Abstract
In the last twenty years, low-energy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four space-time dimensions and in three space-time dimensions. In particular, duals have been found for 3d N=2 supersymmetric QCD theories with gauge group U(N), with F chiral multiplets in the fundamental representation, with F' chiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, F' and k for which the theory preserves supersymmetry. For SU(N) theories the duals have been found in some cases, such as F=F' and F'=0, but not in the general case. In this note we find the IR dual for SU(N) SQCD theories with general values of N, F, F' and a non-zero k, which preserve supersymmetry.
Highlights
Duals have been found for 3d N = 2 supersymmetric QCD theories with gauge group U(N ), with F chiral multiplets in the fundamental representation, with Fchiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, Fand k for which the theory preserves supersymmetry
In this note we find the IR dual for SU(N ) SQCD theories with general values of N, F, Fand k = 0 which preserve supersymmetry
Theory A is dual to theory B which is an SU(F − N + k)−k × U(1)F −N gauge theory, with F fundamental chiral superfields qi and F = F anti-fundamental chiral superfields qi, and with F × F singlets Mii, coupled by the superpotential W = Miiqiqi
Summary
Equivalent results for mass flows involving anti-fundamental flavors can be achieved via a charge conjugation symmetry transformation. It is clear that the D-term equations have a solution at Q = Q = 0, with a vanishing scalar in the vector multiplet In this vacuum Fm chiral superfields in the fundamental representation are massive and may be integrated out. Note that the low-energy theory still satisfies (1.1), as required for consistency This vacuum preserves the full global symmetry preserved by the mass deformation, but only SU(F − Fm) × SU(F )R × U(1)B × U(1)A acts non-trivially on the low-energy theory (where the U(1)’s are some linear combinations of the original U(1)’s and the one coming from SU(F )L). These vacua are infinitely far away in the m → ∞ limit and we will not discuss them here; presumably they can be matched to theory B, as in the U(N ) analysis of [15]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
