Hadronic string, conformal invariance and chiral symmetry

TL;DR

This paper explores how a sigma model approach can address key issues in modeling QCD with string theory, successfully deriving pion interactions and matching observed coefficients, while discussing conformal anomaly concerns.

Contribution

It demonstrates how to avoid fundamental problems in string models of QCD by identifying the correct vacuum and deriving effective pion Lagrangians.

Findings

Derived the non-linear sigma model for pion interactions.

Obtained the Gasser-Leutwyler coefficients matching observations.

Addressed issues related to conformal anomaly in string QCD models.

Abstract

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The `natural' candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally non-invariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the non-linear sigma model of pion interactions. At the next-to-leading order the O(p^4) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.