The O(N) Monolith reloaded: Sum rules and Form Factor Bootstrap

TL;DR

This paper enhances the S-matrix bootstrap approach for 2D gapped O(N) symmetric quantum field theories by incorporating form factors and spectral functions, revealing new bounds on UV conformal data and the nature of boundary theories.

Contribution

It extends the bootstrap framework to include form factors and spectral functions, providing new insights into the UV behavior and bounds of O(N) symmetric theories.

Findings

Boundaries mostly flow from CFTs with infinite central charges

Sum rules constrain UV conformal data

Physical amplitude behavior explains boundary structure

Abstract

We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model appear at special points on the boundary, along with an abundance of unknown models hinting at a non conventional UV behaviour. We extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for the stress-energy tensor and conserved O(N) currents. Sum rules allow us to put bounds on the central charges of the conformal field theory (CFT) in the UV. We find that a big portion of the boundary can only flow from CFTs with infinite central charges. We track this result down to a particular behaviour of the amplitudes in physical kinematics and discuss its physical implications.