arXiv subjects
Publications and source records attributed to Richard Grimm.
In analogy to the chiral-linear multiplet correspondence we establish a relationship between the 3-form (or gaugino condensate) multiplet and a coupled non-minimal (0,1/2) multiplet, illustrated by a simple explicit example.
A concise geometrical formulation of N=4 supergravity containing an antisymmetric tensor gauge field is given in central charge superspace: graviphotons are identified in the super-vielbein on the same footing as the vierbein and the Rarita-Schwinger fields. As a consequence of superspace soldering, Chern-Simons terms in the fieldstrength of the antisymmetric tensor arise as an intrinsic property of superspace with central charge coordinates.
The superspace geometry of Chern-Simons forms is shown to be closely related to that of the 3-form multiplet. This observation allows to simplify considerably the geometric structure of supersymmetric Chern-Simons forms and their coupling to linear multiplets. The analysis is carried through in U_K(1) superspace, relevant at the same time for supergravity-matter couplings and for chirally extended supergravity.
We present a new, alternative interpretation of the vector-tensor multiplet as a 2-form in central charge superspace. This approach provides a geometric description of the (non-trivial) central charge transformations ab initio and is naturally generalized to include couplings of Chern-Simons forms to the antisymmetric tensor gauge field, giving rise to a N=2 supersymmetric version of the Green-Schwarz anomaly cancellation mechanism.
Starting from flat two-dimensional gauge potentials we propose the notion of ${\cal W}$-gauge structure in terms of a nilpotent BRS differential algebra. The decomposition of the underlying Lie algebra with respect to an $SL(2)$ subalgebra is crucial for the discussion conformal covariance, in particular the appearance of a projective connection. Different $SL(2)$ embeddings lead to various ${\cal W}$-gauge structures. We present a general soldering procedure which allows to express zero curvature conditions for the ${\cal W}$-currents in terms of conformally covariant differential operators acting on the ${\cal W}$ gauge fields and to obtain, at the same time, the complete nilpotent BRS differential algebra generated by ${\cal W}$-currents, gauge fields and the ghost fields corresponding to ${\cal W}$-diffeomorphisms. As illustrations we treat the cases of $SL(2)$ itself and to the two different $SL(2)$ embeddings in $SL(3)$, {\it viz.} the ${\cal W}_3^{(1)}$- and ${\cal W}_3^{(2)}$-gauge structures, in some detail. In these cases we determine algebraically ${\cal W}$-anomalies as solutions of the consistency conditions and discuss their Chern-Simons origin.