带角速度的大N矢量模型
The large $N$ vector model with angular velocity
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中文总结 AI 辅助
研究无单态约束的大N临界O(N)矢量模型在带角速度的S¹×S²上的自由能，解析确定主导高温行为，数值分析验证结果，发现自由能主导项在μ̂²r²=1处有极点，留数可通过pp波几何计算且与直接结果一致。
中文摘要 AI 辅助
我们研究了无单态约束的大N临界O(N)矢量模型在S¹×S²上的自由能，其中角速度为μ̂。我们在μ̂r=0和μ̂²r²=1这两种情况下，解析确定了主导高温行为，r为球面半径。我们补充了数值分析结果，该结果与两种区域下的解析展开式一致，且能在两者间平滑插值。自由能的主导高温贡献在μ̂²r²=1处出现极点，这与热有效场论的预期相符，其留数与无质量自由理论的留数一致。然而，次主导项对角速度表现出非解析依赖，使临界不动点结果区别于自由理论的答案。此外，我们可通过将O(N)模型置于pp波几何中得到该极点处的留数，且证明其与直接计算所得结果一致。
英文摘要
We study the free energy of a critical vector model at large $N$ on $S^{1}\times S^{2}$ with an angular velocity $\hatμ$ 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 $\hatμr=0$ and $\hatμ^{2}r^{2}=1$ 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 $\hatμ^{2}r^{2}=1$, 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 $\hatμr=0$ to its free fixed point at $\hatμ^2r^2=1$.
发表机构
- Centre for High Energy Physics, Indian Institute of Science（印度科学学院高能物理中心）
- Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论研究中心）
- Peng Huanwu Center for Fundamental Theory（彭桓武理论基础研究中心）
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