arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2105.02101hep-thhep-phnucl-th
收藏

${\cal N}=4$超对称Yang-Mills热力学到有序$λ^2$

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $λ^2$

Qianqian Du, Michael Strickland, Ubaid Tantary

备注：
28 pages, 8 figures; v3: fix to soft contribution and final result, misc typos fixed, conclusions unchanged
发表信息：
J. High Energ. Phys. 2021, 64 (2021)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

在有限温度和零化学势条件下，通过t Hooft耦合${\cal N}=4$的二阶微扰计算了四维超对称Yang-Mills体系（$\text{SYM}_{4,4}$）的微扰自由能.我们的最终结果是紫外有限的和所有的红外发散产生的三圈水平上的$\text{SYM}_{4,4}$环图的总和被取消。${\cal O}(λ^{3/2}) $和$ {\cal O}(λ^2 \logλ)$处的非解析项通过修饰$A_0$和标量传播子来生成。规范场德拜质量$m_D$和标量热质量$M$由它们相应的有限温度自能确定。在此基础上，我们得到了$\text{SYM}_{4,4}$到${\cal O}(λ^2)$的三圈热力学函数。我们比较我们的最终结果与先前的结果中得到的弱耦合和强耦合的限制，并构造一个广义Padé逼近，弱耦合的结果和大PDMATHAMV强耦合的结果之间的插值。我们的结果表明，${\cal O}(λ^2)$弱耦合的标度熵密度的结果是一个定量可靠的近似$0 \leq λ\lesssim 2$的标度熵密度。

英文摘要：

We calculate the resummed perturbative free energy of ${\cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions ($\text{SYM}_{4,4}$) through second order in the 't Hooft coupling $λ$ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over $\text{SYM}_{4,4}$ ring diagrams. Non-analytic terms at ${\cal O}(λ^{3/2}) $ and $ {\cal O}(λ^2 \logλ)$ are generated by dressing the $A_0$ and scalar propagators. The gauge-field Debye mass $m_D$ and the scalar thermal mass $M$ are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of $\text{SYM}_{4,4}$ to ${\cal O}(λ^2)$. We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-$N_c$ strong-coupling result. Our results suggest that the ${\cal O}(λ^2)$ weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for $0 \leq λ\lesssim 2$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑