Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension

TL;DR

This paper investigates the cusp anomalous dimension in ABJ(M) theory, revealing a solvable resummation approach via a Bethe-Salpeter equation and uncovering unexpected supersymmetry effects and structural insights, with implications for strong coupling behavior.

Contribution

It introduces a novel resummation method for ladder diagrams in ABJ(M) theory, leading to an exactly solvable Schrödinger problem and new understanding of cusp anomalous dimensions.

Findings

Identification of a scaling limit where ladder diagrams dominate

Exact solution via a supersymmetric Schrödinger problem

Discovery of two independent cusp anomalous dimensions

Abstract

We study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentiation structure for the related Wilson loops. While consistent with previous perturbative analysis, the strong coupling limit of our result does not agree with the string theory computation, emphasizing a difference with the analogous resummation in the N=4 case.