D-branes and K-homology
D-branes and K-homology
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D-膜和K-同源性
DOI：
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发表时间：
2013
期刊：
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通讯作者：
B. Jia
中科院分区：
文献类型：
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作者：
B. Jia
本文考察了弦理论中时空流形X的拓扑K-同调群与弦理论中D-膜之间的密切关系。$K$-同调群的一个元素由$K$-圈$[M，E，\phi]$的等价类给出，其中$M$是闭自旋$^c$流形，$E$是$M$上的复向量丛，$\phi：M\rightarrow X$是连续映射。本文提出了一个$K$-圈$[M，E，\phi]$表示一个D-膜结构包裹子空间$\phi（M）$。因此，由$[M，E，\phi]$定义的$K$-同调元表示一类具有相同物理电荷的D-膜构型。此外，D-膜的$K$-循环表示类似于现代描述基本弦的方式，其中弦被表示为二维表面，其映射到时空流形。D-膜的这种分类也暗示了物理解释包裹时空奇异子空间的D-膜的可能性，扩大了弦理论可以科普的已知奇异性类型。
In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,\phi]$ represents a D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.