AI 中文总结
本研究利用亏格二把手体与极值共形场理论的对偶性，通过庞加莱构造解析确定其OPE密度的一阶和二阶修正，证实亏格二时仍存在亏格一的OPE密度负性病态，并分析其急剧转变特性。
AI 中文摘要
在本研究中，我们利用亏格二把手体与极值共形场理论（extremal conformal field theories）的对偶性，计算其算子乘积展开（operator product expansion, OPE）密度。借助庞加莱构造（Poincaré construction），我们通过配分函数的直接反演，解析确定了亏格二OPE密度在捏合参数中的一阶和二阶修正项。作为一致性检验，我们在同一庞加莱框架内计算了亏格一密度，发现其与光锥自举分析（lightcone bootstrap analysis）得到的结果完全吻合。已知在亏格一情形下，极值共形场理论的OPE密度在刚好高于黑洞阈值的态上会出现负性病态；我们证明，尽管存在非平凡反演核，该病态在亏格二时仍持续存在，具体表现为，自旋j_i为奇、偶的态对应的OPE密度，在黑洞阈值上方极窄带内仍保持为负。我们进一步分析了OPE密度沿其取值为零的曲线，从极大正值向极大负值的急剧转变。
英文摘要
In this work, we compute the operator product expansion density for the genus-two handlebody by exploiting its duality with extremal conformal field theories arXiv:0710.2129. Using a Poincaré construction, we analytically determine the first- and second-order corrections in the pinching parameter to the genus-two OPE density through a direct inversion of the partition function. As a consistency check, we also compute the genus-one density within the same Poincaré framework and find perfect agreement with the result obtained from the lightcone bootstrap analysis arXiv: 1906.04184. It is known that, at genus one, the OPE density of extremal CFTs exhibits a negativity pathology for states lying just above the black-hole threshold. We show that this pathology continues to persist at genus two, despite the emergence of a nontrivial inversion kernel. In particular, the OPE density associated with states of both odd and even spin $j_i$ remains negative within a very narrow band above the black-hole threshold. We further analyze the sharp transition from large positive to large negative values of the OPE density across a curve along which the density vanishes.
Comments52 pages, 10 figures, 3 tables
