From QCD Flux Tubes to Gravitational S-matrix and Back

by Victor Gorbenko

Overview

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.

Product Details

ISBN-13:	9783319446035
Publisher:	Springer-Verlag New York, LLC
Publication date:	09/21/2016
Series:	Springer Theses
Sold by:	Barnes & Noble
Format:	eBook
Pages:	133
File size:	2 MB

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.

Table of Contents

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