Between Symmetry and Duality in Supersymmetric Quantum Field Theories

Abstract

We study two cases of interrelations between the enhancement of symmetries in the infrared (IR) and duality properties of supersymmetric quantum field theories in four dimensions. First, we discuss an SU(2) N=1 model with four flavors, singlet fields, and a superpotential. We show that this model flows to a conformal field theory with E_{6}×U(1) global symmetry. The enhancement of the flavor symmetry follows from Seiberg duality. The second example is concerned with an SU(4) gauge theory with matter in the fundamental and antisymmetric representations. We argue that this model has enhanced SO(12) symmetry in the IR, and, guided by this enhancement, we deduce a new IR duality.

Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d

“…In this case, one uses two copies of the SU (2) gauge theory (and a suitable exactly marginal deformation) in order to construct a model which is mapped to itself under the duality transformation, and in which the symmetry enhances in the IR. This is different from the construction of[3] which involves only one copy, and results in an enhancement of the symmetry from SU (8) in the UV to E7 × U (1) in the IR.…”

“…Another, less trivial instance in which certain dualities and models with symmetry enhancement are related was discussed in [3,4] (see also [5]). In this case, we focus on a specific kind of dualities, called "self dualities", in which the gauge sector of the two theories is the same and they may differ only by gauge invariant fields.…”

“…Notice that this relation can also be applied in the other direction, and in some cases a model with symmetry enhancement can be used to find a new self-duality, see [3,4] for explicit examples.…”

3d Self-dualities

“…The other terms are identified with the Higgs branch operators and the symmetric products of the gauge invariant operators in Table 27. Table 28: Self-dual of Spin (8) with (N v , N s , N c ) = (4, 2, 1)…”

“…We will also discuss the connection between the 3d and 4d self-dualities. We will propose self-dualities for SU(2N), Spin (7) and Spin (8) cases and these self-dualities in turn teach us the correct quantum structure of the Coulomb moduli space.…”