The Effective Action in Gauged Supergravity on Hyperbolic Background and Induced Cosmological Constant

TL;DR

This paper computes the one-loop effective action in 4D gauged supergravity with negative cosmological constant on hyperbolic backgrounds, deriving explicit curvature expansions and calculating induced cosmological and Newton constants.

Contribution

It provides a detailed expansion of the effective action and explicit calculations of induced constants using heat-kernel and zeta-regularization methods.

Findings

Explicit curvature expansion of the effective action.

Computed induced cosmological constant.

Calculated induced Newton constant.

Abstract

The one-loop effective action for 4-dimensional gauged supergravity with negative cosmological constant, is investigated in space-times with compact hyperbolic spatial section. The explicit expansion of the effective action as a power series of the curvature on hyperbolic background is derived, making use of heat-kernel and zeta-regularization techniques. The induced cosmological and Newton constants are computed.