Les Houches Lectures on Strings and Arithmetic

TL;DR

This paper reviews the interplay between number theory and string theory, focusing on modular forms in AdS/CFT and the attractor mechanism in supergravity, highlighting new questions in these areas.

Contribution

It introduces new perspectives on the role of modular forms and the attractor mechanism in string compactifications, connecting number theory with physical models.

Findings

Rademacher expansion's relevance in AdS/CFT correspondence

Attractor mechanism's role in selecting arithmetic Calabi-Yau's

Raises new questions about number theory and string compactification

Abstract

These are lecture notes for two lectures delivered at the Les Houches workshop on Number Theory, Physics, and Geometry, March 2003. They review two examples of interesting interactions between number theory and string compactification, and raise some new questions and issues in the context of those examples. The first example concerns the role of the Rademacher expansion of coefficients of modular forms in the AdS/CFT correspondence. The second example concerns the role of the ``attractor mechanism'' of supergravity in selecting certain arithmetic Calabi-Yau's as distinguished compactifications.