TT¯ deformation of N=(1,1) off-shell supersymmetry…

We construct the superaction for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi><a:mover accent="true"><a:mi>T</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> deformation of 2D free <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">N</e:mi><e:mo>=</e:mo><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mo>,</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:math> supersymmetric model with a deformed superfield. We show that the <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:mo stretchy="false">(</j:mo><j:mn>1</j:mn><j:mo>,</j:mo><j:mn>1</j:mn><j:mo stretchy="false">)</j:mo></j:math> off-shell supersymmetry in the free theory is deformed under the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>T</o:mi><o:mover accent="true"><o:mi>T</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> deformation, which is incorporated in the deformed superfield. We interpret this superaction as an effective action of the Goldstone superfield for the partial spontaneous breaking of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi mathvariant="script">N</s:mi><s:mo>=</s:mo><s:mo stretchy="false">(</s:mo><s:mn>2</s:mn><s:mo>,</s:mo><s:mn>2</s:mn><s:mo stretchy="false">)</s:mo></s:math> supersymmetry to <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi mathvariant="script">N</x:mi><x:mo>=</x:mo><x:mo stretchy="false">(</x:mo><x:mn>1</x:mn><x:mo>,</x:mo><x:mn>1</x:mn><x:mo stretchy="false">)</x:mo></x:math>. We show that the unbroken and broken supersymmetry of the effective superaction corresponds to the off-shell <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi mathvariant="script">N</cb:mi><cb:mo>=</cb:mo><cb:mo stretchy="false">(</cb:mo><cb:mn>1</cb:mn><cb:mo>,</cb:mo><cb:mn>1</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math> supersymmetry and the off-shell Fermi global nonlinear symmetry in the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>T</hb:mi><hb:mover accent="true"><hb:mi>T</hb:mi><hb:mo stretchy="false">¯</hb:mo></hb:mover></hb:math>-deformed theory, respectively. We demonstrate that this effective superaction can be obtained by the nonlinear realization of the partially broken global supersymmetry (PBGS) from the coset superspace. Furthermore, we reproduce the superaction by the constrained superfield method accompanied by a field redefinition.