Universal Confining Strings: From Compact QED to the Hadron Spectrum
Abstract
We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological θ-term, in the dyon condensation phase, is described by a {\it massive} two-form field Bμν that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling, reached along a double-scaling renormalization trajectory on which the cutoff can be removed. This corresponds to a UV-complete quantum string in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the Bμν field, instead of living in a higher-dimensional space. Interestingly, it contains a world-sheet excitation, in addition to the Nambu-Goto phonons, whose nature depends on the sign of the string stiffness: for the negative stiffness favoured by lattice data it appears as a broad, overdamped mode rather than a sharp resonance, consistent with the broad phase shift seen in lattice SU(N) scattering data. On the other hand, we determine the confining potential and show that it reproduces a generalized Arvis potential V(L)= aL√(1−c/L2) with running parameters $a(L), c(L)$. With this, we compute the mass difference ratios for the heaviest quarkonium and find 2.5\% agreement with experiment already at the infrared fixed point, from a two-parameter fit of both the reduced quark mass and a boundary-condition parameter, to this fixed functional form. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value α0= 1/12. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.
Related
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BibTeX
@misc{diamantini2026universal,
title = {{Universal Confining Strings: From Compact QED to the Hadron Spectrum}},
author = {M. C. Diamantini and F. Quevedo and C. A. Trugenberger and L. Zapata},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.13791},
eprint = {2605.13791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.13791},
}
RIS
TY - UNPB
TI - Universal Confining Strings: From Compact QED to the Hadron Spectrum
AU - M. C. Diamantini
AU - F. Quevedo
AU - C. A. Trugenberger
AU - L. Zapata
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2605.13791
UR - https://arxiv.org/abs/2605.13791
AB - We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological θ-term, in the dyon condensation phase, is described by a {\it massive} two-form field B_μν that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling, reached along a double-scaling renormalization trajectory on which the cutoff can be removed. This corresponds to a UV-complete quantum string in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the B_μν field, instead of living in a higher-dimensional space. Interestingly, it contains a world-sheet excitation, in addition to the Nambu-Goto phonons, whose nature depends on the sign of the string stiffness: for the negative stiffness favoured by lattice data it appears as a broad, overdamped mode rather than a sharp resonance, consistent with the broad phase shift seen in lattice SU(N) scattering data. On the other hand, we determine the confining potential and show that it reproduces a generalized Arvis potential V(L)= aL√(1−c/L^2) with running parameters $a(L), c(L)$. With this, we compute the mass difference ratios for the heaviest quarkonium and find 2.5\% agreement with experiment already at the infrared fixed point, from a two-parameter fit of both the reduced quark mass and a boundary-condition parameter, to this fixed functional form. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value α_0= 1/12. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.
ER -