Electromagnetic Strings: Complementarity between Time and Temperature

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.

32 pages, 2 figures, renamed title, added clarification on winding modes, corrected typos, added references

References in corpus (8)

• Remarks on Time-Space Noncommutative Field Theories
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• String Theory in Electromagnetic Fields
• Bosonic D-branes at finite temperature with an external field
• The Higgs Mechanism in Non-commutative Gauge Theories
• On the Nature of the Hagedorn Transition in NCOS Systems
• Transport equation and hard thermal loops in noncommutative Yang-Mills theory
• Noncommutativity and Spontaneously Broken Gauge Theories

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