Abstract
We study the stress tensor four-point function for mathcal{N} = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.
Highlights
Holographic correlators are correlation functions in a CFTd that are dual to scattering of particles in string theory or M-theory on AdSd+1 times some compact manifold
We study the stress tensor four-point function for N = 4 SYM with gauge group G = SU(N ), SO(2N + 1), SO(2N ) or USp(2N ) at large N
We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit
Summary
Holographic correlators are correlation functions in a CFTd that are dual to scattering of particles in string theory or M-theory on AdSd+1 times some compact manifold. As in the previously studied SU(N ) case, we will fix the protected R4 tree level corrections using the localization constraint derived in [17], which related an integral of the correlator to derivatives ∂τ ∂τ∂m2 F (m)|m=0 of the mass deformed N = 2∗ free energy This latter quantity was computed using localization in terms of a Rank(G) dimensional matrix model integral [33], which we computed to any order in large N and finite λ ∼ gY2 MN following the SU(N ) case considered in [15]. If we write these quantities in terms of τs, from the AdS/CFT dictionary τs = 2τ for USp(2N ) and τs = τ for the other gauge groups, we find that results in all cases are modular invariant in terms of τs This had to be the case in the flat space limit where the type IIB S-matrix is modular. We discuss how the 10d flat space type IIB string theory S-matrix can be used to constrain the SYM correlator by taking the flat space limit
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