Supersymmetric J $$ \overline{T} $$ and T $$ \overline{J} $$ deformations
Hongliang Jiang, Gabriele Tartaglino-Mazzucchelli
Abstract
A bstract We explore the J $$ \overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and T $$ \overline{J} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>J</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformations of two-dimensional field theories possessing $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (0 , 1) , (1 , 1) and (0 , 2) supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the J $$ \overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> /T $$ \overline{J} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>J</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional J $$ \overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> /T $$ \overline{J} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>J</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> operator on-shell. We also present some examples of J $$ \overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> /T $$ \overline{J} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>J</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.