D-branes and K-homology
| dc.contributor.author | Jia, Bei | en |
| dc.contributor.committeechair | Haskell, Peter E. | en |
| dc.contributor.committeemember | Floyd, William J. | en |
| dc.contributor.committeemember | Linnell, Peter A. | en |
| dc.contributor.committeemember | Sharpe, Eric R. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T20:34:36Z | en |
| dc.date.adate | 2013-06-03 | en |
| dc.date.available | 2014-03-14T20:34:36Z | en |
| dc.date.issued | 2013-04-19 | en |
| dc.date.rdate | 2013-06-03 | en |
| dc.date.sdate | 2013-04-29 | en |
| dc.description.abstract | 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. | en |
| dc.description.degree | Master of Science | en |
| dc.identifier.other | etd-04292013-182032 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-04292013-182032/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/32039 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | Jia_B_T_2013_R1.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | D-brane | en |
| dc.subject | K-theory | en |
| dc.subject | K-homology | en |
| dc.subject | String theory | en |
| dc.title | D-branes and K-homology | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |
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