Melvin Models and Diophantine Approximation

Abstract

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.

arXiv comment26pp. harvmac(b); v2: Some clarifications and references added. One small error corrected; v3: reference added

References in corpus (21)

• Pair Creation of Dilaton Black Holes
• Strings in Time-Dependent Orbifolds
• On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
• The Decay of Magnetic Fields in Kaluza-Klein Theory
• Fluxbranes in String Theory
• Time-dependent Orbifolds and String Cosmology
• Magnetic flux tube models in superstring theory
• Nucleation of $P$-Branes and Fundamental Strings
• The Kaluza-Klein Melvin Solution in M-theory
• Localized Tachyons and RG Flows
• Les Houches Lectures on Strings and Arithmetic
• Closed String Tachyon Condensation on Twisted Circles
• Closed String Tachyon Condensation: An Overview
• Magnetic backgrounds and tachyonic instabilities in closed superstring theory and M-theory
• Tension is Dimension
• Some Properties of (Non) Critical Strings
• Defects, Decay, and Dissipated States
• On the short-distance structure of irrational non-commutative gauge theories
• Orientifolds of String Theory Melvin backgrounds
• On 6d "Gauge" Theories with Irrational Theta Angle
• Duality Cascade and Oblique Phases in Non-Commutative Open String Theory

Cited by in corpus (6)

• AdS Bubbles, Entropy and Closed String Tachyons
• Les Houches Lectures on Strings and Arithmetic
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• The abelian cosets of the Heisenberg group
• Open Strings and Supersymmetry Breaking
• A New Lorentz Violating Nonlocal Field Theory From String-Theory