Flat space (higher spin) gravity with chemical potentials

TL;DR

The paper develops flat space spin-3 gravity with chemical potentials in three dimensions using a Chern-Simons isl(3) framework. It derives the on shell structure and canonical charges and shows holonomy conditions yield an entropy and grand canonical free energy for flat space cosmologies with spin-3 hair. The results reveal multiple thermodynamic branches and phase transitions, including instability of the spin-2 connected branch at high temperature or large spin-3 chemical potential. It also discusses singularity resolutions and outlines generalizations to broader higher spin holography and holographic dictionaries.

Abstract

We introduce flat space spin-3 gravity in the presence of chemical potentials and discuss some applications to flat space cosmology solutions, their entropy, free energy and flat space orbifold singularity resolution. Our results include flat space Einstein gravity with chemical potentials as special case. We discover novel types of phase transitions between flat space cosmologies with spin-3 hair and show that the branch that continuously connects to spin-2 gravity becomes thermodynamically unstable for sufficiently large temperature or spin-3 chemical potential.

Figures (1)

• Figure 1: Plots of free energy as function of temperature. In all plots $\Omega=1$, $\Omega_{\textrm{\tiny U}}=0.1$. Upper Left: $\Omega_{\textrm{\tiny V}}=0.4$. Upper Middle: $\Omega_{\textrm{\tiny V}}=0.2$. Upper Right: $\Omega_{\textrm{\tiny V}}=0.18$. Lower Left: $\Omega_{\textrm{\tiny V}}=0.15$. Lower Middle: $\Omega_{\textrm{\tiny V}}=0.12$. Lower Right: $\Omega_{\textrm{\tiny V}}=0.01$. The branch with smooth spin-2 limit is displayed as thick line, the second branch as dashed line, the other two branches as dotted lines (in the upper plots these lines are at positive $F$). For a movie of these plots see http://quark.itp.tuwien.ac.at/g̃rumil/mp3/free_energy_fs3.avi.