Generalised Geometric Structures in String Theory

在弦理论中，额外的时空维度被卷曲在一个小的内部空间中。物理预测，如粒子的光谱，很大程度上取决于内部空间的选择，因此理解可能的内部空间，提供一致的字符串背景是一个重要的问题。合理的物理限制导致了丰富的可能的内部几何类型，具有深刻的数学结构，导致了数学和物理之间富有成效的相互作用，从而导致了双方的重要结果和理解。这项研究的目的是将其扩展到发现和研究更广泛的内部空间，包括那些有通量的和那些没有传统几何形状的空间，因为最近的发展表明，有一个深层的潜在结构涉及数学中的新思想。非常规几何实际上可能在弦理论中是通用的，研究它们将为弦理论的本质提供超越通常应用的场论近似的新见解。

In string theory, extra dimensions of spacetime are curled up in a small internal space. Physical predictions, such as the spectrum of particles, are largely determined by the choice of internal space, so that understanding the possible internal spaces that give consistent string backgrounds is an important question. Reasonable physical restrictions lead to a rich class of possible internal geometries with a deep mathematical structure that has led to a productive interplay between mathematics and physics that has led to important results and understanding on both sides. The aim of the research is to extend this to find and study a wider class of internal spaces, including those with fluxes and those which do not have conventional geometries, as recent developments suggest that there is a deep underlying structure that involves new ideas in mathematics. The non-conventional geometries may in fact be generic in string theory, and studying them will provide new insights into the nature of string theory that go beyond the field theory approximation that is often applied.