On the Quantum Geometry of Multi-critical CDT
We discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is again described by a matrix model. The resolvent, a simple o...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1826257497919324160 |
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| author | Atkin, MR Zohren, S |
| author_facet | Atkin, MR Zohren, S |
| author_sort | Atkin, MR |
| collection | OXFORD |
| description | We discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is again described by a matrix model. The resolvent, a simple observable of the quantum geometry which is accessible from the matrix model is calculated for arbitrary multi-critical points. We go beyond the matrix model by determining the propagator using the peeling procedure which is used to extract the effective quantum Hamiltonian and the fractal dimension in agreement with earlier results by Ambjorn et al. With this at hand a string field theory formalism for multi-critical CDT is introduced and it is shown that the Dyson-Schwinger equations match the loop equations of the matrix model. We conclude by commenting on how to formally obtain the sum over topologies and a relation to stochastic quantisation. |
| first_indexed | 2024-03-06T18:19:10Z |
| format | Journal article |
| id | oxford-uuid:05ad9a32-44ee-4173-8263-d5951e6424ba |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:19:10Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:05ad9a32-44ee-4173-8263-d5951e6424ba2022-03-26T08:58:28ZOn the Quantum Geometry of Multi-critical CDTJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:05ad9a32-44ee-4173-8263-d5951e6424baEnglishSymplectic Elements at Oxford2012Atkin, MRZohren, SWe discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is again described by a matrix model. The resolvent, a simple observable of the quantum geometry which is accessible from the matrix model is calculated for arbitrary multi-critical points. We go beyond the matrix model by determining the propagator using the peeling procedure which is used to extract the effective quantum Hamiltonian and the fractal dimension in agreement with earlier results by Ambjorn et al. With this at hand a string field theory formalism for multi-critical CDT is introduced and it is shown that the Dyson-Schwinger equations match the loop equations of the matrix model. We conclude by commenting on how to formally obtain the sum over topologies and a relation to stochastic quantisation. |
| spellingShingle | Atkin, MR Zohren, S On the Quantum Geometry of Multi-critical CDT |
| title | On the Quantum Geometry of Multi-critical CDT |
| title_full | On the Quantum Geometry of Multi-critical CDT |
| title_fullStr | On the Quantum Geometry of Multi-critical CDT |
| title_full_unstemmed | On the Quantum Geometry of Multi-critical CDT |
| title_short | On the Quantum Geometry of Multi-critical CDT |
| title_sort | on the quantum geometry of multi critical cdt |
| work_keys_str_mv | AT atkinmr onthequantumgeometryofmulticriticalcdt AT zohrens onthequantumgeometryofmulticriticalcdt |