Dynamical Dimension Change in Supercritical String Theory

TL;DR

This paper investigates how closed string tachyon condensation causes a dynamic change in spacetime dimensions within heterotic string theory, revealing a compensatory mechanism in the dilaton gradient that maintains critical central charge.

Contribution

It introduces a large-n limit analysis of dimension change due to tachyon condensation, showing the dilaton gradient adjustment preserves worldsheet criticality.

Findings

The change in dilaton gradient magnitude compensates for the change in spacelike central charge.

The total worldsheet central charge remains constant during the dimension change.

The results support a CFT interpretation of the dynamical dimension reduction.

Abstract

We study tree-level solutions to heterotic string theory in which the number of spacetime dimensions 10+n changes dynamically due to closed string tachyon condensation. Taking the large-n limit, we compute the amount by which the dilaton gradient changes during the condensation process. At leading order in n we find that the change in the invariant magnitude of the dilaton gradient compensates the change in spacelike central charge on the worldsheet, so that the total worldsheet central charges are equal at early and late times. This result supports our interpretation of the worldsheet theory as a CFT of critical central charge which describes a dynamical reduction in the total number of spacetime dimensions.