Type II Actions from 11-Dimensional Chern-Simons Theories

TL;DR

This paper develops a holographic approach to formulating Ramond-Ramond fields in type II supergravity using 11-dimensional Chern-Simons theories, revealing new topological restrictions on consistent backgrounds.

Contribution

It introduces a novel formulation of RR partition functions via 11D Chern-Simons theory and establishes a new topological restriction involving the Wu class for type IIA supergravity.

Findings

RR partition function expressed as an 11D Chern-Simons wavefunction

Formulation of an action principle for RR fields with RR current

Identification of a topological restriction involving the Wu class

Abstract

This paper continues the discussion of hep-th/0605038, applying the holographic formulation of self-dual theory to the Ramond-Ramond fields of type II supergravity. We formulate the RR partition function, in the presence of nontrivial H-fields, in terms of the wavefunction of an 11-dimensional Chern-Simons theory. Using the methods of hep-th/0605038 we show how to formulate an action principle for the RR fields of both type IIA and type IIB supergravity, in the presence of RR current. We find a new topological restriction on consistent backgrounds of type IIA supergravity, namely the fourth Wu class must have a lift to the H-twisted cohomology.