Abstract
In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models.
Highlights
A number of remarkable connections have been observed between gauge theories and integrable systems
In this paper we focus on an important object in this class, the so-called instanton partition function and its relation with quantum integrable systems
We present the integral representation of the instanton partition function for pure SU(N) N = 2 super-Yang-Mills and the corresponding thermodynamic Bethe ansatz (TBA) equation
Summary
A number of remarkable connections have been observed between gauge theories and integrable systems. Nekrasov and Shatashvili [19] proposed that upon taking the limit 2 → 0 and interpreting 1 as Plank constant, one obtains a correspondence between supersymmetric vacua of a given gauge theory and eigenstates of the corresponding quantum integrable model. There is an elegant way to prove that this equality holds to all orders in the instanton counting parameter q It is based on rewriting the grand canonical partition function of the non-ideal gas in terms of a (0 + 1)-dimensional path integral. A slight modification of the argument in [52], together with the calculation of the contribution from the short range interactions corresponding to the dilogarithm, shows that the instanton partition function in the 2 → 0 limit is obtained by the saddle point evaluation of the path integral. For this reason on it will be denoted by Z
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
