Topological Quantum Gravity of the Ricci Flow- [electronic resource]
Topological Quantum Gravity of the Ricci Flow- [electronic resource]
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214095855
- ISBN
- 9798380620222
- DDC
- 530
- 서명/저자
- Topological Quantum Gravity of the Ricci Flow - [electronic resource]
- 발행사항
- [S.l.]: : University of California, Berkeley., 2021
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2021
- 형태사항
- 1 online resource(122 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
- 주기사항
- Advisor: Horava, Petr.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Berkeley, 2021.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약In this thesis we construct a family of topological quantum gravity theories with the goal of finding a regime in which these theories' localization equations are Perelman's celebrated Ricci flow equations. The natural setting for these theories is a nonrelativistic N = 2 superspace in which the spacetime is foliated by leaves of constant time. The basis for this construction is a "primitive" topological theory involving the spatial metric and its corresponding spatial diffeomorphism invariance, with N = 2 BRST symmetry. The algebra of the BRST charges is chosen so that the localization equations derived from a BRST-invariant action are flow equations and the couplings in the action are chosen so that these flow equations take the exact form of Hamilton's Ricci flow equations. Gauging spatial diffeomorphisms and foliation-preserving time reparametrizations (initially in two separate steps, but later in a single sweeping step) leads us to a set of geometric constraints that produce three distinct classes of field content in the BRST multiplets involved. Notably, the superpotential of the gauged theory is precisely Perelman's F-functional and the role of his dilaton is played by our nonrelativistic lapse function. Perelman's Ricci flow equations are then obtained as localization equations from the gauged theory in the same way as Hamilton's were obtained from the primitive theory (up to an interesting reframing), satisfying our goal.
- 일반주제명
- Physics.
- 일반주제명
- Quantum physics.
- 키워드
- Gauged theory
- 기타저자
- University of California, Berkeley Physics
- 기본자료저록
- Dissertations Abstracts International. 85-04B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.