IMSc Webinar

A New Disorder Operator For SU(N) Lattice Gauge Theory

Atul Rathor

SN Bose Center, Kolkata

The Wilson Loop order operators create and destroy the fundamental SU(N) electric fluxes and are characterized by all possible discrete eigenvalues of the (N-1) SU(N) Casimir operators. However, the
dual 't Hooft operators create and destroy Z_N magnetic fluxes only in the center of the SU(N) group. Therefore, they are characterized by a single magnetic quantum number taking only (N-1) discrete
values for all SU(N). This huge mismatch between the equivalent electric and magnetic sectors has been noticed in the past. In this work we remove the above disparity by constructing exact SU(N)
duality transformations leading to the most general magnetic disorder operator for SU(N) lattice gauge theories in (2+1) dimensions. The new dual Wilson loop or disorder operators are characterized by
(N-1) continuous angles and remove the above discrepancy. The most general order-disorder algebra is also obtained. It reduces to the standard Wilson-'t Hooft order disorder algebra in a special
limit.

We also construct exactly solvable SU(N ) toric code model and use the above SU(N) disorder operators to create non-abelian anyons which are required for topological quantum computing. The model has
N^2 topologically degenerate ground states which are constructed as coherent superpositions of SU(N) spin network states. We show that the braiding statistics of the SU(N) anyons is encoded in the
SU(N) Wigner rotation matrices."

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