Abstract
We discuss models with no dynamical vector fields in various dimensions which we claim might have exceptional symmetry on some loci of their parameter space. In particular we construct theories with four supercharges flowing to theories with global symmetry enhancing to F 4, E 6, and E 7. The main evidence for these claims is based on extracting information about the symmetry properties of the theories from their supersymmetric partition functions.
Highlights
We discuss models with no dynamical vector fields in various dimensions which we claim might have exceptional symmetry on some loci of their parameter space
The arguments in favor of enhancement of global symmetry are based on analysis of partition functions
First we show that the partition functions are invariant under the action of the Weyl group of that symmetry on the parameters, and in case these are indices can be expanded in characters of the enhanced flavor group
Summary
The arguments in favor of enhancement of global symmetry are based on analysis of partition functions. We will present an argument in three dimensions, generalizing the four dimensional claim [4] that in a certain order of the expansion of the index one can extract the number of marginal operators minus the currents This will let us identify the currents of the enhanced symmetry. We claim that the SU(2) symmetry here enhances to SO(8) We can check this by studying different supersymmetric partition functions in various dimensions. For notations and definitions of supersymmetric partition functions the reader can consult [5] This theory has symmetry SO(10) × U(1)t , where SO(8) × U(1)α enhances to SO(10). The fact that the superpotential 2.5 gives rise to E6 symmetry is not surprising One can realize this symmetry as the group of transformations fixing the determinant of a three by three hermitian matrix built from octonions. Since the supersymmetric partition functions are insensitive to such parameters we allow ourselves to be agnostic about them in our discussion
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