Geometric QCD III: Exact transition amplitudes and the glueball spectrum
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915977096069120 |
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| author | Migdal, Alexander |
| author_facet | Migdal, Alexander |
| contents | We complete the analysis of planar Makeenko--Migdal loop equations in the continuum limit. Using the confining twistor-string representation, we compute the quantum fluctuation determinant. In Minkowski space, this reduces to a discrete product of finite-dimensional matrix quadratures. The $ζ$-regularized weight is independent of winding number $w$. Near the mass shell, the pole singularity is generated by $w \to \infty$, suppressing fluctuation variance as $1/w$. The path integral localizes on the classical trajectory, rendering the pole spectrum and transition residues parametrically exact in the large-$w$ WKB limit.For the open-string meson sector, we fit 40 states across five topological sectors ($h=0, \pm 1, \pm 2$). The holonomy shift $h$ dictates exact geometric degeneracies between parity families, reproducing mass splittings without phenomenological spin-orbit parameters. Evaluated one-loop residues yield relative transition cross-sections, demonstrating nontrivial topology- and flavor-dependent scaling that captures heavy-mass quenching and phase-space enhancement for high-spin light states.For the pure Yang--Mills closed string, we demonstrate dynamical stability of the pure-gauge minimal surface in the planar limit: the conformal Liouville anomaly drives the string strictly to the trigonometric minimum ($q=0$). The complex elliptic geometry analytically collapses, yielding linear Regge trajectories. The translation zero-mode measure dynamically nullifies the transition amplitude of the massless scalar ghost, providing an explicit analytic mechanism for a purely gluonic mass gap. Anchoring parameter-free glueball trajectories to the string tension natively recovers the L"uscher intercept $α(0)=1/12$, yielding a macroscopic spectrum that provides a suggestive baseline for established PDG unassigned isoscalar candidates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_02373 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric QCD III: Exact transition amplitudes and the glueball spectrum Migdal, Alexander High Energy Physics - Theory We complete the analysis of planar Makeenko--Migdal loop equations in the continuum limit. Using the confining twistor-string representation, we compute the quantum fluctuation determinant. In Minkowski space, this reduces to a discrete product of finite-dimensional matrix quadratures. The $ζ$-regularized weight is independent of winding number $w$. Near the mass shell, the pole singularity is generated by $w \to \infty$, suppressing fluctuation variance as $1/w$. The path integral localizes on the classical trajectory, rendering the pole spectrum and transition residues parametrically exact in the large-$w$ WKB limit.For the open-string meson sector, we fit 40 states across five topological sectors ($h=0, \pm 1, \pm 2$). The holonomy shift $h$ dictates exact geometric degeneracies between parity families, reproducing mass splittings without phenomenological spin-orbit parameters. Evaluated one-loop residues yield relative transition cross-sections, demonstrating nontrivial topology- and flavor-dependent scaling that captures heavy-mass quenching and phase-space enhancement for high-spin light states.For the pure Yang--Mills closed string, we demonstrate dynamical stability of the pure-gauge minimal surface in the planar limit: the conformal Liouville anomaly drives the string strictly to the trigonometric minimum ($q=0$). The complex elliptic geometry analytically collapses, yielding linear Regge trajectories. The translation zero-mode measure dynamically nullifies the transition amplitude of the massless scalar ghost, providing an explicit analytic mechanism for a purely gluonic mass gap. Anchoring parameter-free glueball trajectories to the string tension natively recovers the L"uscher intercept $α(0)=1/12$, yielding a macroscopic spectrum that provides a suggestive baseline for established PDG unassigned isoscalar candidates. |
| title | Geometric QCD III: Exact transition amplitudes and the glueball spectrum |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.02373 |