Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space

Abstract

We study the dynamical breaking of chiral and color symmetries of dense quark matter in the ultrastatic hyperbolic spacetime $R\otimes H^3$ in the framework of an extended Nambu--Jona-Lasinio model. On the basis of analytical expressions for chiral and color condensates as functions of curvature and temperature, the phenomenon of dimensional reduction and gravitational catalysis of symmetry breaking in strong gravitational field is demonstrated in the regime of weak coupling constants. In the case of strong couplings it is shown that curvature leads to small corrections to the flat-space values of condensate and thus enhances the symmetry breaking effects. Finally, using numerical calculations phase transitions under the influence of chemical potential and negative curvature are considered and the phase portrait of the system is constructed.

arXiv comment14 pages, 5 figures

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• A curvature bound from gravitational catalysis
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• Gravitational instantons and anomalous chiral symmetry breaking
• A curvature bound from gravitational catalysis in thermal backgrounds
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• The Higgs oscillator on the hyperbolic plane and Light-Front Holography
• On Effective Dimensional Reduction in Hyperbolic Spaces
• Quantum Monte Carlo simulation with a black hole
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Fate of chiral symmetry in Riemann-Cartan geometry