Gauge Fields, Scalars, Warped Geometry, and Strings

TL;DR

This paper reviews phenomena in warped M theory compactifications, focusing on gauge fields, scalar fields, domain wall solutions, and brane excitations, highlighting new insights into holography, geometry, and string dynamics.

Contribution

It provides a comprehensive overview of gauge behavior, scalar field roles, and brane excitations in warped geometries, with new analysis on domain wall solutions without fine-tuning.

Findings

Gauge fields exhibit specific behaviors under dimensional reduction.

Scalar fields enable stable domain wall solutions without fine-tuning.

Wrapped brane excitations grow in effective thickness with energy.

Abstract

We review results on several interesting phenomena in warped compactifications of M theory, as presented at Strings 2000. The behavior of gauge fields in dimensional reduction from $d+1$ to $d$ dimensions in various backgrounds is explained from the point of view of the holographic duals (and a point raised in the question session at the conference is addressed). We summarize the role of additional fields (in particular scalar fields) in 5d warped geometries in making it possible for Poincare-invariant domain wall solutions to exist to a nontrivial order in a controlled approximation scheme without fine-tuning of parameters in the $5d$ action (and comment on the status of the singularities arising in the general relativistic description of these solutions). Finally, we discuss briefly the emergence of excitations of wrapped branes in warped geometries whose effective thickness, as measured along the Poincare slices in the geometry, grows as the energy increases.