13 research outputs found
Tensor calculus for supergravity on a manifold with boundary
Using the simple setting of 3D N=1 supergravity, we show how the tensor
calculus of supergravity can be extended to manifolds with boundary. We present
an extension of the standard F-density formula which yields supersymmetric
bulk-plus-boundary actions. To construct additional separately supersymmetric
boundary actions, we decompose bulk supergravity and bulk matter multiplets
into co-dimension one submultiplets. As an illustration we obtain the
supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature
boundary term. We emphasize that our construction does not require any boundary
conditions on off-shell fields. This gives a significant improvement over the
existing orbifold supergravity tensor calculus.Comment: 20 pages, JHEP format; published versio
The supermultiplet of boundary conditions in supergravity
Boundary conditions in supergravity on a manifold with boundary relate the
bulk gravitino to the boundary supercurrent, and the normal derivative of the
bulk metric to the boundary energy-momentum tensor. In the 3D N=1 setting, we
show that these boundary conditions can be stated in a manifestly
supersymmetric form. We identify the Extrinsic Curvature Tensor Multiplet, and
show that boundary conditions set it equal to (a conjugate of) the boundary
supercurrent multiplet. Extension of our results to higher-dimensional models
(including the Randall-Sundrum and Horava-Witten scenarios) is discussed.Comment: 22 pages. JHEP format; references added; published versio
Supersymmetric Boundaries and Junctions in Four Dimensions
We make a comprehensive study of (rigid) N=1 supersymmetric sigma-models with
general K\"ahler potentials K and superpotentials w on four-dimensional
space-times with boundaries. We determine the minimal (non-supersymmetric)
boundary terms one must add to the standard bulk action to make it off-shell
invariant under half the supersymmetries without imposing any boundary
conditions. Susy boundary conditions do arise from the variational principle
when studying the dynamics. Upon including an additional boundary action that
depends on an arbitrary real boundary potential B one can generate very general
susy boundary conditions. We show that for any set of susy boundary conditions
that define a Lagrangian submanifold of the K\"ahler manifold, an appropriate
boundary potential B can be found. Thus the non-linear sigma-model on a
manifold with boundary is characterised by the tripel (K,B,w). We also discuss
the susy coupling to new boundary superfields and generalize our results to
supersymmetric junctions between completely different susy sigma-models, living
on adjacent domains and interacting through a "permeable" wall. We obtain the
supersymmetric matching conditions that allow us to couple models with
different K\"ahler potentials and superpotentials on each side of the wall.Comment: 38 pages, 1 figur