Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass
- Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
We solve two-dimensional large-N QCD in the presence of a nonzero baryon number B, and for arbitrary quark mass m and volume L. We fully treat the dynamics of the gluonic zero modes and check how this affects results from previous studies of the B=0 and B=1 systems. For a finite density of baryons, and for any m>0, we find that the ground state contains a baryon crystal with expectation values for <{psi}{gamma}{sub {mu}}{psi}> that have a helixlike spatial structure. We study how these evolve with B and see that the volume integral of <{psi}{psi}> strongly changes with the baryon density. We compare this emerging crystal structure with the sine-Gordon crystal, which is expected to be a good approximation for light quarks, and find that it is a very good approximation for surprisingly heavy quarks. We also calculate the way the ground state energy E changes as a function of the baryon number B, and find that for sufficiently large densities the function E(B) is well described by the equation of state for free massless quarks, thus suggesting a quark-Hadron continuity. From {partial_derivative}E(B)/{partial_derivative}B we calculate the quark chemical potential {mu} as a function of B and see that the baryons repel each other. The way {mu} depends on B also allows us to translate our findings to the grand-canonical ensemble. The resulting phase structure along the {mu} axis contains a phase transition that occurs at a value of {mu} equal to the baryon mass divided in N, and that separates a {mu}-independent phase with intact translation symmetry from a {mu}-dependent phase with spontaneously broken translation symmetry. Finally, our calculations confirm the presence of a partial large-N Eguchi-Kawai volume independence, as described in [Phys. Rev. D 79, 105021 (2009)], that arises only if one treats the gluonic zero modes correctly.
- OSTI ID:
- 21301013
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 12; Other Information: DOI: 10.1103/PhysRevD.79.125006; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
APPROXIMATIONS
B QUARKS
BARYON NUMBER
BARYONS
C QUARKS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
D QUARKS
EQUATIONS OF STATE
GROUND STATES
MASS
MATHEMATICAL SOLUTIONS
PHASE TRANSFORMATIONS
POTENTIALS
QUANTUM CHROMODYNAMICS
SINE-GORDON EQUATION
SYMMETRY
T QUARKS
TWO-DIMENSIONAL CALCULATIONS
U QUARKS