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Article Dans Une Revue Journal of High Energy Physics Année : 2023

Integrated Correlators in $\mathcal{N}=4$ SYM via $SL(2,\mathbb{Z})$ Spectral Theory

Résumé

We perform a systematic study of integrated four-point functions of half-BPS operators in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(N)$. These observables, defined by a certain spacetime integral of $\langle\mathcal{O}_2\mathcal{O}_2\mathcal{O}_p\mathcal{O}_p\rangle$ where $\mathcal{O}_p$ is a superconformal primary of charge $p$, are known to be computable by supersymmetric localization, yet are non-trivial functions of the complexified gauge coupling $\tau$. We find explicit and remarkably simple results for several classes of these observables, exactly as a function of $N$ and $\tau$. Their physical and formal properties are greatly illuminated upon employing the $SL(2,\mathbb{Z})$ spectral decomposition: in this S-duality-invariant eigenbasis, the integrated correlators are fixed simply by polynomials in the spectral parameter. These polynomials are determined recursively by linear algebraic equations relating different $N$ and $p$, such that all integrated correlators are ultimately fixed in terms of the integrated stress tensor multiplets in the $SU(2)$ theory. Our computations include the full matrix of integrated correlators at low values of $p$, and a certain infinite class involving operators of arbitrary $p$. The latter satisfy an open lattice chain equation for all $N$, reminiscent of the Toda equation obeyed by extremal correlators in $\mathcal{N}=2$ superconformal theories. We compute ensemble averages of these observables and analyze our solutions at large $N$, confirming and predicting features of semiclassical AdS$_5\, \times$ S$^5$ supergravity amplitudes.

Dates et versions

hal-03791499 , version 1 (29-09-2022)

Identifiants

Citer

Hynek Paul, Eric Perlmutter, Himanshu Raj. Integrated Correlators in $\mathcal{N}=4$ SYM via $SL(2,\mathbb{Z})$ Spectral Theory. Journal of High Energy Physics, 2023, 01, pp.149. ⟨10.1007/JHEP01(2023)149⟩. ⟨hal-03791499⟩
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