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The electric Melvin solution in string theory Gardezi, Jaffer

Abstract

An electric version of the well-known magnetic Melvin solution of closed string theory is derived. By analogy with the Kaluza-Klein Melvin solution, which is flat space with points identified under a simultaneous rotation and translation in a compact dimension, an orbifold of Minkowski space involving identifications under a Lorentz boost and a translation is introduced. When dimensional reduction to 9 dimensions is performed, the resulting background involves an electric Kaluza-Klein gauge field, giving rise to the electric Melvin interpretation. As was done by other authors for the magnetic Melvin background, a curved generalization of this orbifold is derived using a series of T-duality transformations. The closed string is quantized on the resulting space, and the string spectrum and partition function are calculated.

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