The large N vector model with angular velocity
Abstract
We study the free energy of a critical vector model at large N on S1× S2 with an angular velocity μ̂ without the singlet constraint. We study the model for which the large N dynamics is controlled by the uniform saddle point of the auxiliary field arising in the Hubbard-Stratanovich transformation. The leading high-temperature behaviour is determined analytically both as an expansion about μ̂r=0 and μ̂2r2=1 where r is the radius of the sphere. We supplement the analytic results with a numerical analysis that agrees with both the analytical expansions in their respective regimes and smoothly interpolates between them. The leading high-temperature contribution to the free energy develops a pole at μ̂2r2=1, in agreement with expectations from the thermal effective field theory. Its residue coincides with that of the massless free theory. Sub-leading terms, however, exhibit non-analytic dependence on the angular velocity and distinguish the critical fixed-point result from the free theory answer. The residue at the pole can also be obtained by placing the model on the pp-wave geometry. We show that the residue agrees with that obtained from the direct computation. The free energy of the model connects the non-trivial fixed point of the O(N) model at μ̂r=0 to its free fixed point at μ̂2r2=1.
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BibTeX
@misc{david2026large,
title = {{The large $N$ vector model with angular velocity}},
author = {Justin R. David and Srijan Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.31151},
eprint = {2608.31151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31151},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The large N vector model with angular velocity
AU - Justin R. David
AU - Srijan Kumar
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2608.31151
UR - https://arxiv.org/abs/2608.31151
AB - We study the free energy of a critical vector model at large N on S^1× S^2 with an angular velocity μ̂ without the singlet constraint. We study the model for which the large N dynamics is controlled by the uniform saddle point of the auxiliary field arising in the Hubbard-Stratanovich transformation. The leading high-temperature behaviour is determined analytically both as an expansion about μ̂r=0 and μ̂^2r^2=1 where r is the radius of the sphere. We supplement the analytic results with a numerical analysis that agrees with both the analytical expansions in their respective regimes and smoothly interpolates between them. The leading high-temperature contribution to the free energy develops a pole at μ̂^2r^2=1, in agreement with expectations from the thermal effective field theory. Its residue coincides with that of the massless free theory. Sub-leading terms, however, exhibit non-analytic dependence on the angular velocity and distinguish the critical fixed-point result from the free theory answer. The residue at the pole can also be obtained by placing the model on the pp-wave geometry. We show that the residue agrees with that obtained from the direct computation. The free energy of the model connects the non-trivial fixed point of the O(N) model at μ̂r=0 to its free fixed point at μ̂^2r^2=1.
ER -