Schreiber
infinity-Chern-Simons functionals

Contents

This page is where Chris Rogers and myself are developing a text on \infty-Chern-Simons theory

Contents

Abstract

Familiar notions from Chern-Weil theory for Lie algebras, such as invariant polynomials, have natural generalizations to L L_\infty-algebras and more generally to \infty-Lie algebroids. One aspect of the resulting \infty-Chern-Weil theory is a notion of \infty-Chern-Simons elements for every invariant polynomial on an \infty-Lie algebroid: the elements in the Weil algebra that witness the transgression to a cocycle. We discuss how these elements induce action functionals on spaces of \infty-Lie algebroid-valued connections that generalize the standard Chern-Simons theory action functional. Examples include higher Chern-Simons theories, supergravity theories, also BF-theory coupled to topological Yang-Mills theory as well as all action functionals of AKSZ-theory type induced from symplectic \infty-Lie algebroids, such as that of the Poissson σ\sigma-model for the topological string, and the Courant σ\sigma-model for the topological membrane.

Survey

for the moment see ∞-Chern-Weil theory introduction

\infty-Lie algebroids

for the moment see ∞-Lie algebroid

\infty-Chern-Simons elements

for the moment see Chern-Simons element

\infty-Chern-Simons action functionals

see for the moment connection on an ∞-bundle.

∞-Chern-Simons theory

Last revised on September 29, 2010 at 08:48:50. See the history of this page for a list of all contributions to it.