On Inherited Duality in N=1 d=4 Supersymmetric Gauge Theories

Details On Inherited Duality in N=1 d=4 Supersymmetric Gauge Theories On Inherited Duality in N=1 d=4 Supersymmetric Gauge Theories

1999-10-29

arxiv.org/abs/hep-th/9910250v3

JHEP 0004 (2000) 029

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX; v2 (v3) has minor changes in wording (references)

Scientific paper

10.1088/1126-6708/2000/04/029

Four-dimensional N=1 supersymmetric gauge theories with two adjoints and a quartic superpotential are believed, from AdS/CFT duality, to have SL(2,Z) invariance. In this note we review an old, unpublished argument for this property, based solely on field theory. The technique involves a complexified flavor rotation which deforms an N=2 supersymmetric gauge theory with matter to an N=1 theory, leaving all holomorphic invariants unchanged. We apply this to the N=1 gauge theory with two massless adjoints and show that it has the same auxiliary torus as that of N=4 gauge theory, from which SL(2,Z) invariance follows. In an appendix, we check that our arguments are consistent with earlier work on the SU(2) case. Our technique is general and applies to many other N=1 theories.

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