Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory

TL;DR

This paper explores open strings in a constant electric field, revealing a new noncritical string theory on noncommutative spacetime near the critical electric field, unlike the magnetic case.

Contribution

It introduces a novel noncritical string theory arising from the limit approaching the critical electric field, highlighting differences from magnetic background scenarios.

Findings

Critical electric field prevents a noncommutative field theory limit.

Approaching the critical field yields a new noncritical string theory.

The theory differs fundamentally from magnetic background cases.

Abstract

Searching for space/time noncommutativity we reconsider open strings in a constant background electric field. The main difference between this situation and its magnetic counterpart is that here there is a critical electric field beyond which the theory does not make sense. We show that this critical field prevents us from finding a limit in which the theory becomes a field theory on a noncommutative spacetime. However, an appropriate limit toward the critical field leads to a novel noncritical string theory on a noncommutative spacetime.