Strominger’s system on non-Kähler hermitian manifolds
<p>In this thesis, we investigate the Strominger system on non-Kähler manifolds.</p><p>We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holo...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
2011
|
| Subjects: |
| _version_ | 1826298439328071680 |
|---|---|
| author | Lee, H |
| author2 | de la Ossa, X |
| author_facet | de la Ossa, X Lee, H |
| author_sort | Lee, H |
| collection | OXFORD |
| description | <p>In this thesis, we investigate the Strominger system on non-Kähler manifolds.</p><p>We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³).</p><p>We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08].</p><p>Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.</p> |
| first_indexed | 2024-03-07T04:46:51Z |
| format | Thesis |
| id | oxford-uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:46:51Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef2022-03-27T08:12:20ZStrominger’s system on non-Kähler hermitian manifolds Thesishttp://purl.org/coar/resource_type/c_db06uuid:d3956c4f-c262-4bbf-8451-8dac35f6abefDifferential geometryPartial differential equationsEnglishOxford University Research Archive - Valet2011Lee, Hde la Ossa, X<p>In this thesis, we investigate the Strominger system on non-Kähler manifolds.</p><p>We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³).</p><p>We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08].</p><p>Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.</p> |
| spellingShingle | Differential geometry Partial differential equations Lee, H Strominger’s system on non-Kähler hermitian manifolds |
| title | Strominger’s system on non-Kähler hermitian manifolds |
| title_full | Strominger’s system on non-Kähler hermitian manifolds |
| title_fullStr | Strominger’s system on non-Kähler hermitian manifolds |
| title_full_unstemmed | Strominger’s system on non-Kähler hermitian manifolds |
| title_short | Strominger’s system on non-Kähler hermitian manifolds |
| title_sort | strominger s system on non kahler hermitian manifolds |
| topic | Differential geometry Partial differential equations |
| work_keys_str_mv | AT leeh stromingerssystemonnonkahlerhermitianmanifolds |