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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Relativistic Quantum Mechanics, Field Theory, Brane Theory (Including Strings)

J. Math. Phys. 53, 022302 (2012); http://dx.doi.org/10.1063/1.3682640 (26 pages)

On flavor symmetry in lattice quantum chromodynamics

El Hassan Saidi

 Lab of High Energy Physics, Modeling and Simulation, Faculty of Sciences, University Mohammed V-Agdal, 4, Avenue Ibn Battouta, Rabat, Morocco

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(Received 27 December 2011; accepted 14 January 2012; published online 9 February 2012)

Using a well established method to engineer non-abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al. [PoS: Lattice 2010, 078 (2010) and Creutz et al. JHEP 041, 1012 (2010)] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD2N, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of [SU(2)]2N. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form iγ1F1+iγ2F2+iγ3F3+mathγ4F4, are related with the small resolution of conifold singularity that live at sin α = 0. Other related features are also studied.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. POINT-SPLITTING METHOD OF CREUTZ
    1. Specific features of Karsten-Wilczek fermion
      1. Special properties of D KW
      2. Expansions of D KW near the zero modes
    2. The point splitting method
  3. NAIVE FERMIONS AND TORIC SINGULARITIES
    1. The naive D NF operator and toric manifolds
      1. Explicit features of D NF in QCD 2
      2. Implicit features of D NF
    2. Zeros of complexified naive D and point splitting method
      1. The four zeros of D
      2. Point splitting method
  4. TORIC SINGULARITIES AND CREUTZ FLAVORS
    1. Two examples of toric singularities
    2. The complex surface CP 1 × CP 1
    3. Creutz flavors
  5. KW FERMIONS AND CONIFOLD
    1. Zero of D KW as fix points of math2 symmetry
    2. F 4 as a resolved conifold singularity
      1. Useful tools on singularities
        1. SU (2) singularity.
        2. 3d-conifold singularity.
      2. The F4 term
    3. F4 -term and the complexified D KW operator
  6. CONCLUSION AND COMMENT

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KEYWORDS and PACS

Keywords

Dirac equation, flavour model, lattice field theory, quantum chromodynamics, SU(2) theory, superstrings

PACS

  • 12.38.Aw

    General properties of QCD (dynamics, confinement, etc.)

  • 11.30.Ly

    Other internal and higher symmetries

  • 11.25.-w

    Strings and branes

  • 12.39.-x

    Phenomenological quark models

  • 12.38.Gc

    Lattice QCD calculations

  • 11.10.Cd

    Axiomatic approach

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682640

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    F. Wilczek, Phys. Rev. Lett. 59, 2397 (1987).


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