Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories

TL;DR

This paper derives exact behaviors of Wilson loops in N=2 superconformal quiver gauge theories using localization and saddle-point methods, revealing non-exponential growth and holographic duals involving non-critical string theories.

Contribution

It provides the first exact analysis of Wilson loops in N=2 superconformal theories, showing their asymptotic behaviors and holographic interpretations, including non-critical string duals.

Findings

Wilson loop in SU(N) with 2N hypermultiplets grows at most polynomially with 't Hooft coupling.

Wilson loop in untwisted sector of SU(N) x SU(N) theory grows exponentially, similar to N=4 SYM.

Wilson loop in twisted sector exhibits non-analytic behavior and interpolates between different regimes.

Abstract

Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in N=4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loop in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both type theories holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicate that holographic dual of these gauge theories is provided by certain non-critical string theories.