Supergravity in Twelve Dimension

TL;DR

This paper develops a twelve-dimensional supergravity framework that unifies eleven-dimensional, IIA, and IIB supergravities, providing insights into F-theory, T-duality, and the structure of higher-dimensional field theories.

Contribution

It introduces a twelve-dimensional supergravity model that encompasses various lower-dimensional theories and clarifies their interrelations through compactification and duality mechanisms.

Findings

Unifies eleven-dimensional, IIA, and IIB supergravities in 12D framework.

Provides a field-theoretic description of F-theory.

Reinterprets T-duality as different compactification routes.

Abstract

We consider supergravity in twelve dimension, whose dimensional reduction yields eleven-dimensional, IIA, and IIB supergravities. This also provides the effective field theory of F-theory. We must take one direction as a compact circle, so that the Poincar\'e symmetry and the zero-mode field contents are identical to those of eleven-dimensional supergravity. We also have a tower of massive Kaluza-Klein states to be viewed as the wrapping modes of M2-branes. The twelfth dimension decompactifies only if other two directions are compactified on a torus, restoring different ten dimensional Poincar\'e symmetry of IIB supergravity, whose missing graviton is provided by components of the rank three tensor field. This condition prevents us from violating the condition on the maximal number of real supercharges, which should be thirty-two. The self-duality condition of the IIB four-form fields is understood from twelve-dimensional Hodge duality. In this framework T-duality is re-interpreted as taking different compactification routes.