From QCD Flux Tubes to Gravitational S-matrix and Back

Introduction 1

1 Effective Field Theory for Relativistic Strings 7

1.1 Introduction and Summary . . . . . . . . . . . . . . . . . . . . . . . 7

2 Worldsheet S-matrix 24

2.1 Current Algebra for Branes . . . . . . . . . . . . . . . . . . . . . . 26

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

3.3 Absence of Local O_-Shell Observables . . . . . . . . . . . . . . . . 74

3.4 Quantum Black Holes and String Uncertainty Principle . . . . . . . 82

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