Finite factorization equations and sum rules for BPS correlators in N=4 SYM theory

• Published in: Nuclear physics. B Vol. 641; no. 1; pp. 131 - 187
• Main Authors: Corley, Steve, Ramgoolam, Sanjaye
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 07.10.2002
• Subjects: 11.25.Hf; 12.60.Jv; 11.15.-g
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/S0550-3213(02)00573-4

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=∞, 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× S background. We comment on an intriguing symmetry between KK modes and giant gravitons.