g-functions and gluon scattering amplitudes at strong coupling

Abstract

We study gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS 3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T-and Yfunctions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the relation between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T-and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.for the Y-functions from the g-functions and determine the analytic form of the remainder function near the CFT point.In this paper, we study the remainder function for 2ñ-point gluon scattering amplitudes at strong coupling, which correspond to minimal surfaces in AdS 3 with a 2ñ-gonal light-like boundary. This corresponds to the case where the gluon momenta are in R 1,1 . In [9] the related integrable system was shown to be the homogeneous sine-Gordon model (HSG) [17] with purely imaginary resonance parameters. The relevant CFT is the generalized parafermions SU(ñ − 2) 2 /U(1)ñ −2 [18]. In this paper we will study the boundary and bulk perturbation of the generalized parafermions and calculate the ratios of the g-functions. For the octagon (ñ = 4) and the decagon (ñ = 5), we will calculate the perturbative corrections to the T-/Y-functions, the free energy and the remainder function explicitly. We compare these analytic expressions of the remainder function with the 2-loop formulas proposed in [19][20][21] around the CFT limit.The above analytic results are important to understand the structure and the momentum dependence of the amplitudes at strong coupling exactly. The purpose of this paper is to take a step toward this direction by analyzing the TBA system near the CFT point from the conformal perturbation theory (CPT). A point in our discussion is that not only the free energy but also the Y-functions can be discussed in this framework owing to the relation between the T-/Y-functions and the g-functions.This paper is organized as follows. In section 2, we review the TBA system for the minimal surfaces in AdS 3 . In section 3, we discuss the HSG model and the free energy for the integrable bulk perturbations. In section 4, we study the HSG model from the CPT of the generalized parafermions and the relation between the Tfunctions and the g-functions. In section 5, we investigate the small mass expansions of the g-function and the remainder function for the octagon. In section 6, we argue the corrections to the free energy, the T-/Y-fu...

Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

“…point remainder functions in [26], and that of the general 2ñ-point remainder function in [27]. We observed that the appropriately rescaled remainder functions are close to those evaluated at two loops [29][30][31].…”

“…Before discussing the perturbation with single mass scale for the AdS 4 minimal surfaces, let us first recall those for the AdS 3 case [26,27]. The minimal surfaces embedded in AdS 3 with 2ñ cusps are described by the TBA system of the SU(ñ − 2) 2 /U(1)ñ −3 HSG model, which is obtained as the perturbed SU(ñ − 2) 2 /U(1)ñ −3 generalized parafermion model by the weight-zero su(ñ − 2) adjoint operators with dimension ∆ =∆ = (ñ − 2)/ñ.…”

“…In particular, when r = 1, this perturbed diagonal coset model becomes equivalent to the nonunitary minimal model Mñ −2,ñ perturbed by φ (1,3) . For the 10-point remainder function, the results from these unitary and non-unitary minimal models and their continuation to complex masses are enough to completely determine the leading-order analytic expansion around the UV limit [26].…”

“…This was used to determine the UV expansion of the remainder function for the 10-cusp minimal surfaces [26]. In the next section, we use the relation for the AdS 4 case with n = N + 4 = 7, 25) to determine the UV expansion for the 7-cusp minimal surfaces.…”

“…We have carried out the above program for the minimal surfaces embedded in AdS 3 [26,27]. In this case, the relevant CFT is the SU(ñ − 2) 2 /U(1)ñ −3 generalized parafermion theory [28] and, by turning off some mass parameters so as to leave only one mass scale (single-mass case), the TBA system is reduced to simpler ones for the perturbed SU(2) diagonal coset and minimal models.…”