Regge trajectories for the (2,0) theories

TL;DR

This paper explores the structure and constraints of conformal Regge trajectories in six-dimensional (2,0) superconformal theories, revealing new interactions, bounds, and a bootstrap approach for four-point functions.

Contribution

It uncovers how super-descendant trajectories interact and introduces an iterative bootstrap scheme using the Lorentzian inversion formula for these theories.

Findings

Super-descendant trajectories interact, imposing new shape constraints.

Supersymmetry softens Regge behavior, enabling analyticity in spin for spins > -3.

Numerical experiments show OPE data aligns with bootstrap results for higher-rank theories.

Abstract

We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2,0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that 'analyticity in spin' holds for all spins greater than -3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.