On the ABJM four-point amplitude at three loops and BDS exponentiation

The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d N = 4 super YangMills theory and the ABJM theory. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions, which may provide useful insight into the worldvolume theory of M5-branes (if it enjoys such a symmetry). We find that 6d dual conformal symmetry uniquely fixes the integrand of the one-loop 4-point amplitude, and its structure suggests a Lagrangian with more than two derivatives. On integrating out the loop momentum in 6 − 2 dimensions, the result is very similar to the corresponding amplitude of N = 4 super Yang-Mills theory. We confirm this result holographically by generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space to a minimal volume M2-brane ending on a pillow-shaped surface in the boundary whose seams correspond to a null-polygon. This involves careful treatment of a prefactor which diverges as 1/ , and we comment on its possible interpretation. We also study 2-loop 4-point integrands with 6d dual conformal symmetry and speculate on the existence of an all-loop formula for the 4-point amplitude.

Section: Introductionmentioning

confidence: 53%

6d dual conformal symmetry and minimal volumes in AdS

Bhattacharya

Lipstein

2016

“…Throughout the computation dimensional regularization in the DRED scheme is assumed [47] (see also [48] and [24,34,36,49,50] for applications in perturbation theory in Chern-Simons models).…”

Section: Perturbative Results For the Latitude Wilson Loopmentioning

confidence: 99%

A matrix model for the latitude Wilson loop in ABJM theory

Bianchi

Mauri

Penati

et al. 2018

Self Cite

113

In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in U(N 1 |N 2 ) Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the fermionic Wilson loop the leading planar behavior agrees with a previous string theory prediction. For the bosonic operator our result provides a clue for finding the corresponding string dual configuration. Our matrix model is consistent with recent proposals for computing Bremsstrahlung functions exactly in terms of latitude Wilson loops. As a by-product, we extend the conjecture for the exact B θ 1/6 Bremsstrahlung function to generic representations and test it with a four-loop perturbative computation. Finally, we propose an exact prediction for B 1/2 at unequal gauge group ranks.

“…We expect to find scattering matrices that are unitary precisely because they transform under crossing symmetry in the unusual manner conjectured in [36]. It would be particularly interesting to find explicit results for the N = 6 theory in order to facilitate a detailed comparison with the perturbative computations of S matrices in ABJM theory [14][15][16][17][18][19][20], which appear to report results that are crossing symmetric but (at least naively) conflict with unitarity.…”

Section: Sectormentioning

confidence: 90%

“…While this quantity has been somewhat studied for highly supersymmetric Chern-Simons theories, the results currently available (see e.g. [14][15][16][17][18][19][20]) have all be obtained in perturbation theory. Methods based on supersymmetry have not yet proved powerful enough to obtain results for S matrices at all orders in the coupling constant, even for the maximally supersymmetric ABJ theory.…”

mentioning

confidence: 99%

Unitarity, crossing symmetry and duality in the scattering of N = 1 $$ \mathcal{N}=1 $$ susy matter Chern-Simons theories

Inbasekar

Jain

Mazumdar

et al. 2015

186

We study the most general renormalizable N = 1 U(N ) Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large N limit we present computations and conjectures for the 2 × 2 S matrix in these theories; our results apply at all orders in the 't Hooft coupling and the matter self interaction. Our S matrices are in perfect agreement with the recently conjectured strong weak coupling self duality of this class of theories. The consistency of our results with unitarity requires a modification of the usual rules of crossing symmetry in precisely the manner anticipated in arXiv:1404.6373, lending substantial support to the conjectures of that paper. In a certain range of coupling constants our S matrices have a pole whose mass vanishes on a self dual codimension one surface in the space of couplings.