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.
Highlights
The PST (Pasti-Sorokin-Tonin) approach [1, 2] provides a manifestly Lorentz invariant Lagrangian description of the self-dual gauge fields as well as of more general dualityinvariant theories
We study the Lagrangian description of chiral bosons, p-form gauge fields withself-dual gauge field strengths, in D = 2p + 2 dimensional spacetime of nontrivial topology
In section 3.3. we show that in the da-timelike branch of the PST system, as well as in its gauge fixed version described by HT action, the semi-local symmetry is a gauge symmetry, while in the da-spacelike branch of the PST system and in its gauge fixed version described by the PS action, this is an infinite dimensional rigid symmetry
Summary
The PST (Pasti-Sorokin-Tonin) approach [1, 2] provides a manifestly Lorentz invariant Lagrangian description of the self-dual gauge fields as well as of more general dualityinvariant theories. The main aim of the present paper is to show that this is not the case: the PST approach is pretty consistent and is able to produce the wanted (anti–)self-duality equations in the case of topologically nontrivial spacetime To see this one has to notice the presence of an unusual type of symmetry parametrized by function(s) of the PST scalar, f (a(t, x)), which we call “semi-local symmetry”.1. We show that in the da-timelike branch of the PST system, as well as in its gauge fixed version described by HT action, the semi-local symmetry is a gauge symmetry, while in the da-spacelike branch of the PST system and in its gauge fixed version described by the PS action, this is an infinite dimensional rigid symmetry (similar to 2d conformal symmetry) This allows us to derive (in section 3.4.) the anti-self-duality equations as gauge fixed version of the Lagrangian equations of motion which follows from the da-timelike PST action and HT action. PS is used for Perry-Schwarz action (2.26) [7]. FJ is used for Floreanini-Jackiw action [20] which can be found in eq (4.13)
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