Brane Universality Classes in non-Minimal String Theory

非最小弦理论中的膜普遍性类

• 批准号: 1734476
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1734476
• 关键词: Brane; Universality; Classes; non; Minimal

In this work non-minimal strings are defined through the world sheet picture to be Liouville gravity plus matter content which is non-minimal conformal. By contrast with minimal strings, whose boundary states - equivalently branes - have been thoroughly studied there are many unanswered questions when the matter has an extended algebra and there are extra conserved currents in the bulk system. Typically it appears that branes are classified by whether or not these extra currents are conserved at the boundary (ie by the brane) - of course the stress-tensor itself is always conserved to keep the particle content massless. Those branes that have the same current conservation structure are known in some cases to exhibit Seiberg-Shih equivalence (SSE). In work with previous STFC funded graduate student, Ben Niedner, we established that in the simplest case of a single extra current (the matter is essentially the critical point excitations of a Q=3 Potts model) there is a natural holomorphic structure which underlies the SSE and that this structure exists regardless of regularisation (it was constructed explicitly in terms of the planar random graph and spin-system formulation of Liouville gravity coupled to matter).In this project we will do two things. Firstly we will explore the boundary renormalization flows in the previously established holomorphic structure perturbed by the appropriate operators and examine whether the behaviour is consistent with the boundary c-theorem. This involves extending the calculations that lead to the holomorphic structure to include the perturbations which essentially take the form of generalised boundary magnetic fields. It is not clear whether these flows between fixed points sustain the holomorphic structure, although recent work on the simplest case suggests that they do. The second phase of the project will explore whether the holomorphic structure generalises to other cases of an extended system of conserved currents. Essentially we are investigating whether the possible sets of SSEs can be regarded as being classified by the possible holomorphic structures. Clearly to establish this in more generality would be a very clean way of understanding the relationships between the possible boundary states of these systems.

本文通过世界片图定义了非最小弦为刘维尔引力加物质含量，它是非最小共形的。与最小弦相比，它的边界状态--等价于膜--已经得到了彻底的研究，当物质具有扩展的代数并且在体系统中有额外的守恒流时，还有许多问题没有回答。典型的情况是，膜是根据这些额外的电流在边界（即膜）是否守恒来分类的--当然，应力张量本身总是守恒的，以保持粒子内容无质量。那些具有相同的当前守恒结构的膜在某些情况下表现出Seiberg-Shih等价（SSE）。在与以前的STFC资助的研究生，本Niedner，我们已经确定，在最简单的情况下，（问题本质上是一个Q=3波茨模型的临界点激发）有一个自然的全纯结构，它是SSE的基础，这个结构存在，不管正则化（它是根据平面随机图和耦合到物质的刘维尔引力的自旋系统公式明确构造的）。首先，我们将探讨边界重整化流在以前建立的全纯结构扰动适当的运营商和检查是否符合边界c定理的行为。这涉及到扩展的计算，导致全纯结构，包括基本上采取广义边界磁场的形式的扰动。目前还不清楚这些固定点之间的流动是否维持全纯结构，尽管最近对最简单情况的研究表明它们是这样的。该项目的第二阶段将探讨全纯结构是否推广到守恒流扩展系统的其他情况。从本质上讲，我们正在研究是否可以被视为是由可能的全纯结构分类的可能的SSE集。显然，更普遍地建立这一点，将是理解这些系统的可能边界状态之间关系的一种非常清晰的方式。