Off-shell invariants of linearized 4D,N=2 supergravity in the harmonic approach

Using the harmonic superspace approach, we construct, at the linearized level, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>2</a:mn></a:math> supersymmetric curvatures generalizing scalar curvature, Ricci curvature and Weyl tensor. These supercurvatures are the building blocks of various linearized <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mn>4</d:mn><d:mi>D</d:mi><d:mo>,</d:mo><d:mi mathvariant="script">N</d:mi><d:mo>=</d:mo><d:mn>2</d:mn></d:math> Einstein supergravity invariants. The supercurvatures involving the scalar and Ricci curvatures are analytic harmonic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="script">N</g:mi><g:mo>=</g:mo><g:mn>2</g:mn></g:math> superfields, while the Weyl supertensor is a chiral <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi mathvariant="script">N</j:mi><j:mo>=</j:mo><j:mn>2</j:mn></j:math> superfield. As the basic distinguished feature of our construction, all these objects are expressed through the fundamental analytic gauge prepotentials <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>h</m:mi><m:mrow><m:mo>+</m:mo><m:mo>+</m:mo><m:mi>M</m:mi></m:mrow></m:msup><m:mo>,</m:mo><m:mi>M</m:mi><m:mo>=</m:mo><m:mo stretchy="false">(</m:mo><m:mi>α</m:mi><m:mover accent="true"><m:mi>α</m:mi><m:mo>˙</m:mo></m:mover><m:mo>,</m:mo><m:mi>α</m:mi><m:mo>+</m:mo><m:mo>,</m:mo><m:mover accent="true"><m:mi>α</m:mi><m:mo>˙</m:mo></m:mover><m:mo>+</m:mo><m:mo>,</m:mo><m:mn>5</m:mn><m:mo stretchy="false">)</m:mo></m:math>. The related characteristic features are the heavy use of harmonic derivatives and harmonic zero-curvature equations. On a number of instructive examples, we describe the component reduction of the superfield invariants constructed.