Integrated four-point correlators in N=4 super Yang-Mills

Abstract: We will study the correlation function of four superconformal primaries in N=4 super Yang-Mills (SYM) with SU(N) gauge group. Recently, very powerful methods have been developed to compute this correlator at finite coupling based on a new concept of integrated correlators, which are defined by integrating the correlator over spacetime coordinates with suitable integration measures. The integrated correlators can be computed using supersymmetric localisation. We will mostly focus on one of the integrated correlators. An exact expression was found for this integrated correlator for arbitrary values of coupling and N. The integrated correlator can be expressed as a two-dimensional lattice sum, which manifests the SL(2, Z) modular invariance of N=4 SYM. Furthermore, the result obeys an elegant Laplace-difference equation that relates the correlator of SU(N) theory with those of SU(N-1) and SU(N+1) theories. In perturbation, the formula is checked to be consistent with known results from more standard methods. Finally, one can reconstruct the unintegrated correlator with finite coupling for first few orders in large-N expansion, the results are shown to agree with known type IIB superstring amplitudes due to AdS/CFT duality. This talk will be mainly based on arxiv.org/abs/2102.09537 (a short version can be found at arxiv.org/abs/2102.08305).

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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