An exact integrated correlator in $N=4$ SU(N) SYM

Abstract: Between all the magical properties of $\mathcal{N} = 4$ SU(N) super Yang-Mills perhaps one of the most important is Montonen-Olive electric-magnetic $SL(2,Z)$ duality.In particular this leads to the constraint that observables must be invariant under inversion of the complex YM coupling $\tau$, i.e. under $\tau \to -1 / \tau$. In this talk we will focus on one such physical quantity, namely an integrated correlator of four super-conformal primaries of the stress-tensor multiplet. I will firstly review how this correlator can be computed via supersymmetric localisation on $S^4$, and then discuss how this quantity can be rewritten in a manifestly $SL(2,Z)$ invariant way for any number of colours N, and any value of the complex YM coupling \tau. Thanks to this novel expression we can explore various different regimes: perturbative SYM, large-N supergravity approximation, large-N 't Hooft expansion. All of these regimes are connected via a remarkable Laplace-difference equation relating the SU(N) to the SU(N + 1) and SU(N − 1) correlators.

HEP - theory

Audience: researchers in the topic

( paper )

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Rencontres Théoriciennes

Series comments: Description: Bi-weekly meeting of string theorists in greater Paris

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