Electromagnetic Strings: Complementarity between Time and Temperature

TL;DR

This paper explores the interplay between time and temperature in string theory under electromagnetic fields, revealing a phase where time reemerges at high temperature and short distances, with implications for noncommutative gauge theories.

Contribution

It introduces a novel analysis of gauge-string windings near the Hagedorn temperature, showing a phase transition with spontaneous symmetry breaking and time-temperature complementarity.

Findings

Time becomes small at the EM-string scale.

Hagedorn temperature induces gauge-string condensation.

Noncommutative U(1) symmetry spontaneously breaks.

Abstract

We investigate some of the intricate features in a gravity decoupling limit of a open bosonic string theory, in a constant electromagnetic (EM-) field. We explain the subtle nature of space-time at short distances, due to its entanglement with the gauge field windings in the theory. Incorporating the mass-shell condition in the theory, we show that the time coordinate is small, of the order of EM-string scale, and the space coordinates are large. We perform a careful analysis in the critical regime to describe the decoupling of a series of gauge-string windings in successions, just below the Hagedorn temperature. We argue for the condensation of gauge-string at the Hagedorn temperature, which is followed by the decoupling of tachyonic particles. We demonstrate the phenomena by revoking the effective noncommutative dynamics for the D(3)-brane and obtain nonlinear corrections to U(1) gauge theory. We discuss the spontaneous breaking of noncommutative U(1) symmetry and show that the Hagedorn phase is described by the noninteracting gauge particles. The notion of time reappears in the phase at the expense of temperature. It suggests a complementarity between two distinct notions, time and temperature, at short distances.