Deformations of quantum field theories and integrable models

TL;DR

This paper explores a general framework for deforming quantum field theories that maintain key symmetries, providing explicit examples and applications to construct integrable models, especially in two dimensions.

Contribution

It introduces a broad class of deformation techniques for quantum field theories, extending existing methods like warped convolution, applicable across all space-time dimensions.

Findings

Constructed explicit deformation examples on the Borchers-Uhlmann algebra.

Deformations can produce integrable models with non-trivial S-matrix in 2D.

Deformations are independent of space-time dimension.

Abstract

Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an infinite class of explicit examples is constructed on the Borchers-Uhlmann algebra underlying Wightman quantum field theory. These deformations exist independently of the space-time dimension, and contain the recently studied warped convolution deformation as a special case. In the special case of two-dimensional Minkowski space, they can be used to deform free field theories to integrable models with non-trivial S-matrix.