3d Carrollian Chern-Simons theory and 2d Yang-Mills
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arXiv
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| Format: | Preprint |
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2024
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| author | Bagchi, Arjun Lipstein, Arthur Mandlik, Mangesh Mehra, Aditya |
| author_facet | Bagchi, Arjun Lipstein, Arthur Mandlik, Mangesh Mehra, Aditya |
| contents | With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS$_4$/CFT$_3$, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light $c\to0$) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS$_4$) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with $SU(N) \times SU(M)$ CS theory coupled to bi-fundamental matter and show that when $N=M$, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when $N \neq M$ and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 3d Carrollian Chern-Simons theory and 2d Yang-Mills Bagchi, Arjun Lipstein, Arthur Mandlik, Mangesh Mehra, Aditya High Energy Physics - Theory With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS$_4$/CFT$_3$, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light $c\to0$) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS$_4$) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with $SU(N) \times SU(M)$ CS theory coupled to bi-fundamental matter and show that when $N=M$, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when $N \neq M$ and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT. |
| title | 3d Carrollian Chern-Simons theory and 2d Yang-Mills |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.13574 |