Dual Representation of SU(N) Lattice Gauge Theory with Local Dynamics

by Atul Rathor (S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India)

Monday 23 Jun 2025, 15:00 → 17:00 Europe/Berlin

Nußallee 14-16/3.013 (HISKP) - Seminar Room III (HISKP)

We present an exact dual formulation of pure SU(N) Hamiltonian lattice gauge theory in (2+1) dimensions, obtained by making a series of iterative canonical transformations on the electric field operators and their conjugate vector potentials associated with the links around each plaquette. This transformation maps the original gauge degrees of freedom to dual variables defined on plaquettes: SU(N) magnetic scalar fields corresponding to plaquette flux operators, and their conjugate electric scalar potentials. Under SU(N) gauge transformations, both transform like adjoint matter fields. The dual Hamiltonian describes the nonlocal self-interactions of these plaquette flux loops in terms of the electric scalar potentials and with inverted coupling. We show that these nonlocal loop interactions can be made local and converted into minimal couplings by introducing SU(N) auxiliary gauge fields along with new plaquette constraints.

Our construction provides an exactly equivalent reformulation of SU(N) lattice gauge theory that completely simplifies the magnetic part of the Hamiltonian, which dominates near the continuum (g² → 0) limit. This reformulation may offer significant advantages for both analytical and numerical investigations of nonperturbative dynamics, including confinement, dual superconductivity, weak-coupling loop perturbation theory, and quantum simulations near the continuum limit.

Remote talk:
https://uni-bonn.zoom-x.de/j/63364062643?pwd=tZmoFpLd037U4DzlVDbvfjaacgblSK.1