Tachyon Condensates, Carrollian Contraction of Lorentz Group, and Fundamental Strings

TL;DR

This paper explores how tachyon condensates and gauge fields influence the effective metric and causal structure in string theory, revealing a connection to fundamental strings through a Carrollian contraction of the Lorentz group.

Contribution

It demonstrates how gauge fields modify the effective metric in tachyon condensates, leading to a Carrollian limit and propagating degrees of freedom along electric flux lines, suggesting a link to fundamental strings.

Findings

In the absence of gauge fields, the lightcone collapses, indicating no signal propagation.

Presence of gauge fields squeezes the lightcone into a fan shape, allowing signal propagation along electric flux.

The causal structure change is a general feature of tachyon effective Lagrangians with runaway potentials.

Abstract

We study the rolling tachyon condensate in the presence of a gauge field. The generic vacuum admits both a rolling tachyon, \dot{T}, and a uniform electric field, \vec{E}, which together affect the effective metric governing the fluctuations of open string modes. If one suppresses the gauge field altogether, the light-cone collapses completely. This is the Carrollian limit, with vanishing speed of light and no possible propagation of signals. In the presence of a gauge field, however, the lightcone is squeezed to the shape of a fan, allowing propagation of signals along the direction of \pm \vec{E} at speed |E|=<1. This shows that there are perturbative degrees of freedom propagating along electric flux lines. Such causal behavior appears to be a very general feature of tachyon effective Lagrangian with runway potentials. We speculate on how this may be connected to appearance of fundamental strings.