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Effective potential and warp factor dynamics

Michael R. Douglas

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.

Effective potential and warp factor dynamics

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.

Paper Structure

This paper contains 27 sections, 107 equations.

Table of Contents

  1. Introduction
  2. Questions addressed in this work
  3. Effective potential
  4. General discussion
  5. Einstein equations
  6. Incorporating the warp factor
  7. Effective potential
  8. Solving the constraint
  9. Interpreting the constraint
  10. Incorporating the dilaton and other fields
  11. Physical discussion
  12. Physical regimes
  13. Slowly varying warp factor
  14. The ground state approximation
  15. Basic picture
  16. ...and 12 more sections

Theorems & Definitions (1)

  • Conjecture 1