Euihun Joung

We present the first formulation of linearized gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e., treats the two frames related by electric-magnetic duality on equal footing. It is well known that four-dimensional linearized gravity belongs to a class of singleton representations of the four-dimensional conformal algebra so ( 2 , 4 ) . Our key insight is viewing this algebra as the isometry of AdS 5 and realising the massless spin-2 field as edge modes of a five-dimensional topological field taking values in a specific finite-dimensional representation of so ( 2 , 4 ) . The desired four-dimensional action is then found by a covariant boundary reduction procedure.

We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the s = 1 Floreanini-Jackiw and s = 2 Alekseev-Shatashvili actions to arbitrary spin s. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the SL(3, ℝ) case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.

We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its sl(2, ℝ) BF theory description with the asymptotic AdS₂ boundary condition. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as “would-be gauge mode”. We clarify the relation between the wiggling boundary and the would-be gauge mode. We demonstrate a natural top-down derivation of PSL(2, ℝ) gauging and the path integral measure of the Schwarzian theory. In the sl(2, ℝ) BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with PSL(2, ℝ) gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of PSL(2, ℝ).

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.