Quantum integrability of N=2 $$ \mathcal{N}=2 $$ 4d gauge theories

Journal of High Energy Physics

Jean-Emile Bourgine¹  Davide Fioravanti² 

[1] Korea Institute for Advanced Study (KIAS), Quantum Universe Center (QUC);Sezione INFN di Bologna, Dipartimento di Fisica e Astronomia, Università di Bologna;

关键词: Bethe Ansatz;    Integrable Field Theories;    Lattice Integrable Models;    Supersymmetric Gauge Theory;   

DOI  :  10.1007/JHEP08(2018)125

来源: DOAJ

【 摘 要 】

Abstract We provide a description of the quantum integrable structure behind the Thermodynamic Bethe Ansatz (TBA)-like equation derived by Nekrasov and Shatashvili (NS) for N=2 $$ \mathcal{N}=2 $$ 4d Super Yang-Mills (SYM) theories. In this regime of the background, — we shall show —, the instanton partition function is characterised by the solution of a TQ-equation. Exploiting a symmetry of the contour integrals expressing the partition function, we derive a ‘dual’ TQ-equation, sharing the same T-polynomial with the former. This fact allows us to evaluate to 1 the quantum Wronskian of two dual solutions (for Q) and, then, to reproduce the NS TBA-like equation. The latter acquires interestingly the deep meaning of a known object in integrability theory, as its two second determinations give the usual non-linear integral equations (nlies) derived from the ‘dual’ Bethe Ansatz equations.

【 授权许可】

Unknown