Les Houches Lectures on Strings and Arithmetic

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.

61pp. harvmac b-mode, 3 figures;v2: minor changes;v3: added refs; v4: Important mistake concerning the ``Fareytail transform'' has been fixed

References in corpus (7)

• Wormholes in AdS
• Gravity solutions for the D1-D5 system with angular momentum
• Flux Compactifications on Calabi-Yau Threefolds
• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• The Challenging Cosmic Singularity
• Melvin Models and Diophantine Approximation
• Complex Multiplication of Exactly Solvable Calabi-Yau Varieties

Cited by in corpus (45)

• Black Hole Attractors and the Topological String
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Building a Better Racetrack
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• The Non-BPS Black Hole Attractor Equation
• New Attractors
• Enumerating Flux Vacua with Enhanced Symmetries
• Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications
• On N=8 attractors
• New Attractors and Area Codes
• String Theory Effects on Five-Dimensional Black Hole Physics
• Strings, Black Holes, and Quantum Information
• Schwinger pair production in AdS2
• stu Black Holes Unveiled
• Fixing All Moduli for M-Theory on K3xK3
• A Review of Distributions on the String Landscape
• Attractors and Black Rings
• Bound state transformation walls
• Lectures on black holes and the AdS_3 / CFT_2 correspondence
• Polyakov formulas for GJMS operators from AdS/CFT
• Arithmetic of N=8 Black Holes
• Supersymmetry breaking, heterotic strings and fluxes
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity
• Enhanced Symmetries in Multiparameter Flux Vacua
• An Index for 2D field theories with large N=4 superconformal symmetry
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• Flux vacua as supersymmetric attractors
• Theta-problem and the String Swampland
• Extremal Black Holes in Supergravity
• On Quantum Special Kaehler Geometry
• Issues in Complex Structure Moduli Inflation
• On the Classification of Elliptic Fibrations modulo Isomorphism on K3 Surfaces with large Picard Number
• Large-small dualities between periodic collapsing/expanding branes and brane funnels
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Melvin Models and Diophantine Approximation
• Revisiting arithmetic solutions to the $W=0$ condition
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• Metastable Flux Configurations and de Sitter Spaces
• A Comment on Quantum Distribution Functions and the OSV Conjecture
• First-order attractor flow equations for supersymmetric black rings in N=2, D=5 supergravity
• W=0 Complex Structure Moduli Stabilization on CM-type K3 x K3 Orbifolds:---Arithmetic, Geometry and Particle Physics---
• Extremal Black Holes, Stueckelberg Scalars and Phase Transitions
• Attractor Flows in st^2 Black Holes
• New perspectives in the duality of M-theory, heterotic strings, and F-theory