发表机构
Sun Yat-sen University; Aristotle University of Thessaloniki（中山大学; 塞萨洛尼基亚里士多德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用质量参数 $m$ 诊断奇数维热两点函数临界点，通过维度提升将关联函数映射到高阶导数理论，并识别热 CFT 条件。
AI 中文摘要
我们探索了质量参数 $m$ 可作为诊断工具的想法，用于识别奇数 $d$ 维中大量自由标量场热两点函数的临界点。对于 $m$ 的一般值，这些关联函数允许展开为与具有确定标度维度的对称无迹算子相关的热共形块。对于每个自旋，高扭曲贡献可以重求和为前导扭曲系数的闭式 dressing 因子。在 $m$ 的特殊值下，当能量-动量张量的热迹消失时，它们被识别为热 CFT 的两点函数。通过适用于所有 $m$ 的维度提升，我们将这些关联函数映射到 $d+2$ 维中高阶导数大质量理论的热两点函数。我们证明了 $d+2$ 维理论能量-动量张量的热迹与原始 $d$ 维理论的自由能成正比。当该热迹在 $m\ eq 0$ 时消失，提升后的关联函数被识别为高阶导数非幺正热 CFT$_{d+2}$ 的两点函数，但它们不同于原始幺正 CFT$_d$ 的提升非平凡热两点函数。
英文摘要
We explore the idea that the mass parameter $m$ can be used as a diagnostic tool for identifying the critical points of thermal two-point functions of massive free scalar fields in odd $d$ dimensions. For general values of $m$ these correlators admit an expansion in thermal conformal blocks associated with symmetric traceless operators of definite scaling dimension. For each spin the higher-twist contributions can be resummed into a closed-form dressing factor of the leading-twist coefficient. At special values of $m$ for which the thermal trace of the energy-momentum tensor vanishes they are identified as two-point functions of thermal CFTs. Through a dimensional uplift, valid for all $m$, we map these correlators to thermal two-point functions of higher-derivative massive theories in $d+2$ dimensions. We show that the thermal trace of the energy-momentum tensor of the $d+2$-dimensional theory is proportional to the free energy of the original $d$-dimensional theory. When that thermal trace vanishes for $m\neq 0$ the uplifted correlators are identified as two-point functions of a higher-derivative nonunitary thermal CFT$_{d+2}$, but they differ from the uplifted nontrivial thermal two-point functions of the original unitary CFT$_d$.
Comments29 pages, 1 figure
