Vector mesons on the wall
Ryuichiro Kitano, Ryutaro Matsudo
Abstract
A bstract A domain-wall configuration of the η′ meson bounded by a string (called a pancake or a Hall droplet) is recently proposed to describe the baryons with spin N c /2. In order to understand its baryon number as well as the flavor quantum number, we argue that the vector mesons (the ρ and ω mesons) should play an essential role for the consistency of the whole picture. We determine the effective theory of large- N c QCD with N f massless fermions by taking into account a mixed anomaly involving the θ -periodicity and the global symmetry. The anomaly matching requires the presence of a dynamical domain wall on which a $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi><mml:msub><mml:mfenced><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math> Chern-Simons theory is supported. We consider the boundary conditions that should be imposed on the edge of the domain wall, and conclude that there should be a boundary term that couples the $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi><mml:msub><mml:mfenced><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math> gauge field to the vector mesons. We discuss the impact on physics of the chiral phase transition and the relation to the “duality” of QCD.