Twelve-dimensional Effective Action and T-duality

TL;DR

This paper introduces a twelve-dimensional supergravity framework for F-theory, clarifying T-duality through dimensional reduction and addressing self-duality in IIB supergravity.

Contribution

It proposes a novel twelve-dimensional supergravity action that unifies various supergravity theories and makes T-duality explicit.

Findings

Dimensional reduction yields 11D, IIA, and IIB supergravities.

Self-duality of the IIB four-form is naturally understood.

T-duality is realized as a relation between different compactifications.

Abstract

We propose a twelve-dimensional supergravity action, which describes low energy dynamics of F-theory. Dimensional reduction leads the theory to eleven-dimensional, IIA, and IIB supergravities. Self-duality of the four-form field in IIB supergravity is understood. It is necessary to abandon twelve-dimensional Poincare symmetry by making one dimension compact, which is to be decompactified in some region of parameter space, such that the physical degrees of freedom are the same as those of eleven-dimensional supergravity. This makes T-duality explicit as a relation between different compactification schemes.