Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion
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arXiv
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2026
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| _version_ | 1866914512474472448 |
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| author | Hamada, Yudai Misumi, Tatsuhiro |
| author_facet | Hamada, Yudai Misumi, Tatsuhiro |
| contents | We numerically investigate whether the center-symmetric confined phase of large-$N$ $SU(N)$ gauge theory with one adjoint Dirac fermion persists under spatial compactification on $\mathbb{R}^3 \times S^1$. To this end, we employ a partially reduced twisted Eguchi-Kawai (TEK) model on a $1^3 \times L_4$ lattice with an adjoint Wilson fermion, and measure both the Polyakov loop around $S^1$ and order parameters for volume independence in the reduced directions. For $N=36$, $L_4=2$, $b=0.30\text{-}0.46$, and $κ=0.03\text{-}0.16$, we find that, with periodic boundary conditions, the Polyakov loop remains near zero in the light-fermion regime as the circle size is reduced. For the modified twist, the volume-independence order parameters are also consistent with zero in the explored region, supporting the validity of the partially reduced description. These results provide numerical evidence, within the reduced-model setup and parameter range studied, for an adiabatic-continuity scenario in which the confined phase is smoothly connected between large and small circles. By contrast, with antiperiodic boundary conditions, the Polyakov loop exhibits a clear deconfinement transition. We also discuss how this scenario is compatible with the anomaly constraints of the underlying four-dimensional theory. The symmetric twist is examined as a useful comparison, although its volume-independence properties appear less robust at the present value of $N$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion Hamada, Yudai Misumi, Tatsuhiro High Energy Physics - Lattice High Energy Physics - Theory We numerically investigate whether the center-symmetric confined phase of large-$N$ $SU(N)$ gauge theory with one adjoint Dirac fermion persists under spatial compactification on $\mathbb{R}^3 \times S^1$. To this end, we employ a partially reduced twisted Eguchi-Kawai (TEK) model on a $1^3 \times L_4$ lattice with an adjoint Wilson fermion, and measure both the Polyakov loop around $S^1$ and order parameters for volume independence in the reduced directions. For $N=36$, $L_4=2$, $b=0.30\text{-}0.46$, and $κ=0.03\text{-}0.16$, we find that, with periodic boundary conditions, the Polyakov loop remains near zero in the light-fermion regime as the circle size is reduced. For the modified twist, the volume-independence order parameters are also consistent with zero in the explored region, supporting the validity of the partially reduced description. These results provide numerical evidence, within the reduced-model setup and parameter range studied, for an adiabatic-continuity scenario in which the confined phase is smoothly connected between large and small circles. By contrast, with antiperiodic boundary conditions, the Polyakov loop exhibits a clear deconfinement transition. We also discuss how this scenario is compatible with the anomaly constraints of the underlying four-dimensional theory. The symmetric twist is examined as a useful comparison, although its volume-independence properties appear less robust at the present value of $N$. |
| title | Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.17848 |