Duality Invariant Supergravity, String Geometry and Global Properties of T-Duality in arbitrary Dimension and Signature

任意维度和签名中的对偶不变超引力、弦几何和T-对偶的全局性质

• 批准号: 2751314
• 金额: --
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2751314
• 关键词: Duality; Invariant; Supergravity; String; Geometry

T-duality is one of the symmetries that sets string theory apart from theories based on point particles. It states that a string theory compactified on a circle of radius R is equivalent to another string theory compactified on a circle of radius 1/R. This shows that string theory requires us to replace the Riemannian geometry underlying general relativity with a new type of geometry, for which various working proposals exist. While T-duality with respect to spatial dimensions is well understood, T-duality transformations with respect to time-like dimensions are also possible and lead to new exotic string theories, which can have non-standard kinetic terms for some of the fields, or a non-standard number of time-like dimensions. Understanding the status of these exotic string theories is crucial for understanding what string theory fundamentally is, and what type of geometry should replace Riemannian geometry.The embedding of solutions into string theory will be used to study their lifts to 10 and 11 dimensions. By identifying the fundamental constituents of solutions in terms of D-branes, Euclidean branes and other string solitons, the underlying microscopic degrees of freedom will be identified. This will allow to relate the thermodynamic partition functions derived from four-dimensional solutions with statistical partition functions.The methods used in this project combine those of supergravity and string theory with differential geometry. Geometrical formalisms which aim at making T-duality a manifestly geometrical symmetry, such as doubled and exceptional geometry will be adapted to study black holes and cosmological spacetimes globally. A particularly interesting question is how horizons get mapped to other types of interfaces, and whether some singularities are removed by stringy effects. The formalism of doubled and exceptional field theory can be used to build string-effective supergravity theories which are manifestly invariant under string dualities. Another objective of this project is to investigate whether the exceptional formulations of maximal supergravities in five and four dimensions can be consistently truncated to N=2 supergravities. This will give insight into whether these frameworks can be applied more broadly to non-maximally supersymmetric string compactifications. It would be interesting to study whether these formalisms can provide new insights into black hole and cosmological space-time geometries. Since type-II double field theory naturally includes type-II* supergravity, a natural starting point is to investigate the action of T-duality on non-extremal Killing horizons and on singularities. Another point to investigate is how doubled spacetimes describing black holes and cosmologies can be characterised in terms of para-Hermitian geometry.

T 对偶性是使弦理论有别于基于点粒子的理论的对称性之一。它指出，在半径为 R 的圆上压缩的弦理论等价于在半径 1/R 的圆上压缩的另一个弦理论。这表明弦理论要求我们用一种新型几何取代广义相对论背后的黎曼几何，对此存在各种工作建议。虽然关于空间维度的 T 对偶性已被很好地理解，但关于类时间维度的 T 对偶变换也是可能的，并导致新的奇异弦理论，该理论可能对某些场具有非标准动力学项，或者非标准数量的类似时间的维度。了解这些奇异弦理论的现状对于理解弦理论的本质以及什么类型的几何应该取代黎曼几何至关重要。将解决方案嵌入到弦理论中将用于研究它们向 10 维和 11 维的升力。通过识别 D 膜、欧几里得膜和其他弦孤子解的基本组成部分，将识别潜在的微观自由度。这将允许将从四维解导出的热力学配分函数与统计配分函数联系起来。该项目中使用的方法将超重力和弦理论与微分几何相结合。旨在使 T 对偶性成为明显的几何对称性的几何形式主义，例如双重几何和特殊几何，将适用于全球范围内的黑洞和宇宙时空研究。一个特别有趣的问题是视界如何映射到其他类型的界面，以及某些奇点是否被弦效应消除。双重场论和例外场论的形式主义可用于构建弦有效超引力理论，该理论在弦对偶性下明显不变。该项目的另一个目标是研究五维和四维最大超重力的特殊公式是否可以一致地截断为 N=2 超重力。这将深入了解这些框架是否可以更广泛地应用于非最大超对称字符串压缩。研究这些形式主义是否可以为黑洞和宇宙时空几何提供新的见解将会很有趣。由于 II 型双场理论自然包括 II 型* 超引力，因此一个自然的起点是研究 T 对偶性对非极值杀伤视界和奇点的作用。另一点需要研究的是如何用准厄米几何来描述描述黑洞和宇宙学的双时空。