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Register a new userThe Bethe Roots of Regge Cuts in Strongly Coupled N=4 SYM Theory
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We describe a general algorithm for the computation of the remainder function for n-gluon scattering in multi-Regge kinematics for strongly coupled planar N=4 super Yang-Mills theory. This regime is accessible through the infrared physics of an auxiliary quantum integrable system describing strings in AdS5xS5. Explicit formulas are presented for n=6 and n=7 external gluons. Our results are consistent with expectations from perturbative gauge theory. This paper comprises the technical details for the results announced in arXiv:1405.3658 .
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A novel way of computing high-order amplitudes in the multi-Regge limit of planar maximally supersymmetric Yang-Mills theory is presented. In this framework, we are able to obtain high-loop and high-leg results by an easy operation on known amplitudes with fewer loops and lower multiplicity. This mechanism will be reviewed, along with an ensuing factorisation which allows us to determine leading logarithmic MHV results for any number of legs at a fixed loop order.
Very recently in arXiv:0705.0303 Alday and Maldacena gave a string theory prescription for computing (all) planar amplitudes in N=4 supersymmetric gauge theory at strong coupling using the AdS/CFT correspondence. These amplitudes are determined by a classical string solution and contain a universal exponential factor involving the action of the classical string. On the gauge theory side, expressions for perturbative amplitudes at strong coupling were previously proposed only for specific helicities of external particles -- the maximally helicity violating or MHV amplitudes. These follow from the exponential ansatz of Bern, Dixon and Smirnov for MHV amplitudes in N=4 SYM. In this paper we examine the amplitudes dependence on helicities and particle-types of external states. We consider the prefactor of string amplitudes and give arguments suggesting that the prefactor at strong coupling should be the same as the Yang-Mills tree-level amplitude for the same process. This implies that scattering amplitudes in N=4 SYM simplify dramatically in the strong coupling limit. It follows from our proposal that in this limit all (MHV and non-MHV) n-point amplitudes are given by the (known) tree-level Yang-Mills result times the helicity-independent (and particle-type-independent) universal exponential.
It was recently shown that the string theory duals of certain deformations of the N=4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting the dual integrable spin chain and its Bethe ansatz. We derive the Bethe equations for the complete twisted N=4 gauge theory at one and higher loops. These have a natural generalization which we identify as twists involving the Cartan generators of the conformal algebra. The underlying model appears to be a form of noncommutative deformation of N=4 SYM.
We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.
We use AdS/CFT duality to compute in N=4 Yang-Mills theory the finite temperature spatial correlator G(r) of the scalar operator F^2, integrated over imaginary time. The computation is carried out both at zero frequency and integrating the spectral function over frequencies. The result is compared with a perturbative computation in finite T SU(N_c) Yang-Mills theory.
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