A Generalized Landau-Ginzburg/Gromov-Witten Correspondence.
dc.contributor.author | Acosta, Pedro | en_US |
dc.date.accessioned | 2015-09-30T14:24:00Z | |
dc.date.available | NO_RESTRICTION | en_US |
dc.date.available | 2015-09-30T14:24:00Z | |
dc.date.issued | 2015 | en_US |
dc.date.submitted | en_US | |
dc.identifier.uri | https://hdl.handle.net/2027.42/113514 | |
dc.description.abstract | The celebrated Landau-Ginzburg/Calabi-Yau correspondence asserts that the Gromov-Witten theory of a Calabi-Yau hypersurface in weighted projective space is equivalent to its corresponding FJRW-theory via analytic continuation. It is well known that this correspondence fails in non-Calabi-Yau cases. The main obstruction is a collapsing or dimensional reduction of the state space of the Landau-Ginzburg model in the Fano case, and a similar collapsing of the state space of Gromov-Witten theory in the general type case. We state and prove a modified version of the cohomological correspondence that describes this collapsing phenomenon at the level of state spaces. This result confirms a physical conjecture of Witten-Hori-Vafa. The main purpose of this thesis is to provide a quantum explanation for the collapsing phenomenon. A key observation is that the corresponding Picard-Fuchs equation develops irregular singularities precisely at the points where the collapsing occurs. Our main idea is to replace analytic continuation with asymptotic expansion in this non-Calabi-Yau setting. The main result of this article is that the reduction in rank of the Gromov-Witten I-function due to power series asymptotic expansions matches precisely the dimensional reduction of the corresponding state space. Furthermore, asymptotic expansion under a different asymptotic sequence yields a different I-function which can be considered as the mathematical counterpart to the additional "massive vacua" of physics. | en_US |
dc.language.iso | en_US | en_US |
dc.subject | Gromov-Witten theory | en_US |
dc.subject | LG/CY correspondence | en_US |
dc.subject | FJRW theory | en_US |
dc.title | A Generalized Landau-Ginzburg/Gromov-Witten Correspondence. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.contributor.committeemember | Ruan, Yongbin | en_US |
dc.contributor.committeemember | Pando Zayas, Leopoldo A. | en_US |
dc.contributor.committeemember | Jarvis, Tyler J. | en_US |
dc.contributor.committeemember | Smith, Karen E. | en_US |
dc.contributor.committeemember | Fulton, William | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/113514/1/peacosta_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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