On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology

TL;DR

This paper investigates the Lagrangian formulation of self-dual gauge fields in spacetimes with nontrivial topology, demonstrating the consistency of the PST approach and analyzing topological effects on different formulations.

Contribution

It extends the PST Lagrangian framework to nontrivial topologies, showing its consistency and exploring topological influences on gauge field formulations.

Findings

PST approach remains consistent in nontrivial topologies.

Topological features affect the equivalence of different gauge formulations.

The study clarifies conditions distinguishing 'da-timelike' and 'da-spacelike' branches.

Abstract

We study the Lagrangian description of chiral bosons, p-form gauge fields with (anti-)self-dual gauge field strengths, in D=2p+2 dimensional spacetime of nontrivial topology. We show that the manifestly Lorentz and diffeomorphism invariant Pasti-Sorokin-Tonin (PST) approach is consistent and produces the (anti-)self-duality equation also in topologically nontrivial spacetime. We discuss in what circumstances the nontrivial topology makes difference between two disconnected, `da-timelike' and `da-spacelike' branches of the PST system, the gauge fixed version of which are described by not manifestly invariant Henneaux-Teitelboim (HT) and Perry-Schwarz (PS) actions, respectively.