| dc.identifier.uri | http://hdl.handle.net/11401/76720 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | Supersymmetry has been fruitful source of new Physics and Mathematics advancement. In particular, supersymmetric theories on curved manifolds often leads to very interesting connections between integrable geometry and supersymmetric physical quantities. In this dissertation, we summarize the author’s recent work on 5d N = 1 supersymmetric theories on curved 5d Riemannian manifolds and its relation to contact geometry, which is the odd- dimensional counterpart of symplectic geometry in even dimension. We will discuss the geometric implications of the Killing spinor equations derived from the rigid limit of 5d N = 1 supergravity. Combining with the dilatino equations, we see that a large class of supersymmetric backgrounds are transversal holomorphic foliations. With these, we go on to discuss the Higgs branch localization of N = 1 theories on K-contact manifolds, in which case we discover that the BPS solutions are generalized Seiberg-Witten equations on K-contact manifolds. These solutions are in one-to-one correspondence with the poles of the Coulomb branch 1-loop determinant. Finally we will discuss the properties of contact instantons that arise from Coulomb branch localization of N = 1 theories. | |
| dcterms.abstract | Supersymmetry has been fruitful source of new Physics and Mathematics advancement. In particular, supersymmetric theories on curved manifolds often leads to very interesting connections between integrable geometry and supersymmetric physical quantities. In this dissertation, we summarize the author’s recent work on 5d N = 1 supersymmetric theories on curved 5d Riemannian manifolds and its relation to contact geometry, which is the odd- dimensional counterpart of symplectic geometry in even dimension. We will discuss the geometric implications of the Killing spinor equations derived from the rigid limit of 5d N = 1 supergravity. Combining with the dilatino equations, we see that a large class of supersymmetric backgrounds are transversal holomorphic foliations. With these, we go on to discuss the Higgs branch localization of N = 1 theories on K-contact manifolds, in which case we discover that the BPS solutions are generalized Seiberg-Witten equations on K-contact manifolds. These solutions are in one-to-one correspondence with the poles of the Coulomb branch 1-loop determinant. Finally we will discuss the properties of contact instantons that arise from Coulomb branch localization of N = 1 theories. | |
| dcterms.available | 2017-09-20T16:51:03Z | |
| dcterms.contributor | Nieuwenhuizen, Peter | en_US |
| dcterms.contributor | Rocek, Martin | en_US |
| dcterms.contributor | McCarthy, Robert | en_US |
| dcterms.contributor | Sun, Song | en_US |
| dcterms.contributor | Rocek, Martin. | en_US |
| dcterms.creator | Pan, Yiwen | |
| dcterms.dateAccepted | 2017-09-20T16:51:03Z | |
| dcterms.dateSubmitted | 2017-09-20T16:51:03Z | |
| dcterms.description | Department of Physics. | en_US |
| dcterms.extent | 112 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76720 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:51:03Z (GMT). No. of bitstreams: 1
Pan_grad.sunysb_0771E_12453.pdf: 854423 bytes, checksum: cca019b301c8d946f471548ffdf621d0 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | geometry, supersymmetry | |
| dcterms.subject | Physics | |
| dcterms.title | 5d Supersymmetry and Contact Geometry | |
| dcterms.type | Dissertation | |
