Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory

TL;DR

This paper explores exact non-renormalized correlators in N=4 SYM, revealing finite factorization equations and sum rules that connect gauge theory correlators with topological and Chern-Simons theories, highlighting semiclassical dual objects.

Contribution

It introduces finite factorization equations and sum rules for BPS correlators in N=4 SYM, extending their applicability and linking them to topological gauge theories and dual semiclassical objects.

Findings

Finite factorization equations hold for extremal correlators.

Sum rules relate correlators to Verlinde formula limits.

Connections established between gauge theory correlators and topological models.

Abstract

A class of exact non-renormalized extremal correlators of half-BPS operators in N=4 SYM, with U(N) gauge group, is shown to satisfy finite factorization equations reminiscent of topological gauge theories. The finite factorization equations can be generalized, beyond the extremal case, to a class of correlators involving observables with a simple pattern of SO(6) charges. The simple group theoretic form of the correlators allows equalities between ratios of correlators in N=4 SYM and Wilson loops in Chern-Simons theories at k=\infty, correlators of appropriate observables in topological G/G models and Wilson loops in two-dimensional Yang-Mills theories. The correlators also obey sum rules which can be generalized to off-extremal correlators. The simplest sum rules can be viewed as large k limits of the Verlinde formula using the Chern-Simons correspondence. For special classes of correlators, the saturation of the factorization equations by a small subset of the operators in the large N theory is related to the emergence of semiclassical objects like KK modes and giant gravitons in the dual ADS \times S background. We comment on an intriguing symmetry between KK modes and giant gravitons.