Three-form multiplet and Inflation

TL;DR

The paper proposes that the stabilizer field in large-field supergravity inflation is naturally a three-form multiplet, with the inflaton shift symmetry and three-form gauge invariance uniquely fixing the inflaton–stabilizer coupling through a boundary-term structure. It demonstrates both non-supersymmetric and supersymmetric dual formulations where a massive three-form carries the inflaton and stabilizer degrees of freedom, yielding a scalar potential of the form $V(\varphi)=\frac{1}{2}(\mu\varphi - f_0)^2$ (up to model-dependent terms) and preserving a discrete remnant of the shift symmetry via flux quantization $f_0=n e^2$. The work extends to supergravity, where the three-form multiplet can be embedded with a consistent mass term and boundary contributions, and explores two inflationary realizations: chaotic inflation and the Starobinsky model, both admitting a three-form origin and a clear dual description. Finally, it discusses embeddings in string theory, where inflaton dynamics arise from Wilson lines and RR-form couplings to branes, providing UV completions with axion-monodromy-like features and flux-induced mass scales, while noting that full moduli stabilization and SUSY breaking remain important future challenges.

Abstract

Most successful models of inflation in supergravity have a shift symmetry for the inflaton and contain a stabilizer field coupled to the inflaton in a particular way. We argue that the natural interpretation of the stabilizer, from the viewpoint of the shift symmetry, is a three-form multiplet. Its coupling to the inflaton is uniquely determined by the shift symmetry and the invariance under three-form gauge transformations and has a natural string theory interpretation.