Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

165

392

We bootstrap loop corrections to AdS 5 supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of N = 4 super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading O(1/N 4 ) corrections to certain double-trace anomalous dimensions.

Section: Completion To a Crossing Symmetric Amplitudementioning

confidence: 99%

Quantum gravity from conformal field theory

Aprile

Drummond

Heslop

et al. 2018

165

392

“…, Z 6 ), the rows correspond to their components, and the limit amounts to √ u 2 u 3 τ → 0. In the Euclidean region, loop corrections to the BDS-normalized amplitude vanish in the multi-Regge limit [40], due to its conformal equivalence to a soft limit [24,106]. Nontrivial behavior in the limit is obtained by analytically continuing into physical 2 → 4 Minkowski kinematics.…”

Section: Multi-regge Kinematicsmentioning

confidence: 99%

“…This observation significantly simplifies the computation of the dispersion integrals (3.17), since the holomorphic part comes only from the residues satisfying iν = −n/2 [109,110] (see also ref. [106]).…”

Section: Multi-regge Kinematicsmentioning

confidence: 99%

Six-Gluon amplitudes in planar $$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops

Caron-Huot

Dixon

Dulat

et al. 2019

Self Cite

169

225

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

“…This makes it hard to rule out the possibility that any given pair of cluster coordinates appears together in a cluster, as no closed-form expression for this infinite set of cluster coordinates (or the clusters into which they combine) is known in these cases. Even so, this complication can in some cases be circumvented, for instance by identifying finite subalgebras of Gr(4, n > 7) [10,23] (as can be done, for instance, in the multi-Regge limit [24]). Here we instead utilize the Sklyanin Poisson bracket [25,26], which can be computed for any pair of cluster coordinates.…”

Section: Introductionmentioning

confidence: 99%

The Sklyanin bracket and cluster adjacency at all multiplicity

Golden

McLeod²,

Spradlin

et al. 2019

We argue that the Sklyanin Poisson bracket on Gr(4, n) can be used to efficiently test whether an amplitude in planar N = 4 supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one-and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities. 1 We in particular thank M. Gekhtman for correspondence and discussions on this topic.