On the center-vortex baryonic area law

TL;DR

This paper clarifies that in center-vortex QCD with gauge group SU(3), the baryonic area law follows a Y-shaped minimal surface configuration, aligning with recent lattice results, correcting previous misconceptions.

Contribution

It corrects earlier claims by establishing that the baryonic area law in SU(3) center-vortex QCD is a Y law, not a Delta law, and discusses extensions to SU(N).

Findings

The baryonic area law in SU(3) is a Y law with a minimal Steiner surface.

The Y law agrees with recent lattice calculations.

The work corrects previous misconceptions about the baryonic area law.

Abstract

We correct an unfortunate error in an earlier work of the author, and show that in center-vortex QCD (gauge group SU(3)) the baryonic area law is the so-called $Y$ law, described by a minimal area with three surfaces spanning the three quark world lines and meeting at a central Steiner line joining the two common meeting points of the world lines. (The earlier claim was that this area law was a so-called $\Delta$ law, involving three extremal areas spanning the three pairs of quark world lines.) We give a preliminary discussion of the extension of these results to $SU(N), N>3$. These results are based on the (correct) baryonic Stokes' theorem given in the earlier work claiming a $\Delta$ law. The $Y$-form area law for SU(3) is in agreement with the most recent lattice calculations.