Results 1 
6 of
6
Supersymmetry on curved spaces and superconformal anomalies, JHEP 1310
, 2013
"... We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the Rcurrent is determined by the Weyl tensor of the background metric. In Euclidean signature, the ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the Rcurrent is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite Rcharge are preserved, otherwise the (anti)selfdual part of the vector fieldstrength is fixed by the Weyl tensor. As a result of this relation, the trace and Rcurrent anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite Rcharge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and Rcurrent anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography. ar
SUBMAXIMAL CONFORMAL SYMMETRY SUPERALGEBRAS FOR LORENTZIAN MANIFOLDS OF LOW DIMENSION
"... Abstract. We consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed twoform that is invariant under the Lie algebra of conformal Killing vectors. The invariant twoform is constrained in a particul ..."
Abstract
 Add to MetaCart
Abstract. We consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed twoform that is invariant under the Lie algebra of conformal Killing vectors. The invariant twoform is constrained in a particular way by the conformal geometry of the manifold. In three dimensions, the conformal Killing vector must be everywhere causal (or null if the invariant twoform vanishes identically). In four dimensions, the conformal Killing vector must be everywhere null and the invariant twoform vanishes identically if the geometry is everywhere of Petrov type N or O. To the conformal class of any such geometry, it is possible to assign a particular Lie superalgebra structure, called a conformal symmetry superalgebra. The even part of this superalgebra contains conformal Killing vectors and constant Rsymmetries while the odd part contains (charged) twistor spinors. The largest possible dimension of a conformal symmetry superalgebra is realised only for geometries that are locally conformally flat. We determine precisely which nontrivial conformal classes of metrics admit a conformal symmetry superalgebra with the next largest possible dimension, and compute all the associated submaximal conformal symmetry superalgebras. In four dimensions, we also compute symmetry superalgebras for a class of Ricciflat Lorentzian geometries not of Petrov type N or O which admit a null Killing vector. Date: 20th June 2014.