Singlet sector of the vector model with angular potential
Abstract
We study the singlet sector of large-N, O(N) vector model on S1β× S2r in presence of an angular potential Ω. We compute the free energy of the model both at the free fixed point as well as the non-trivial fixed point. The model undergoes a phase transition when the temperature T and angular potential attain the relation T2r2∼ N (1−ω2), where ω=rΩ and r is the radius of S2, with Tr≫1, at both the fixed points, with different numerical coefficients. The transition was studied earlier at zero angular potential at Tr∼ √N. The holonomy eigenvalue distribution, having support on the full circle below the transition, develops a gap above it, called the Gross-Witten-Wadia transition. The angular potential introduces an additional parameter to such a transition, tuning it, the transition can occur even at a fixed temperature. We show that for the free model transition can occur as 1−ω2∼ 1/N while Tr∼ O(1). For the interacting model the computation is performed at a limit Tr≫1, thus we show the same at a large but fixed temperature which does not scale as √N. In the ungapped phase, the free energy exhibits a double pole near ω2=1 for both the fixed points. This is possibly due to the fact that the theory projected onto the singlets is non-local and therefore need not obey the leading simple pole scaling of a local thermal effective action.
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BibTeX
@misc{kumar2026singlet,
title = {{Singlet sector of the vector model with angular potential}},
author = {Srijan Kumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09815},
eprint = {2610.09815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09815},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singlet sector of the vector model with angular potential
AU - Srijan Kumar
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09815
UR - https://arxiv.org/abs/2610.09815
AB - We study the singlet sector of large-N, O(N) vector model on S^1_β× S^2_r in presence of an angular potential Ω. We compute the free energy of the model both at the free fixed point as well as the non-trivial fixed point. The model undergoes a phase transition when the temperature T and angular potential attain the relation T^2r^2∼ N (1−ω^2), where ω=rΩ and r is the radius of S^2, with Tr≫1, at both the fixed points, with different numerical coefficients. The transition was studied earlier at zero angular potential at Tr∼ √N. The holonomy eigenvalue distribution, having support on the full circle below the transition, develops a gap above it, called the Gross-Witten-Wadia transition. The angular potential introduces an additional parameter to such a transition, tuning it, the transition can occur even at a fixed temperature. We show that for the free model transition can occur as 1−ω^2∼ 1/N while Tr∼ O(1). For the interacting model the computation is performed at a limit Tr≫1, thus we show the same at a large but fixed temperature which does not scale as √N. In the ungapped phase, the free energy exhibits a double pole near ω^2=1 for both the fixed points. This is possibly due to the fact that the theory projected onto the singlets is non-local and therefore need not obey the leading simple pole scaling of a local thermal effective action.
ER -