Galileons as Wess-Zumino Terms

TL;DR

This paper demonstrates that galileons can be understood as Wess-Zumino terms arising from the spontaneous breaking of space-time symmetries, connecting them to Lie algebra cohomology and extending their theoretical framework.

Contribution

It introduces galileon algebras and constructs the relevant co-cycles, revealing the topological origin of galileons and related theories within the cohomological structure.

Findings

Galileons are linked to non-trivial Lie algebra cohomology classes.

The presence of galileons in all dimensions is counted by specific cohomology groups.

Most DBI and conformal galileons are not Wess-Zumino terms, except for one case each.

Abstract

We show that the galileons can be thought of as Wess-Zumino terms for the spontaneous breaking of space-time symmetries. Wess-Zumino terms are terms which are not captured by the coset construction for phenomenological Lagrangians with broken symmetries. Rather they are, in d space-time dimensions, d-form potentials for (d+1)-forms which are non-trivial co-cycles in Lie algebra cohomology of the full symmetry group relative to the unbroken symmetry group. We introduce the galileon algebras and construct the non-trivial (d+1)-form co-cycles, showing that the presence of galileons and multi-galileons in all dimensions is counted by the dimensions of particular Lie algebra cohomology groups. We also discuss the DBI and conformal galileons from this point of view, showing that they are not Wess-Zumino terms, with one exception in each case.