QFT with Stubs

TL;DR

This paper introduces a non-local deformation of the BV-action in quantum field theory by adding stubs, which regularizes the BV-Laplacian and simplifies anomaly calculations, demonstrated through quantum electrodynamics.

Contribution

It presents a novel non-local deformation method inspired by string theory that regularizes the BV-Laplacian and maintains classical BV-invariance.

Findings

The deformed action satisfies the quantum master equation with standard regularization.

Anomalies are reduced to standard calculations.

The deformed action can be obtained via a canonical transformation.

Abstract

The BV-Laplacian $\Delta$ in quantum field theory is singular, by construction, but can be regularized by deforming the classical BV-action. Taking inspiration from string theory we describe a non-local deformation of the latter by adding stubs to the interaction vertices while keeping classical BV-invariance manifest. This is achieved using a version of homotopy transfer resulting in a non-polynomial action for which the quantum master equation is now well defined and will be satisfied by adding additional vertices at loop level. The latter can be defined with the help of standard regularization schemes and is independent of the definition of $\Delta$. In particular, the determination of anomalies reduces to the standard text-book calculation. Finally, we describe how the deformed (quantum) action can be obtained as a canonical transformation. As an example, we illustrate this procedure for quantum electrodynamics.