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

147

252

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar N = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N 3 LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.

Section: Jhep06(2014)116supporting

confidence: 53%

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory

Dixon

Drummond

Duhr

et al. 2014

147

252

“…For the six-point case studied in the present paper, ref. [72] has compared the two-loop and strong-coupling rescaled remainder functions along a curve which runs from (u, v, w) = (1/4, 1/4, 1/4) to (1, 0, 0), as well as analytically in the expansion around (1/4, 1/4, 1/4) using conformal perturbation theory, and the results are very similar. The curve runs from the ultraviolet to the infrared region of the renormalization group flow associated with an integrable two-dimensional system.…”

Section: Jhep12(2013)049mentioning

confidence: 97%

“…The six-point case we consider in this paper has also been studied at strong coupling using a Z 4 symmetric integrable model [71] and using the homogeneous sine-Gordon model and conformal perturbation theory [72]. In the latter work, the strong-coupling result was compared with the two-loop one along a onedimensional curve in the space of the three cross ratios, corresponding to the trajectory of an integrable renormalization group flow.…”

Section: Jhep12(2013)049mentioning

confidence: 99%

Hexagon functions and the three-loop remainder function

Dixon

Drummond

Hippel

et al. 2013

165

398

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar N = 4 superYang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multiRegge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The nearcollinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to −7.

“…Around the limit where the null boundary becomes regular polygonal, corresponding to the UV limit of the two-dimensional systems, the remainder functions are calculated analytically for lower point amplitudes [20][21][22]. There, the free-energy part is evaluated by the standard bulk conformal perturbation theory (CPT).…”

Section: Jhep08(2014)162mentioning

confidence: 99%

Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

Hatsuda¹,

Ito

Satoh

et al. 2014

Self Cite

Abstract:We study the six-point gluon scattering amplitudes in N = 4 super YangMills theory at strong coupling based on the twisted Z 4 -symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model.