Holographic integral equations and walking technicolour

TL;DR

This paper develops holographic integral equations to analyze chiral symmetry breaking and pion properties in models with walking coupling, with implications for Technicolour theories, using D3-D7 and D3-D5 systems.

Contribution

It introduces simple integral equations relating the running coupling and quark self-energy for holographic models, extending understanding of walking Technicolour via holography.

Findings

Derived integral equations for quark condensate and pion decay constant.

Identified a light pion in the holographic D3-D7 system.

Proposed a non-supersymmetric D3-D5 model as a walking theory with specific condensate dimension.

Abstract

We study chiral symmetry breaking in the holographic D3-D7 system in a simple model with an arbitrary running coupling. We derive equations for the D7 embedding and show there is a light pion. In particular we present simple integral equations, involving just the running coupling and the quark self energy, for the quark condensate and the pion decay constant. We compare these to the Pagels-Stokar or constituent quark model equivalent. We discuss the implications for walking Technicolour theories. We also perform a similar analysis in the four dimensional field theory whose dual is the non-supersymmetric D3-D5 system and propose that it represents a walking theory in which the quark condensate has dimension 2 + sqrt{3}.