N=1/2 supergravity with matter in four Euclidean dimensions

Details N=1/2 supergravity with matter in four Euclidean dimensions N=1/2 supergravity with matter in four Euclidean dimensions

2007-07-28

arxiv.org/abs/0707.4218v2

Nucl.Phys.B794:495-511,2008

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, LaTeX, no figures; a reference added

Scientific paper

10.1016/j.nuclphysb.2007.10.020

An N=1/2 supergravity in four Euclidean spacetime dimensions, coupled to both vector- and scalar-multiplet matter, is constructed for the first time. We begin with the standard (1,1) conformally extended supergravity in four Euclidean dimensions, and freeze out the graviphoton field strength to an arbitrary (fixed) self-dual field (the so-called C-deformation). Though a consistency of such procedure with local supersymmetry is not guaranteed, we find a simple consistent set of algebraic constraints that reduce the local supersymmetry by 3/4 and eliminate the corresponding gravitini. The final field theory (after the superconformal gauge-fixing) has the residual local N=(0,1/2) or just N=1/2 supersymmetry with only one chiral gravitino as the corresponding gauge field. Our theory is not `Lorentz'-invariant because of the non-vanishing self-dual graviphoton vacuum expectation value, which is common to the C-deformed N=1/2 rigidly supersymmetric field theories constructed in a non-anticommutative superspace.

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