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

TL;DR

This paper constructs the first N=1/2 supergravity theory in four Euclidean dimensions coupled with matter, achieved by a C-deformation that reduces supersymmetry and eliminates gravitini, resulting in a non-Lorentz-invariant theory.

Contribution

It introduces a novel N=1/2 supergravity framework in four Euclidean space with matter, derived via a consistent C-deformation of standard supergravity.

Findings

Reduces local supersymmetry by 3/4

Eliminates gravitini through algebraic constraints

Results in a non-Lorentz-invariant theory with residual N=1/2 supersymmetry

Abstract

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.