String theory
Introductory
Polchiski, String theory, vols 1 & 2
Hatfield, Quantum field theory of point particles and strings
West, Introduction to strings and branes
Becker, Becker and Schwarz, String theory and M-theory: a modern introduction
Ibanez et al, String theory and particle physics: an introduction to string phenomenology
Deligne et al, Quantum fields and strings: a course for mathematicians
Jost, Bosonic strings: a mathematical treatment
Albeveiro et al, A mathematical introduction to string theory
Relevant mathematics: Everything needed for general relativity and quantum field theory plus:
- conformal field theory
- theory of (pseudo-)harmonic maps
- some Teichmuller theory
- moduli spaces of Riemann surfaces
- spin geometry and index theory
- some topological K-theory
- some complex and Kahler geometry
- some algebraic geometry
- basic theory of G-structures
Advanced
A. (Super)string perturbation theory
Witten, Superstring perturbation theory via super Riemann surfaces: an overview
B. Calabi-Yau compactifications
Yau and Nadis, The shape of inner space
Greene, String theory on Calabi-Yau manifolds
Yau, A survey of Calabi-Yau manifolds
Joyce, Compact manifolds with special holonomy
Gross, Joyce & Huybrechts, Calabi-Yau manifolds and related geometries
C. Topological string theory
Marino, Chern Simons theory, matrix models and topological strings
Alim, Lectures on mirror symmetry and topological string theory
Nietzke and Vafa, Topological strings and their physcal applications
Marino, An introduction to topological string theory
D. Mirror Symmetry (ordinary and homological)
Abramovich et al, Enumerative invariants in algebraic geometry and string theory
Cox and Katz, Mirror symmetry and algebraic geometry
Hori et al, Mirror Symmetry
Bocklandt, A gentle introduction to homological mirror symmetry
Wang Yao, A glimpse into homological mirror symmetry
Aspinwall et al, Dirichlet branes and mirror symmetry
Huybrechts, Fourier-Mukai transforms in algebraic geometry
Auroux, A beginner's introduction to Fukaya categories
Smith, A symplectic prolegomenon
Seidel, Lectures on categorical dynamics and symplectic topology
Seidel, Fukaya categories and Picard-Lefschetz theory
Fukaya et al: Lagrangian intersection Floer theory: anomaly and obstruction, vols 1 & 2
Jarvis and Priddis (eds), Singularities, Mirror Symmetry and the Gauged Linear Sigma Model
E. Mathematical foundations of string and supergravity theories
Relevant mathematics:
- Complex and Kahler geometry
- Algebraic geometry (including toric geometry)
- noncommutative algebraic geometry
- Symplectic geometry and topology
- Gromow-Witten theory
- G-manifolds
- G-structures
- theory of foliations
- noncommutative geometry in the sense of Connes
- singularity theory and Thom-Mather theory (a.k.a. "catastrophe theory")
- Triangulated and derived categories
- Floer homology and Fukaya categories
- algebraic K-theory
- differential topology
- moduli spaces (differential and algebraic)
- basic theory of differential and algebraic stacks
- algebraic homotopy theory
- theory of gerbes
- simplicial methods and higher category theory
- geometric analysis