Melvin Models and Diophantine Approximation

Details Melvin Models and Diophantine Approximation Melvin Models and Diophantine Approximation

2004-07-16

arxiv.org/abs/hep-th/0407150v3

Commun.Math.Phys. 256 (2005) 491-511

Physics

High Energy Physics

High Energy Physics - Theory

26pp. harvmac(b); v2: Some clarifications and references added. One small error corrected; v3: reference added

Scientific paper

10.1007/s00220-005-1306-9

Melvin models with irrational twist parameter provide an interesting example of conformal field theories with non-compact target space, and localized states which are arbitrarily close to being delocalized. We study the torus partition sum of these models, focusing on the properties of the regularized dimension of the space of localized states. We show that its behavior is related to interesting arithmetic properties of the twist parameter $\gamma$, such as the Lyapunov exponent. Moreover, for $\gamma$ in a set of measure one the regularized dimension is in fact not a well-defined number but must be considered as a random variable in a probability distribution.

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