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; 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偶尔是设置弦理论与基于点粒子的理论不同的对称性之一。它指出，在半径r圆上压实的弦理论等于在半径1/r圆上压实的另一个弦理论。这表明弦理论要求我们用一种新的几何形状代替一般相对性的基本几何形状，为此，存在各种工作建议。虽然对空间维度的T偶对性有充分的理解，但T二维的转换相对于时间样的维度也是可能的，并且导致了新的外来弦理论，这可能具有某些字段的非标准动力学术语，或者是非标准的时间次数。了解这些异国情调的弦理论的状态对于理解弦理论从根本上是什么是至关重要的，以及哪种类型的几何形状应取代riemannian几何形状。将解决方案嵌入弦理论将用于研究其升力至10和11维度。通过确定解决方案的基本成分，从D-BRANES，EUCLIDEAN BRANES和其他弦乐器方面，可以确定基本的显微镜自由度。这将允许将来自四维解的热力学分区功能与统计分区函数相关联。该项目中使用的方法将超级和弦理论的方法与差异几何形状相结合。旨在使T偶偶性成为明显的几何对称性的几何形式主义，例如翻倍和异常的几何形状将在全球范围内研究黑洞和宇宙学的空间。一个特别有趣的问题是，如何将视野映射到其他类型的界面，以及是否通过刺激效果消除了某些奇异性。可以使用加倍和特殊场理论的形式主义来构建弦乐有效的超级重力理论，这些理论显然在弦上二重性下是不变的。该项目的另一个目的是研究五个维度和四个维度中最大超级最大超级的特殊表述是否可以始终如一地截断为n = 2个超级重力。这将深入了解这些框架是否可以更广泛地应用于非最大的超对称弦线压缩。研究这些形式主义是否可以为黑洞和宇宙时空几何形状提供新的见解将很有趣。由于II型双场理论自然包含II*超级重力，因此自然的起点是研究T偶偶性对非超级杀戮视野和奇异性的作用。要研究的另一点是如何以para-hermitian几何形状来描述黑洞和宇宙学的两倍时间。