15 research outputs found
Holographic Chern-Simons Theories
Chern-Simons theories in three dimensions are topological field theories that
may have a holographic interpretation for suitable chosen gauge groups and
boundary conditions on the fields. Conformal Chern-Simons gravity is a
topological model of 3-dimensional gravity that exhibits Weyl invariance and
allows various holographic descriptions, including Anti-de Sitter, Lobachevsky
and flat space holography. The same model also allows to address some aspects
that arise in higher spin gravity in a considerably simplified setup, since
both types of models have gauge symmetries other than diffeomorphisms. In these
lectures we summarize briefly recent results.Comment: 20 pp, invited lectures prepared for the 7th Aegean Summer School
"Beyond Einstein's Theory of Gravity", 201
Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie
algebras (with space isotropy) have recently been classified in all dimensions.
In this paper, we continue the study of these "maximally symmetric" spacetimes
by investigating their local geometry. For each such spacetime and relative to
exponential coordinates, we calculate the (infinitesimal) action of the
kinematical symmetries, paying particular attention to the action of the
boosts, showing in almost all cases that they act with generic non-compact
orbits. We also calculate the soldering form, the associated vielbein and any
invariant aristotelian, galilean or carrollian structures. The (conformal)
symmetries of the galilean and carrollian structures we determine are typically
infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the
space of invariant affine connections on each homogeneous spacetime and work
out their torsion and curvature.Comment: 62 pages, 3 figures, 4 tables, v2: Matches published version, mistake
corrected in Section 4.1.3., 10.2, 10.3, other minor improvements, added
reference
Strolling along gauge theory vacua
We consider classical, pure Yang-Mills theory in a box. We show how a set of
static electric fields that solve the theory in an adiabatic limit correspond
to geodesic motion on the space of vacua, equipped with a particular Riemannian
metric that we identify. The vacua are generated by spontaneously broken global
gauge symmetries, leading to an infinite number of conserved momenta of the
geodesic motion. We show that these correspond to the soft multipole charges of
Yang-Mills theory.Comment: 46 pages, 1 figure, Published versio