Analytic Results in 2D Causal Dynamical Triangulations: A Review
We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity...
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| Format: | Thesis |
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2006
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| _version_ | 1826312165767774208 |
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| author | Zohren, S |
| author_facet | Zohren, S |
| author_sort | Zohren, S |
| collection | OXFORD |
| description | We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. We show that in the continuum limit there is a finite density of infinitesimal wormholes. Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity. |
| first_indexed | 2024-03-07T08:24:56Z |
| format | Thesis |
| id | oxford-uuid:99a0effa-5c9f-4d29-9d81-c4e969144f97 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T08:24:56Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:99a0effa-5c9f-4d29-9d81-c4e969144f972024-02-12T11:31:22ZAnalytic Results in 2D Causal Dynamical Triangulations: A ReviewThesishttp://purl.org/coar/resource_type/c_db06uuid:99a0effa-5c9f-4d29-9d81-c4e969144f97Symplectic Elements at Oxford2006Zohren, SWe describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. We show that in the continuum limit there is a finite density of infinitesimal wormholes. Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity. |
| spellingShingle | Zohren, S Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title | Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title_full | Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title_fullStr | Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title_full_unstemmed | Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title_short | Analytic Results in 2D Causal Dynamical Triangulations: A Review |
| title_sort | analytic results in 2d causal dynamical triangulations a review |
| work_keys_str_mv | AT zohrens analyticresultsin2dcausaldynamicaltriangulationsareview |