3d Carrollian Chern-Simons theory & 2d Yang-Mills

Bagchi, Arjun; Lipstein, Arthur; Mandlik, Mangesh; Mehra, Aditya

Abstract

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 AdS4/CFT3, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light c → 0) 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 (BMS4) 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) × 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 ≠ M and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT.

Citation

Bagchi, A., Lipstein, A., Mandlik, M., & Mehra, A. (2024). 3d Carrollian Chern-Simons theory & 2d Yang-Mills. Journal of High Energy Physics, 2024(11), Article 6. https://doi.org/10.1007/jhep11%282024%29006

• Journal Article Type: Article
• Acceptance Date: Oct 12, 2024
• Online Publication Date: Nov 5, 2024
• Publication Date: Nov 5, 2024
• Deposit Date: Nov 6, 2024
• Publicly Available Date: Nov 6, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 11
• Article Number: 6
• DOI: https://doi.org/10.1007/jhep11%282024%29006
• Keywords: Scale and Conformal Symmetries, Field Theories in Lower Dimensions, Gauge-Gravity Correspondence, Chern-Simons Theories
• Public URL: https://durham-repository.worktribe.com/output/3082711
• Additional Information: Received: 13 August 2024; Revised: 8 October 2024; Accepted: 12 October 2024; First Online: 5 November 2024