Meet biform singletons in your area! Topological actions for edge modes

Abstract

We present topological field theories propagating biform singleton fields as edge modes. In even spacetime dimensions $D=2p$, these are irreducible representations of the conformal algebra $\mathfrak{so}(2,2p)$ with two-column Young diagrams of height $p$. Their duality properties depend on the parity of $p$: They propagate chiral degrees of freedom for odd $p$, and exhibit electric--magnetic duality for even $p$. We are able to construct the topological actions by realising the hidden conformal symmetry inherent to singletons geometrically in terms of an auxiliary bulk $\text{AdS}_{2p+1}$ geometry. Using these as a starting point, we are able to apply a recently established covariant boundary reduction procedure to yield novel action formulations with manifest Lorentz covariance. We also show how, breaking manifest Lorentz covariance, we recover known formulations of biform singletons.