Chiral Dynamics and Meson with Non-commutative Dipole Field in Gauge/Gravity Dual

TL;DR

This paper explores how non-commutative dipole fields influence chiral symmetry and meson spectra in gauge/gravity duality, revealing that such fields do not induce chiral symmetry breaking and affect meson energies differently depending on supersymmetry.

Contribution

It demonstrates that non-commutative dipole fields do not cause chiral symmetry breaking and shows their distinct effects on meson spectra in supersymmetric versus non-supersymmetric theories.

Findings

Dipole field does not induce chiral symmetry breaking.

Dipole field does not modify meson spectrum in supersymmetric theory.

Dipole field reduces meson bound-state energy in non-supersymmetric theory.

Abstract

Apply the T-duality and smeared twist to the D3-brane solution one can construct the supergravity backgrounds which may dual to supersymmetric or non-supersymmetric non-commutative dipole field theory. We introduce D7-brane probe into the dual supergravity background to study the chiral dynamics and meson spectrum therein. We first find that the non-commutative dipole field does not induce the chiral symmetry breaking even if the supersymmetry was completely broken, contrast to the conventional believing that the chiral symmetry will be broken in the non-supersymmetric theory. Next, we find that the dipole field does not modify the meson spectrum in the supersymmetric theory while it will reduce the meson bound-state energy in the non-supersymmetric theory. We also evaluate the static quark anti-quark potential and see that the dipole field has an effect to produce attractive force between the quark and anti-quark.