Chiral dynamics from the hadronic string: general formalism

TL;DR

This paper derives the chiral Lagrangian from a string theory perspective, connecting QCD string dynamics with chiral symmetry breaking and gauge invariance, including both parity-even and parity-odd components.

Contribution

It presents a novel derivation of the chiral Lagrangian from string theory principles, incorporating conformal invariance and boundary interactions to reproduce known terms.

Findings

Derived the parity-even chiral Lagrangian from string dynamics.

Reproduced the Wess-Zumino-Witten term in 2D unambiguously.

Outlined modifications for the parity-odd part in 4D.

Abstract

QCD at long distances can be described by the chiral Lagrangian. On the other hand there is overwhelming evidence that QCD and all non-abelian theories admit an effective string description. Here we review a derivation of the (intrinsic) parity-even chiral Lagrangian by requiring that the propagation of the QCD string takes place on a background where chiral symmetry is spontaneously broken. Requiring conformal invariance leads to the equation of motion of the chiral Lagrangian. We then proceed to coupling the string degrees of freedom to external gauge fields and we recover in this way the covariant equations of motion of the gauge-invariant chiral Lagrangian at p^2 order. We consider next the parity-odd part (Wess-Zumino-Witten) action and argue that this require the introduction of the spin degrees of freedom (absent in the usual effective action treatment). We manage to reproduce the Wess-Zumino-Witten term in 2D in an unambiguous way. In 4D the situation is considerably more involved. We outline the modification of boundary interaction that is necessary to induce the parity-odd part of the chiral Lagrangian.