Abstract
AbstractWe study the null-polygonal minimal surfaces in AdS4, which correspond to the gluon scattering amplitudes/Wilson loops in$ \mathcal{N} $= 4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces withncusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n− 4)4/U(1)n−5generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbedWminimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit forn= 6 and 7. We compare the rescaled remainder function forn= 6 with the two-loop one, to observe that they are close to each other similarly to the AdS3case.
Highlights
The AdS/conformal field theory (CFT) correspondence shows that minimal surfaces in AdS space-time are dual to the Wilson loops along their boundary [1, 2], where the area corresponds to the expectation value of the Wilson loops at strong coupling
The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n − 4)4/U(1)n−5 generalized parafermion theory perturbed by the weight-zero adjoint operators
In this paper we have evaluated the regularized area of the null-polygonal minimal surfaces in AdS4, and the remainder function for the corresponding Wilson loops/amplitudes at strong coupling
Summary
The AdS/CFT correspondence shows that minimal surfaces in AdS space-time are dual to the Wilson loops along their boundary [1, 2], where the area corresponds to the expectation value of the Wilson loops at strong coupling. In this case, the corresponding TBA or Y-system is obtained by a projection from that for the minimal surfaces in AdS5 [14]. We argue that a similar correspondence to the perturbed nonunitary diagonal coset and W minimal models holds for the systems with a pair of equal mass parameters These generalize the reduction in the AdS3 case, and are used to find the precise expansion coefficients. We summarize a computation of a three-point function in a non-unitary W minimal model
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