Compactifying the Sen Action: Six Dimensions

TL;DR

This paper explores Kaluza-Klein compactifications of the generalized Sen action with two metrics, addressing challenges of dual towers of fields and showing consistent truncations without doubling degrees of freedom.

Contribution

It demonstrates how to achieve consistent truncations in the doubled field scenario and discusses a natural deformation of the Sen action during compactification.

Findings

Zero-modes from both towers are necessary for consistent truncation.

On-shell, the doubling of degrees of freedom is not realized.

A natural deformation of the Sen action includes an additional form-field without increasing on-shell degrees of freedom.

Abstract

The Sen action for self-dual fields has been generalised by Hull to include two metrics which allows it to be defined on generic manifolds. In this paper we consider Kaluza-Klein compactifications of this action. The existence of two metrics presents novel challenges as there are two Kaluza-Klein towers of fields. We show that to find a consistent truncation one must include zero-modes associated to each of the two towers. Although this naively leads to a doubling of the massless degrees of freedom we show that on-shell this is not the case. We also discuss a deformation of the Sen action to include an additional form-field but which does not lead to new degrees of freedom on-shell but which arises naturally upon compactification.