## From QCD Flux Tubes to Gravitational S-matrix and BackThis 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. |

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### Contents

1 | |

5 | |

3 Worldsheet SMatrix | 17 |

4 Simplest Quantum Gravity | 43 |

5 Natural Tuning | 68 |

6 Flux Tube Spectrum from Thermodynamic Bethe Ansatz | 93 |

A Lorentz Algebra of Weyl Ordered Effective Strings | 125 |

B Scalar Triangle | 129 |

C Calculation of the Entanglement Entropy | 131 |

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### Common terms and phrases

action analytic Bethe Ansatz black hole bosons branon classical coefficient contribution conventional corresponding counterterms crossing symmetry density derivative expansion diagrams dimensions discussion divergences dressing factor Dubovsky effective field theory Effective string theory excited flavor flux tube four-particle function gauge theories GGRT phase GGRT theory Goldstone Gorbenko gravitational dressing ground state energy hierarchy problem High Energy Phys implies integrable interaction Lagrangian lattice data left-moving light-cone lines show Lorentz invariant Lorentz symmetry massive massless matrix momenta Nambu–Goto natural tuning non-linearly realized Lorentz non-trivial Nucl number of particles on-shell one-loop operators phase shift phonons physical sheet Poincaré prediction propagating properties pseudo-energies pseudoscalar QCD Flux Tubes quantization quantum field theory relativistic resonance result right-moving S-matrix scalar scale scattering amplitudes singularities solution space-time static gauge string theory target space TBA equations tensor term theoretical total momentum tree level two-dimensional two-particle unitarity UV complete winding corrections worldsheet worldsheet theory zero