Introduction 1
1 Effective Field Theory for Relativistic Strings 7
1.1 Introduction and Summary . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Lattice Data versus Conventional Perturbative Expansion . . . . . . 16 2 Worldsheet S-matrix 24
2.1 Current Algebra for Branes . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Current Algebra for Strings . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Tree Level Warm-Up . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 One-loop 2 ! 2 Scattering . . . . . . . . . . . . . . . . . . . . . . . 38
2.5 Exact S-Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6 1-Loop Integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.7 Integrable S-matrices with Non-linear Poincare Symmetry . . . . . 57
3 Simplest Quantum Gravity 61
3.1 Thermodynamic Bethe Ansatz . . . . . . . . . . . . . . . . . . . . . 61
3.2 Hagedorn equation of state . . . . . . . . . . . . . . . . . . . . . . . 70 3.3 Absence of Local O_-Shell Observables . . . . . . . . . . . . . . . . 74
3.4 Quantum Black Holes and String Uncertainty Principle . . . . . . . 82
3.5 Classical Solutions: Black Hole Precursors and Cosmology . . . . . 89 4 Natural Tuning 99
4.1 Introduction and Summary . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 Gravitational Shock Waves and Strings . . . . . . . . . . . . . . . . 110
4.3 Natural Tuning from Gravitational Dressing . . . . . . . . . . . . . 115
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5 Flux Tube Spectrum from Thermodynamic Bethe Ansatz 135
5.1 Finite Volume Spectra From Infinite Volume Scattering . . . . . . . 136
5.2 Energy Levels of Flux Tubes . . . . . . . . . . . . . . . . . . . . . . 152
5.3 Future Directions and Conclusions . . . . . . . . . . . . . . . . . . 178
Appendices 183
Bibliography
About the Author: Dr Victor Gorbenko was awarded the PhD degree by New York University in 2015, and is currently with the Physics Department at Stanford University.
