Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons

Bringoltz, Barak

doi:10.1103/PHYSREVD.79.105021

Title: Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons

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Abstract

We take a first step towards the solution of QCD in 1+1 dimensions at nonzero density. We regularize the theory in the UV by using a lattice and in the IR by putting the theory in a box of spatial size L. After fixing to axial gauge we use the coherent states approach to obtain the large-N classical Hamiltonian H that describes color neutral quark-antiquark pairs interacting with spatial Polyakov loops in the background of baryons. Minimizing H we get a regularized form of the 't Hooft equation that depends on the expectation values of the Polyakov loops. Analyzing the L dependence of this equation we show how volume independence, a la Eguchi and Kawai, emerges in the large-N limit, and how it depends on the expectation values of the Polyakov loops. We describe how this independence relies on the realization of translation symmetry, in particular, when the ground state contains a baryon crystal. Finally, we remark on the implications of our results on studying baryon density in large-N QCD within single-site lattice theories and on some general lessons concerning the way four-dimensional large-N QCD behaves in the presence of baryons.

Authors:

Bringoltz, Barak ^[1]

Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)

Publication Date:: Fri May 15 00:00:00 EDT 2009

OSTI Identifier:: 21296384

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles Fields

Additional Journal Information:: Journal Volume: 79; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.79.105021; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANNIHILATION OPERATORS; BARYONS; COLOR MODEL; CRYSTALS; DENSITY; EIGENSTATES; EQUATIONS; FOUR-DIMENSIONAL CALCULATIONS; GROUND STATES; HAMILTONIANS; LATTICE FIELD THEORY; MATHEMATICAL SOLUTIONS; QUANTUM CHROMODYNAMICS; QUARK-ANTIQUARK INTERACTIONS; SYMMETRY; TWO-DIMENSIONAL CALCULATIONS

Citation Formats


                    Bringoltz, Barak. Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons.  United States: N. p., 2009. 
        Web.  doi:10.1103/PHYSREVD.79.105021.

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                    Bringoltz, Barak. Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons.  United States.  https://doi.org/10.1103/PHYSREVD.79.105021

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                    Bringoltz, Barak. 2009.  
        "Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons".  United States.  https://doi.org/10.1103/PHYSREVD.79.105021.

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@article{osti_21296384,

  title        = {Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons},

  author       = {Bringoltz, Barak},

  abstractNote = {We take a first step towards the solution of QCD in 1+1 dimensions at nonzero density. We regularize the theory in the UV by using a lattice and in the IR by putting the theory in a box of spatial size L. After fixing to axial gauge we use the coherent states approach to obtain the large-N classical Hamiltonian H that describes color neutral quark-antiquark pairs interacting with spatial Polyakov loops in the background of baryons. Minimizing H we get a regularized form of the 't Hooft equation that depends on the expectation values of the Polyakov loops. Analyzing the L dependence of this equation we show how volume independence, a la Eguchi and Kawai, emerges in the large-N limit, and how it depends on the expectation values of the Polyakov loops. We describe how this independence relies on the realization of translation symmetry, in particular, when the ground state contains a baryon crystal. Finally, we remark on the implications of our results on studying baryon density in large-N QCD within single-site lattice theories and on some general lessons concerning the way four-dimensional large-N QCD behaves in the presence of baryons.},

  doi          = {10.1103/PHYSREVD.79.105021},

  url          = {https://www.osti.gov/biblio/21296384},
  journal      = {Physical Review. D, Particles Fields},

  issn         = {0556-2821},

  number       = 10,

  volume       = 79,

  place        = {United States},

  year         = {Fri May 15 00:00:00 EDT 2009},

  month        = {Fri May 15 00:00:00 EDT 2009}

}

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