Alladi Ramakrishnan Hall

Duality made Simple: From Ising model to SU(N) lattice gauge theory

Manu Mathur

Retired Professor, SN Bose National Center for Basic Sciences

We use simple canonical transformations to obtain exact dualities in Ising Spin Model (Kramers-Wannier duality) as well as in U(1) & SU(N) Lattice Gauge Theories (LGT) in the Hamiltonian framework. We show that the SU(N) LGT duality can be directly obtained
from the simple U(1) LGT duality through the well known minimal coupling procedure.  Like in the Ising model, the dual construction naturally leads to the SU(N) LGT  Disorder Operators  which  are analogous to the Z_2 Kink operators in the Ising Model.  These
SU(N) disorder operators create SU(N) magnetic vortices and are dual to the SU(N) Wilson loop operators. The SU(N) order-disorder algebra and the plausible role of the SU(N) magnetic vortices in electric color confinement, topological quantum computing will be
briefly discussed.