the XXXsl2 spin chain of N Heisenberg-Weyl modules over Y (sl2). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

AB - We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional 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 sl̂ N current algebra with one of the vertex operators corresponding to the N-dimensional slN representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the XXXsl2 spin chain of N Heisenberg-Weyl modules over Y (sl2). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

KW - Integrable Hierarchies

KW - Nonperturbative Effects

KW - Supersymmetric Gauge Theory

KW - Supersymmetry and Duality

UR - http://www.scopus.com/inward/record.url?scp=85117515894&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2021)120

DO - 10.1007/JHEP10(2021)120

M3 - Article

AN - SCOPUS:85117515894

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 120

ER -