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

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.