Aspects of four-point functions in N = 4 SYM at strong coupling

Abstract

In this thesis we focus on two main topics: the double-trace spectrum of strongly-coupled N = 4 SYM theory and the construction of one-loop four-point functions in AdS5×S 5 . We begin by providing a basic review of N = 4 SYM and its connection to holographic correlators on AdS5×S 5 through the AdS/CFT duality. In the second part, we examine the spectrum of double-trace operators at strong coupling, which are dual to two-particle bound states in AdS. At large N, these states are degenerate and to obtain their order 1/N2 anomalous dimensions one has to solve a mixing problem. We present a compact formula for all tree-level supergravity anomalous dimensions and we observe an interesting pattern of residual degeneracies. Considering further string corrections, we identify a ten-dimensional principle which dictates the structure of the string corrected spectrum. The third part is devoted to the construction of one-loop corrections to four-point correlation functions. We develop an algorithm for bootstrapping one-loop supergravity correlators for arbitrary Kaluza-Klein modes, which relies solely on implementing the consistency of the OPE to order 1/N4 . We illustrate the subtle features of this algorithm by constructing new explicit results for multi-channel correlators. Lastly, we consider one-loop string corrections to the <O_2O_2O_2O_2> correlator. We find that a transcendental weight three function involving a new type of singularity is required, whose presence is a novelty in the context of AdS amplitudes.

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ORCID for Hynek Paul: orcid.org/0000-0002-2202-7971

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