AI 中文总结
研究利用有效场论方法计算纯四维\(\mathcal{N}=2\)超对称杨-米尔斯理论在有限温度下\(t\)胡夫特耦合\(\lambda\)到二阶的弱耦合自由能密度，通过特定计算得到贡献，该理论渐近自由，展开式重现部分结果且有新的\(\lambda^2\)阶项。
AI 中文摘要
我们使用有效场论方法，在有限温度下计算了纯四维\(\mathcal{N}=2\)超对称杨-米尔斯（SYM）理论在\(t\)胡夫特耦合\(\lambda\)下到二阶的弱耦合自由能密度。硬标度\(T\)的贡献来自完整理论中的无质量三圈真空图，电标度\(\sqrt{\lambda}T\)的贡献来自降维三维有效理论中的两圈计算。与\(\mathcal{N}=4\) SYM不同，该理论是渐近自由的，耦合重整化反项与EFT单位算符反项抵消了所有\(1/\epsilon\)极点。剩余的重整化标度依赖性由一圈贝塔函数确定。该展开式重现了到\(\lambda^{3/2}\)阶的早期结果，\(\lambda^2\)阶项是新的。
英文摘要
We compute the weak-coupling free energy density of pure four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory through second order in the 't Hooft coupling $λ$ at finite temperature using effective-field-theory methods. The contribution from the hard scale $T$ is obtained from massless three-loop vacuum diagrams in the full theory, and that from the electric scale $\sqrtλ\,T$ from a two-loop calculation in the dimensionally reduced three-dimensional effective theory. In contrast to $\mathcal{N}=4$ SYM, the theory is asymptotically free: the coupling-renormalization counterterm, together with the EFT unit-operator counterterm, cancels all $1/ε$ poles. The remaining renormalization-scale dependence is fixed by the one-loop beta function. The expansion reproduces earlier results through order $λ^{3/2}$, and the order-$λ^2$ term is new.
Comments13 pages, 9 figures. This work extends the finite-temperature N=4 SYM calculations of arXiv:2105.02101 and arXiv:2111.12160 to pure N=2 SYM. Reproduced diagram figures are identified and attributed in their captions
