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.

渐近广告空间中的M2晶体可以通过ADS/CFT偶性在边界的保形场理论中描述扩展的算子。我们利用此描述来研究半经典级别的扩展运算符。我们在渐近的ADS7空间中研究M2溴，该空间描述了（2,0）6D CFT中的表面算子。 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-与对称性破坏模式。我们还研究ADS4中的M2-branes，其中描述了ABJM理论中的涡旋和Wilson循环。我们使用此描述来计算超出经典限制的1/2和1/3 bps涡流循环的期望值。我们还在使用全息描述来计算操作员在涡旋循环上的相关功能。特别是，我们专注于涡旋循环上的边缘运算符。这涉及在M2-Brane上计算涉及这些边界运算符的M2-Brane图。我们还使用自举方法来研究相关函数，这应该确认我们的全息结果。我们为M2-Brane分区函数的研究开发的工具可以应用于渐近ADS空间中的其他Branes，也可以代表CFT中的扩展操作员。特别是，我们旨在找到代表n = 4 sym中表面算子的D3烧烤的近似经典描述，并使用它来计算这些表面算子的经典异常。