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Holographic QCD and quarkonium melting: Finite temperature, density, and external field effects in self-consistent dynamical models

Bruno Toniato

Abstract

This MSc dissertation is based on the papers arXiv:2502.12694 and arXiv:2408.14813. The AdS/CFT correspondence provides a powerful framework for modeling strongly coupled gauge theories and, as a consequence, investigating non-perturbative phenomena in QCD. In this work, following an overview of the ideas that encapsulate the AdS/CFT correspondence, we present a self-consistent dynamical holographic QCD model within the Einstein-Maxwell-dilaton framework, derived from the coupled field equations, to study the mass spectra and melting behavior of heavy and exotic mesons at finite temperature and density. Finite temperature analyses reveal a confinement-deconfinement transition and sequential quarkonia melting. At finite density, an increase in chemical potential accelerates meson melting, with spectral functions evolving smoothly across the phase transition line. Finally, using a nonlinear Einstein-Born-Infeld-dilaton model, magnetic field effects demonstrate a shift from inverse magnetic catalysis to magnetic catalysis, highlighting the impact of spatial anisotropy on quarkonium stability.

Holographic QCD and quarkonium melting: Finite temperature, density, and external field effects in self-consistent dynamical models

Abstract

This MSc dissertation is based on the papers arXiv:2502.12694 and arXiv:2408.14813. The AdS/CFT correspondence provides a powerful framework for modeling strongly coupled gauge theories and, as a consequence, investigating non-perturbative phenomena in QCD. In this work, following an overview of the ideas that encapsulate the AdS/CFT correspondence, we present a self-consistent dynamical holographic QCD model within the Einstein-Maxwell-dilaton framework, derived from the coupled field equations, to study the mass spectra and melting behavior of heavy and exotic mesons at finite temperature and density. Finite temperature analyses reveal a confinement-deconfinement transition and sequential quarkonia melting. At finite density, an increase in chemical potential accelerates meson melting, with spectral functions evolving smoothly across the phase transition line. Finally, using a nonlinear Einstein-Born-Infeld-dilaton model, magnetic field effects demonstrate a shift from inverse magnetic catalysis to magnetic catalysis, highlighting the impact of spatial anisotropy on quarkonium stability.
Paper Structure (77 sections, 390 equations, 48 figures, 4 tables)

This paper contains 77 sections, 390 equations, 48 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Quantum Field Theory at zero and finite temperature
  3. Correlation functions
  4. Renormalization, running coupling and the $\phi^4$ theory $\beta$-function
  5. Yang-Mills theory
  6. Dynamics of quarks and gluons
  7. Spectral functions in QCD
  8. Planar limit of Yang-Mills theory
  9. QFT at finite temperature
  10. Kubo's linear response theory
  11. An overview of the AdS/CFT correspondence
  12. AdS geometry
  13. Black hole thermodynamics
  14. Conformal Field Theory
  15. Partition functions in CFTs
  16. ...and 62 more sections

Figures (48)

  • Figure 1: $\phi^4$ theory fish, or bubble, diagram.
  • Figure 2: Amputated quark loop diagram.
  • Figure 3: Leading-order continuum spectral density $\rho_V(s)$ as a function of $s$ for three representative quark masses. The threshold occurs at $s=4m^2$, and for $s\gg m^2$ the curves approach the universal plateau $\rho_V(s)\to N_c/(12\pi)=1/(4\pi)$ (for $N_c=3$).
  • Figure 4: Penrose diagram of $AdS_5$ spacetime. Figure taken, and adapted, from Gruppuso:2004db.
  • Figure 5: The first three Bessel functions $J_{\nu}(z)$ (for representative orders) and their zeros.
  • ...and 43 more figures