Extended global symmetries for 4D N=1 SQCD theories

In Spiridonov and Vartanov (2010 Nucl. Phys. B 824 192) the authors, using the superconformal index technique, found that four-dimensional N = 1 SQCD theory with SU(2) gauge group and four flavors has 72 dual representations. Recently, in Dimofte and Gaiotto (2012 J. High Energy Phys. JHEP10(2012) 129), the authors showed that these dual theories when coupled to five-dimensional (5D) hypermultiplets with specific boundary conditions have an extended E7 global symmetry. In this work, we find that for a reduced theory with three flavors the explicit SU(6) global symmetry is enhanced to an E-6 symmetry in the presence of 5D hypermultiplets. We also show connections between indices of different theories in three and four dimensions.