Chiral quark dynamics and topological charge: The role of the Ramond-Ramond U(1) Gauge Field in Holographic QCD

TL;DR

This paper uses holographic QCD models involving D-branes and Ramond-Ramond fields to explore topological charge effects, chiral dynamics, and anomaly-related phenomena in QCD, providing insights into the role of topological structures and interactions.

Contribution

It introduces a string-theoretic framework linking topological charge, D-branes, and RR fields to QCD phenomena, clarifying the origin of topological susceptibility and chiral symmetry breaking mechanisms.

Findings

Topological susceptibility linked to D6 branes as magnetic sources.

RR exchange explains eta' mass and OZI rule features.

Nambu-Jona Lasinio interactions suggest a mechanism for chiral symmetry breaking.

Abstract

The Witten-Sakai-Sugimoto construction of holographic QCD in terms of D4 color branes and D8 flavor branes in type IIA string theory is used to investigate the role of topological charge in the chiral dynamics of quarks in QCD. The QCD theta term arises from a compactified 5-dimensional Chern-Simons term on the D4 branes. This term couples the QCD topological charge to the Ramond-Ramond $U(1)$ gauge field of IIA string theory. The nonzero topological susceptibility of pure-glue QCD can be attributed to the presence of D6 branes, which constitute magnetic sources of the RR gauge field. The topological charge of QCD is required, by an anomaly inflow argument, to coincide in space-time with the intersection of the D6 branes and the D4 color branes. This clarifies the relation between D6 branes and the coherent, codimension-one topological charge membranes observed in QCD Monte Carlo calculations. Using open-string/closed-string duality, we interpret a quark loop (represented by a D4-D8 open string loop) in terms of closed-string exchange between color and flavor branes. The role of the RR gauge field in quark-antiquark annihilation processes is discussed. RR exchange in the s-channel generates a 4-quark contact term which produces an $\eta'$ mass insertion and provides an explanation for the observed spin-parity structure of the OZI rule. The $(\log {\rm Det\;U})^2$ form of the $U(1)$ anomaly emerges naturally. RR exchange in the t-channel of the $q\overline{q}$ scattering amplitude produces a Nambu-Jona Lasinio interaction which may provide a mechanism for spontaneous breaking of $SU(N_f)\times SU(N_f)$.