Dualities are pervasive in Physics and play a central role in statistical mechanics and field theory. I will review a unifying algebraic framework for realizing useful duality transformations. Classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (i.e. emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian or transfer matrices. Dualities are thus characterized as isometries implementing such morphisms. Dual variables (non-local mappings between the elementary degrees of freedom of the theory) which were guessed in the past can be derived in our formalism. If time permits, I will briefly explain a different conformal approach to dualities.
Coffee: 2:30 pm, 241 Compton