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Register a new userTwo-loop world-sheet corrections in AdS_5 x S^5 superstring
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We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the kappa-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalans constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.
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The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.
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 investigate the structure of the quantum S-matrix for perturbative excitations of the Pohlmeyer reduced version of the AdS_5 x S^5 superstring following arXiv:0912.2958. The reduced theory is a fermionic extension of a gauged WZW model with an integrable potential. We use as an input the result of the one-loop perturbative scattering amplitude computation and an analogy with simpler reduced AdS_n x S^n theories with n=2,3. The n=2 theory is equivalent to the N=2 2-d supersymmetric sine-Gordon model for which the exact quantum S-matrix is known. In the n=3 case the one-loop perturbative S-matrix, improved by a contribution of a local counterterm, satisfies the group factorization property and the Yang-Baxter equation, and reveals the existence of a novel quantum-deformed 2-d supersymmetry which is not manifest in the action. The one-loop perturbative S-matrix of the reduced AdS_5 x S^5 theory has the group factorisation property but does not satisfy the Yang-Baxter equation suggesting some subtlety with the realisation of quantum integrability. As a possible resolution, we propose that the S-matrix of this theory may be identified with the quantum-deformed [psu(2|2)]^2 x R^2 symmetric R-matrix constructed in arXiv:1002.1097. We conjecture the exact all-order form of this S-matrix and discuss its possible relation to the perturbative S-matrix defined by the path integral. As in the AdS_3 x S^3 case the symmetry of the S-matrix may be interpreted as an extended quantum-deformed 2-d supersymmetry.
We compute the one-loop world-sheet correction to partition function of $AdS_5 times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
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.
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