# Effective potential and warp factor dynamics

## TL;DR

This paper introduces an off-shell effective potential for supergravity compactifications that includes warp factor dynamics, resolving issues with unboundedness and providing a more complete understanding of the system.

## Contribution

It defines a novel off-shell effective potential incorporating warp factor dynamics, addressing the unboundedness problem in supergravity compactifications.

## Key findings

- The effective potential is unbounded below when neglecting the warp factor.
- Solving the warp factor constraint yields a physically consistent and tractable description.
- The approach improves understanding of massless and massive mode dynamics in string/M theory compactifications.

## Abstract

We define an effective potential describing all massless and massive modes in the supergravity limit of string/M theory compactification which is valid off-shell, i.e. without imposing the equations of motion. If we neglect the warp factor, it is unbounded below, as is the case for the action in Euclidean quantum gravity. By study of the constraint which determines the warp factor, we solve this problem, obtaining a physically satisfying and tractable description of the dynamics of the warp factor.