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Register a new userOn Genus-one String Amplitudes on $AdS_5 times S^5$
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Authors
Luis F. Alday
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We study non-planar correlators in ${cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.
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We study the four point function of the superconformal primary of the stress-tensor multiplet in four dimensional $mathcal{N}=4$ Super Yang Mills, at large t Hooft coupling and in a large $N$ expansion. This observable is holographically dual to four graviton amplitudes in type IIB supergravity on $AdS_5 times S^5$. We construct the most trascendental piece of the correlator at order $N^{-6}$ and compare it with the flat space limit of the corresponding two loops amplitude. This comparison allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.
We discuss some new simple closed bosonic string solutions in AdS_5 x S^5 that may be of interest in the context of AdS/CFT duality. In the first part of this work we consider solutions with two spins (S_1, S_2) in AdS_5. Starting from the flat-space solutions and using perturbation theory in the curvature of AdS_5 space, we construct leading terms in the small two-spin solution. We find corrections to the leading Regge term in the classical string energy and uncover a discontinuity in the spectrum for certain type of a solution. We then analyze the connection between small-spin and large-spin limits of string solutions in AdS_5. We show that the S_1 = S_2 solution in AdS_5 found in earlier papers admits both limits only in simplest cases of the folded and rigid circular strings. In the second part of the paper we construct a new class of chiral solutions in R_t x S^5 for which embedding coordinates of S^5 satisfy the linear Laplace equations. They generalize the previously studied rigid string solutions. We study in detail a simple nontrivial example.
In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $ eta $ deformed $ AdS_5 times S^{5} $ in the so called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both $(R times S^{3})_{eta} $ and $(R times S^{5})_{eta} $ models. The resulting system reveals that in the fast spinning limit, the sigma model on $ eta $ deformed $S^5$ could be $textit{approximately}$ thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed $S^5$ and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary $beta$ deformed background.
We revisit the computation of the 1-loop string correction to the latitude minimal surface in $AdS_5 times S^5$ representing 1/4 BPS Wilson loop in planar $cal N$=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the $AdS_2$ minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on $AdS_2$. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and $k$-wound circle.
We make an ansatz for the Mellin representation of the four-point amplitude of half-BPS operators of arbitrary charges at order $lambda^{-frac{5}{2}}$ in an expansion around the supergravity limit. Crossing symmetry and a set of constraints on the form of the spectrum uniquely fix the amplitude and double-trace anomalous dimensions at this order. The results exhibit a number of natural patterns which suggest that the bootstrap approach outlined here will extend to higher orders in a simple way.
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