On $$ \mathcal{N} $$ = 4 supersymmetry enhancements in three dimensions
Benjamin Assel, Yuji Tachikawa, Alessandro Tomasiello
Abstract
A bstract We introduce a class of 3d theories consisting of strongly-coupled $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 systems coupled to $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 3 Chern-Simons gauge multiplets, which exhibit $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 enhancements when a peculiar condition on the Chern-Simons levels is met. An example is the SU( N ) 3 Chern-Simons theory coupled to the 3d T N theory, which enhances to $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 when 1 /k 1 + 1 /k 2 + 1 /k 3 = 0. We also show that some but not all of these $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 theories which have not been studied previously.