<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> </mml:math> supersymmetric mechanics with spin variables from indecomposable multiplets

We define two new indecomposable (not fully reducible) <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>8</a:mn> </a:math> , <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>d</d:mi> <d:mo>=</d:mo> <d:mn>1</d:mn> </d:math> off-shell multiplets and consider the corresponding models of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi mathvariant="script">N</f:mi> <f:mo>=</f:mo> <f:mn>8</f:mn> </f:math> supersymmetric mechanics with spin variables. Each multiplet is described off shell by a scalar superfield which is a nonlinear deformation of the standard scalar superfield <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>X</i:mi> </i:math> carrying the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>d</k:mi> <k:mo>=</k:mo> <k:mn>1</k:mn> </k:math> multiplet ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mn mathvariant="bold">1</m:mn> <m:mo>,</m:mo> <m:mn mathvariant="bold">8</m:mn> <m:mo>,</m:mo> <m:mn mathvariant="bold">7</m:mn> </m:mrow> </m:math> ). Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet ( <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:mn mathvariant="bold">8</r:mn> <r:mo>,</r:mo> <r:mn mathvariant="bold">8</r:mn> <r:mo>,</r:mo> <r:mn mathvariant="bold">0</r:mn> </r:mrow> </r:math> ). For both systems we present the manifestly <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi mathvariant="script">N</w:mi> <w:mo>=</w:mo> <w:mn>8</w:mn> </w:math> supersymmetric superfield constraints, as well as the component off- and on-shell invariant actions, which for one version exactly match those given in . The two models differ off shell, but prove to be equivalent to each other on shell, with the spin variables sitting in the adjoint representation of the maximal <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>R</z:mi> </z:math> -symmetry group <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mrow> <bb:mi>SO</bb:mi> </bb:mrow> <bb:mo stretchy="false">(</bb:mo> <bb:mn>8</bb:mn> <bb:mo stretchy="false">)</bb:mo> </bb:math> .