We consider $\mathcal{N}=2$ supersymmetric $\text{SU}(2)$ gauge theory with $N_f=4$ massive hypermultiplets. The duality group of this contains transformations acting on the UV-coupling $\tau_{\text{UV}}$ as well running coupling $\tau$. establish that subgroups act separately and $\tau$, while a larger acts simultaneously For special choices masses, we find groups can be identified congruence ...

Let Φ̃ be a root system of type F4, and let G be a group generated by non-trivial subgroups Ar, r ∈ Φ̃, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the element-wise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups sat...

The deconfinement phase transition is studied in the ensemble canonical with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a quantity which is insensitive to Z(N c) symmetry but can reveal a critical behaviour in the theory with dy-namical quarks. Further, we argue that in the canonical ensemble description of full QCD there...

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables solidifies the relationship between supersymmetry and triality.