Consistent Truncation to Three Dimensional (Super-)gravity

TL;DR

This paper presents an algorithm for consistent truncation of general 3D (super-)gravity theories with matter and higher derivatives to simpler pure gravity theories, preserving key physical features.

Contribution

It introduces a systematic method for truncating complex 3D (super-)gravity theories to pure gravity models, including parameter determination, with an explicit example.

Findings

Successfully truncates 5D supergravity with curvature squared terms to a pure gravity theory.

The truncated theory reproduces the exact boundary CFT central charge.

Provides a general algorithm applicable to various 3D (super-)gravity models.

Abstract

For a general three dimensional theory of (super-)gravity coupled to arbitrary matter fields with arbitrary set of higher derivative terms in the effective action, we give an algorithm for consistently truncating the theory to a theory of pure (super-)gravity with the gravitational sector containing only Einstein-Hilbert, cosmological constant and Chern-Simons terms. We also outline the procedure for finding the parameters of the truncated theory. As an example we consider dimensional reduction on S^2 of the 5-dimensional minimal supergravity with curvature squared terms and obtain the truncated theory without any curvature squared terms. This truncated theory reproduces correctly the exact central charge of the boundary CFT.