Extended operators in conformal field theories and the quantum M2-brane.

共形场论和量子 M2 膜中的扩展算子。

• 批准号: 2607349
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2607349
• 关键词: Extended; operators; conformal; field; theories

M2 branes in asymptotically AdS space can describe extended operators in the conformal field theory at the boundary via the AdS/CFT duality. We utilise this description to study extended operators at the semiclassical level.We study M2-branes in asymptotically AdS7 space, which describe surface operators in the (2,0) 6d CFT. By computing the divergence in their semiclassical partition function, we obtain the conformal anomaly for a large class of supersymmetric surface operators directly from their holographic description, matching indirect results for the anomaly in the literature.We aim to extend this to M2-branes dual to non-supersymmetric surface operators (where the M2-brane satisfy Neumann conditions) and ones with non-trivial R-symmetry breaking pattern.We also study M2-branes in AdS4, which describe vortex and Wilson loops in ABJM theory. We use this description to compute the expectation value of 1/2 and 1/3 BPS vortex loops beyond the classical limit. We are also working on computing correlation functions of operators on vortex loops using the holographic description. In particular, we focus on exactly marginal operators on the vortex loop. This involves computing Witten diagrams on the M2-brane involving these marginal operators at the boundary. We also use the bootstrap approach to study the correlation functions, which should confirm our holographic results.The tools we develop for the study of M2-brane partition functions' divergences can be applied to other branes in asymptotically AdS space, also representing extended operators in CFTs. In particular, we aim to find the near-boundary classical description of D3-branes representing surface operators in N=4 SYM, and use it to compute the classical anomaly for these surface operators.

渐近AdS空间中的M2膜可以通过AdS/CFT对偶来描述边界上共形场论中的扩展算子。我们利用这个描述来研究半经典水平上的扩展算子，我们研究了渐近AdS 7空间中的M2-膜，它描述了（2，0）6dCFT中的曲面算子。通过计算它们的半经典配分函数中的散度，我们直接从全息描述中得到了一大类超对称曲面算子的共形反常，匹配文献中异常的间接结果，我们的目标是将其推广到非超对称曲面算子的M2-膜对偶（其中M2-膜满足Neumann条件）和具有非平凡R-对称破缺模式的M2-膜，我们还研究了AdS 4中的M2-膜，它们描述了ABJM理论中的涡旋和Wilson环。我们用这个描述计算了超过经典极限的1/2和1/3BPS涡环的期望值。我们也在使用全息描述计算涡旋环上算子的相关函数。特别是，我们专注于边缘算子的涡循环。这涉及到计算M2-膜上的维滕图，其中包括边界上的这些边缘算子。我们还使用bootstrap方法研究了相关函数，这证实了我们的全息结果.我们为研究M2-膜配分函数的发散性所开发的工具可以应用于渐近AdS空间中的其他膜，也可以代表CFTs中的扩展算子.特别是，我们的目标是找到代表N=4 SYM中的表面算子的D3-膜的近边界经典描述，并使用它来计算这些表面算子的经典异常。