Adjoint BFKL at finite coupling: a short-cut from the collinear limit

166

332

Abstract:We extend the hexagon function bootstrap to the next-to-maximally-helicityviolating (NMHV) configuration for six-point scattering in planar N = 4 super-Yang-Mills theory at three loops. Constraints from theQ differential equation, from the operator product expansion (OPE) for Wilson loops with operator insertions, and from multi-Regge factorization, lead to a unique answer for the three-loop ratio function. The three-loop result also predicts additional terms in the OPE expansion, as well as the behavior of NMHV amplitudes in the multi-Regge limit at one higher logarithmic accuracy (NNLL) than was used as input. Both predictions are in agreement with recent results from the flux-tube approach. We also study the multi-particle factorization of multi-loop amplitudes for the first time. We find that the function controlling this factorization is purely logarithmic through three loops. We show that a function U , which is closely related to the parity-even part of the ratio function V , is remarkably simple; only five of the nine possible final entries in its symbol are non-vanishing. We study the analytic and numerical behavior of both the parity-even and parity-odd parts of the ratio function on simple lines traversing the space of cross ratios (u, v, w), as well as on a few two-dimensional planes. Finally, we present an empirical formula for V in terms of elements of the coproduct of the six-gluon MHV remainder function R 6 at one higher loop, which works through three loops for V (four loops for R 6 ).

“…The NMHV and MHV impact factors are strikingly similar. Our results are completely consistent with the recent all-orders multi-Regge proposal [59].…”

Section: Jhep10(2014)065supporting

confidence: 93%

Section: Jhep10(2014)065mentioning

confidence: 99%

Section: Jhep10(2014)065mentioning

confidence: 99%

Section: Jhep10(2014)065mentioning

confidence: 99%

“…At the next loop order, the relation (4.34) begins to contain ψ functions, 2 We thank Benjamin Basso for discussions on these points prior to the appearance of ref. [59]. Figure 1.…”

Section: Jhep10(2014)065mentioning

confidence: 99%

See 3 more Smart Citations

Bootstrapping an NMHV amplitude through three loops

Dixon

Hippel²

2014

166

332

The four-loop six-gluon NMHV ratio function

Dixon

Hippel

McLeod

2016

142

222

Abstract:We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N = 4 super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of aQ differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leadinglogarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi-Regge predictions at NNLL and N 3 LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all crosschecks are satisfied. We study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. We also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

Regge meets collinear in strongly-coupled N = 4 $$ \mathcal{N}=4 $$ super Yang-Mills

Sprenger

2017

Abstract:We revisit the calculation of the six-gluon remainder function in planar N = 4 super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in [1], which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.