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Baryons in $SO(N)$ vector models and their duals in higher spin theory

Bo Sundborg

Abstract

Black shells, a kind of black hole mimickers, are identified thermodynamically as bulk duals of baryon operators in vector models, indicating that such objects are essential for the consistency of higher spin gravity theories. Thermal baryons, with a spectrum of a 2+1-dimensional relativistic Fermi gas, are found to be precursors of the deconfinement phase transition in vector models, condensing at a slightly lower temperature. The early condensation means that baryons are statistically important already in the phase with weakly interacting higher spin fields. Furthermore, the mysterious scale of the deconfinement transition in vector models is naturally interpreted as the Fermi energy scale in the gas.

Baryons in $SO(N)$ vector models and their duals in higher spin theory

Abstract

Black shells, a kind of black hole mimickers, are identified thermodynamically as bulk duals of baryon operators in vector models, indicating that such objects are essential for the consistency of higher spin gravity theories. Thermal baryons, with a spectrum of a 2+1-dimensional relativistic Fermi gas, are found to be precursors of the deconfinement phase transition in vector models, condensing at a slightly lower temperature. The early condensation means that baryons are statistically important already in the phase with weakly interacting higher spin fields. Furthermore, the mysterious scale of the deconfinement transition in vector models is naturally interpreted as the Fermi energy scale in the gas.
Paper Structure (12 sections, 23 equations, 2 figures, 2 tables)

This paper contains 12 sections, 23 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Simple states in vector models
  3. Simple light operators in vector models
  4. Simple heavy operators in vector models
  5. Boundary baryon thermodynamics
  6. Dual bulk objects and their thermodynamics
  7. Dual bulk objects
  8. Bulk black shell thermodynamics
  9. Discussion of baryon-black shell match
  10. Conclusion
  11. Thermodynamics in the $U(N)$ model
  12. The deconfinement temperature in the $SO(N)$ model

Figures (2)

  • Figure 1: Thermodynamics of the boundary baryons. (a)$U(t)$ increases almost linearly with $t$. (b)$F(t)$ vanishes for $t\approx 0.48$ and is negative for higher $t$. At the zero and at higher temperatures, the condensation of a boundary baryon is thermodynamically favoured.
  • Figure 2: Thermodynamics of black shells. Both plots display one large black shell branch and one small black shell branch, analogous to small and large black holes in AdS and originating at a common solution with minimal temperature. (a) The upper, large black shell branch has a minimal $M_\text{min}$. (b) The large black shell branch has negative free energy above a condensation temperature.