Global symmetries and N = 2 SUSY

Abstract

<p>We prove that <i>N</i> = 2 theories that arise by taking <i>n</i> free hypermultiplets and gauging a subgroup of Sp(<i>n</i>), the non-R global symmetry of the free theory, have a remaining global symmetry, which is a direct sum of unitary, symplectic, and special orthogonal factors. This implies that theories that have SU(<i>N</i>) but not U(<i>N</i>) global symmetries, such as Gaiotto's <i>T_N</i> theories, are not likely to arise as IR fixed points of RG flows from weakly coupled <i>N</i> = 2 gauge theories.</p>