Liouville and Toda Solitons in M-theory

TL;DR

This paper reformulates equations for various branes in superstring and M-theory as Liouville and Toda equations, providing general solutions that include non-extremal cases with finite scalar fields at the horizon.

Contribution

It demonstrates that isotropic p-brane equations can be expressed as integrable Liouville and Toda systems, extending known extremal solutions to non-extremal cases.

Findings

General solutions for non-extremal p-branes derived

Scalar fields remain finite at the horizon in non-extremal solutions

Equations reduce to known extremal solutions in specific limits

Abstract

We study the general form of the equations for isotropic single-scalar, multi-scalar and dyonic $p$-branes in superstring theory and M-theory, and show that they can be cast into the form of Liouville, Toda (or Toda-like) equations. The general solutions describe non-extremal isotropic $p$-branes, reducing to the previously-known extremal solutions in limiting cases. In the non-extremal case, the dilatonic scalar fields are finite at the outer event horizon.