Dynamical content of Chern-Simons Supergravity

TL;DR

This paper explores the dynamical structure of five-dimensional AdS supergravity with a focus on its field content, gauge symmetries, and degrees of freedom, revealing differences between bosonic and fermionic components.

Contribution

It provides a detailed analysis of the field content and degrees of freedom in five-dimensional AdS supergravity, especially for N=4, highlighting the structure of the superalgebra and the effective theory.

Findings

Maximal rank of the symplectic matrix in N=4 case

Identification of dynamical degrees of freedom

Differences in bosonic and fermionic degrees of freedom

Abstract

The dynamical content of local AdS supergravity in five dimensions is discussed. The bosonic sector of the theory contains the vielbein ($e^{a}$), the spin connection ($\omega ^{ab}$) and internal SU(N) and U(1) gauge fields. The fermionic fields are complex Dirac spinors ($\psi ^{i}$) in a vector representation of SU(N). All fields together form a connection 1-form in the superalgebra SU(2,2|N). For N=4, the symplectic matrix has maximal rank in a locally AdS background in which the dynamical degrees of freedom can be identified. The resulting efective theory have different numbers of bosonic and fermionic degrees of freedom.