Minimal models of field theories: SDYM and SDGR

TL;DR

This paper constructs minimal models of self-dual Yang-Mills and gravity theories using $L_$-algebras, revealing their equations of motion as Free Differential Algebras and connecting $Q$-cohomology to physical properties.

Contribution

It explicitly derives minimal models for SDYM and SDGR, providing a new algebraic framework that encodes their dynamics and physical features.

Findings

Minimal models are constructed for SDYM and SDGR.

Equations of motion are represented as Free Differential Algebras.

Physical quantities like actions and anomalies are related to $Q$-cohomology.

Abstract

There exists a natural $L_\infty$-algebra or $Q$-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the $L_\infty$-algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding $Q$-cohomology.