QCD String Axions and $M$-theory

TL;DR

This paper shows that QCD string axions arise naturally on confining strings in M-theory realizations with $G_2$-holonomy, specifically in 4D $ exists abla$ SYM embedded in Bryant–Salamon geometries. By analyzing the interplay between 11D orientation reversal and 4D charge conjugation via internal isometries, it identifies which gauge algebras support a worldsheet pseudoscalar and hence an axion ($rak{su}(N ext{ with }N ext{ }> ext{2}),rak{so}(4N+2),rak{e}_6$ and related quotients) and which do not ($rak{su}(2)$, $rak{so}(2N+1)$, $rak{so}(4N)$, $rak{sp}(N)$, $rak{e}_7$). The analysis yields two regimes, MQCD and SYM, with corresponding worldsheet dynamics: a massless Goldstone sector plus two light scalars, one of which can act as a pseudoscalar axion, whose mass is generated by quantum effects, leading to a 2D EFT consistent with lattice observations for $N eq 2$. In non-supersymmetric YM at large $N$, the same pattern is expected to persist, and the framework suggests concrete lattice tests across gauge algebras of types A, B, C, D, and E. Overall, the work provides a geometric and holographic mechanism for axion-like excitations on QCD strings and clarifies when such excitations must be present or absent.

Abstract

In $SU(N)$ Yang-Mills theory without matter, there exist stable long electric fluxtube strings which carry a 1-form symmetry charge. Over the past decade or so, there has been increasing evidence from lattice calculations that the worldsheet theories of such QCD strings contain a massive pseudoscalar (axion), at least when $N\geq 3$. This has so far been puzzling from the perspective of holographic realizations of strings in confining gauge theories. In this note, we will show how such axions appear naturally in the realization of 4D $\mathcal{N}=1$ Super-Yang-Mills (SYM) from $M$-theory spacetimes in which the extra dimensions are modeled by certain complete metrics of $G_2$-holonomy. This picture predicts that QCD string axions exist only if the gauge group is $SU(N\geq 3)$, $SO(4N+2)$, or $E_6$ (or a quotient/double-cover thereof), and is absent from the spectrum of stable QCD strings if the gauge group is $SU(2)$, $SO(2N+1)$, $SO(4N)$, $Sp(N)$, or $E_7$. We argue why we expect this pattern to persist for non-supersymmetric Yang-Mills strings, at least for large $N$, something which could be tested in future lattice studies of QCD strings for gauge algebras of B, C, D, and E-type.

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