Skyrmions in Yang--Mills Theories with Massless Adjoint Quarks

Abstract

Dynamics of SU(N_c) Yang--Mills theories with N_f adjoint Weyl fermions is quite different from that of SU(N_c) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N_f) --> SO(N_f). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of N_f=2 had been considered previously. Here we discuss N_f >= 3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions (with mass O(N_c^0)) from the standpoint of the low-energy chiral sigma model. We derive the Wess--Zumino--Novikov--Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability. In addition, we consider another microscopic theory -- SO(N_c) Yang--Mills with N_f Weyl fermions in the vectorial representation -- which has the same chiral symmetry breaking pattern and the same chiral Lagrangian. We discuss distinctive features of these two scenarios.

arXiv comment31 pages, 3 figures

References in corpus (16)

• Knots and Particles
• Baryons And Branes In Anti de Sitter Space
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions
• Refining the Proof of Planar Equivalence
• Effective Lagrangians and Chiral Random Matrix Theory
• Baryons and Skyrmions in QCD with Quarks in Higher Representations
• The Hopf Skyrmion in QCD with Adjoint Quarks
• Fermionic quantization of Hopf solitons
• Presentations of the first homotopy groups of the unitary groups
• Toroidal Confugurations As Stable Solitons
• The Cosmological Constant and Domain Walls in Orientifold Field Theories and N=1 Gluodynamics
• Low-Energy Limit of Yang-Mills with Massless Adjoint Quarks: Chiral Lagrangian and Skyrmions
• QCD Flux Tubes as Sigma Model Relics
• Confining Flux Tubes in a Current Algebra Approach

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