Weak coupling large-N transitions at finite baryon density

Abstract

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.

38 pages, 7 figures

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• Gross-Witten-Wadia transition in a matrix model of deconfinement
• A Supersymmetric Color Superconductor from Holography
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes
• Free energy of a Holonomous Plasma
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• Confinement on $R^3\times S^1$: continuum and lattice
• Phase space and phase transitions in the Penner matrix model with negative coupling constant
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential