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Table of contents
1 Introduction
2 Elements of String Theory
2.1 Brief Introduction to Bosonic String Theory
2.2 Bosonic String Spectrum
2.3 Superstring Theory
2.4 Superstring Vertex Operators
2.5 Vacuum Amplitude on the Torus
2.6 The Heterotic Superstring
2.7 The Type I Superstring
3 Compactication
3.1 Toroidal Compactication
3.2 T-Duality
3.3 Orbifold Compactication
3.4 Tensor Products of Free CFTs : Fermionic Models
3.5 Gepner Models
4 Spacetime vs Worldsheet Supersymmetry
4.1 Conditions for N4 = 1 Supersymmetry
4.2 N4 = 2 and N4 = 4 Spacetime Supersymmetry
5 Supersymmetry Breaking
5.1 Explicit Breaking
5.2 Spontaneous Breaking
5.3 Scherk-Schwarz Breaking
6 MSDS Constructions : Algebra & Vacuum Classication
6.1 High Curvature and High Temperature Phases of String Theory
6.2 Maximally Symmetric MSDS Vacua
6.3 ZN2 -Orbifolds with MSDS Structure
7 Deformations and Thermal Interpretation of MSDS Vacua
7.1 Finite Temperature
7.2 Hagedorn Instability in String Theory
7.3 Resolution of the Hagedorn Instability
7.4 Deformations and Stability
7.5 Tachyon-Free MSDS Orbifold Constructions
8 Non-Singular String Cosmology
8.1 `Big Bang’ Cosmology
8.2 String Cosmology
8.3 Hybrid Models in 2d
8.4 Non-Singular Hybrid Cosmology
9 Emergent MSDS algebras & Spinor-Vector Duality
9.1 Spinor-Vector Duality Map
9.2 Spinor-Vector Duality from Twisted N = 4 SCFT Spectral-Flow
A Theta Functions and Lattice Identities
A.1 Theta Functions
A.2 Double Poisson Resummation
A.3 OPEs involving SO(N) Spin-Fields
B Equivalence between Fermionic Constructions and ZN2 -type Orbifolds
C Unfolding the Fundamental Domain
C.1 Decomposition into Modular Orbits
D The `Abstrusa’ Identity of Jacobi
D.1 A `direct’ proof
