QCD with Chemical Potential in a Small Hyperspherical Box

Abstract

To leading order in perturbation theory, we solve QCD, defined on a small three sphere in the large N and Nf limit, at finite chemical potential and map out the phase diagram in the (mu,T) plane. The action of QCD is complex in the presence of a non-zero quark chemical potential which results in the sign problem for lattice simulations. In the large N theory, which at low temperatures becomes a conventional unitary matrix model with a complex action, we find that the dominant contribution to the functional integral comes from complexified gauge field configurations. For this reason the eigenvalues of the Polyakov line lie off the unit circle on a contour in the complex plane. We find at low temperatures that as mu passes one of the quark energy levels there is a third-order Gross-Witten transition from a confined to a deconfined phase and back again giving rise to a rich phase structure. We compare a range of physical observables in the large N theory to those calculated numerically in the theory with N=3. In the latter case there are no genuine phase transitions in a finite volume but nevertheless the observables are remarkably similar to the large N theory.

44 pages, 18 figures, jhep3 format. Small corrections and clarifications added in v3. Conclusions cleaned up. Published version

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Cited by in corpus (31)

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• Towards the phase diagram of dense two-color matter
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• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions
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• SU(3) Polyakov Linear $\sigma$-Model in Magnetic Field: Thermodynamics, Higher-Order Moments, Chiral Phase Structure and Meson Masses
• Complex Langevin calculations in QCD at finite density
• Numerical Study of the Two Color Attoworld
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• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories
• Weak coupling large-N transitions at finite baryon density
• Free energy of a Holonomous Plasma
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• A Universal Lower Bound on the Specific Temperatures of AdS-Reissner-Nordstrom Black Holes with Flat Event Horizons
• Spinning flavour branes and fermion pairing instabilities
• Deconfinement transitions of large N QCD with chemical potential at weak and strong coupling
• Large N lattice QCD and its extended strong-weak connection to the hypersphere
• Phases of circle-compactified QCD with adjoint fermions at finite density
• The Phase Diagram of Two Color QCD
• Color confinement at the boundary of the conformally compactified ${\mathrm{AdS}}_5$
• Thermodynamic properties of the trigonometric Rosen-Morse potential and applications to a quantum gas of mesons
• Color superconductivity on the lattice -- analytic predictions from QCD in a small box
• Confinement on $R^3\times S^1$: continuum and lattice
• Geometric entropy and third order phase transition in d=4 N=2 SYM with flavor
• Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement