Duality Beyond Global Symmetries: the Fate of the B_{\mu\nu} Field

TL;DR

This paper explores the duality between axion and antisymmetric tensor fields after nonperturbative effects break the Peccei-Quinn symmetry, showing that duality persists and describing the resulting massive fields in string theory contexts.

Contribution

It demonstrates that duality between axion and antisymmetric tensor fields remains valid even after symmetry breaking and describes the emergence of massive dual fields in string theory.

Findings

Duality persists after gaugino condensation breaks PQ symmetry.

The axion acquires a mass, and the tensor field becomes a massive 3-form.

The results exemplify a general duality among massive antisymmetric tensor fields in D-dimensions.

Abstract

Duality between the `axion' field $a$ and the antisymmetric tensor field $B_{\mu\nu}$ is traced after a nonperturbative effect, gaugino condensation, breaks the Peccei-Quinn symmetry $a \rightarrow a +c$. Even though the PQ symmetry was at its origin, duality is nevertheless {\it not} broken by this effect. Below condensation scale, the axion simply gets a mass, but in the `stringy' version, the $ B_{\mu\nu}$ field disappears from the propagating spectrum. Its place is taken by a massive 3-index antisymmetric field $H_{\mu\nu\rho}$ which is the one dual to the massive axion. This is a particular case of a general duality in $D$-dimensions among {\it massive} $p$ and $D-p-1$-index antisymmetric tensor fields.