A Gapped Boundary of a Chiral Theory in 2+1d

Explore advanced concepts in topological quantum field theory through this high energy theory seminar examining the gapped boundary conditions of chiral theories in 2+1 dimensions. Delve into the controversial topic of whether topologically ordered gapped local Hamiltonians consisting of commuting terms can realize chiral anyon theories, challenging established beliefs in the field. Learn about the role of tensor product algebras in quantum many-body physics and discover how locally generated, locally finite dimensional operator algebras can be constructed on 2D systems. Examine the construction of local commuting Hamiltonians that realize three-fermion anyon theory, which contradicts conventional wisdom about chiral theories. Investigate the mathematical framework involving chiral central charge calculations through integrals of commutators in bulk Hamiltonian terms. Understand how the boundary of three-fermion theory can be gapped out through specific choices of local operator algebras, exploring boundary conditions that differ from standard boson condensate approaches. Gain insights into cutting-edge research that bridges topological order, quantum many-body systems, and algebraic approaches to quantum field theory.