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

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 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 $c\to 0$) 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 (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 $N\ne M$ and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT.

30 pages