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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2023
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| Accès en ligne: | https://arxiv.org/abs/2310.13503 |
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| _version_ | 1866914765187579904 |
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| author | Abranches, Juan L. A. Pereira, Antonio D. Toriumi, Reiko |
| author_facet | Abranches, Juan L. A. Pereira, Antonio D. Toriumi, Reiko |
| contents | We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson [Phys. Lett. B 678, 222 (2009)]. We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix $A$ and $A^2$ for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13503 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dually weighted multi-matrix models as a path to causal gravity-matter systems Abranches, Juan L. A. Pereira, Antonio D. Toriumi, Reiko Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Lattice High Energy Physics - Theory We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson [Phys. Lett. B 678, 222 (2009)]. We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix $A$ and $A^2$ for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models. |
| title | Dually weighted multi-matrix models as a path to causal gravity-matter systems |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.13503 |