1:30 pm MCP 201
Solving the Lattice Chern-Simons-Maxwell Theory.
Putting U(1) Chern-Simons theory on the lattice has been an interesting problem for over decades. Over time, it has become clear that there are two key points. The first key point is, a chiral Chern-Simons theory cannot be purely topological (no matter on the lattice or in the continuum), some non-topological term, such as the Maxwell term, must be needed. The second key point is to use the Villainized U(1) gauge field to capture the topological properties of U(1). While these two ideas have been around, people have yet to seriously put them together into a theory and analyze the theory.
We defined and solved such a theory (which is free) and obtained all the interesting features: the bosonic/fermionic level quantizations; the bulk and chiral edge spectrum; the Wilson loop flux attachment with point-split framing or geometrical framing depending on the Maxwell coupling; the Wilson loop spin; the ground state degeneracy; and most non-trivially, the gravitational/framing anomaly. Our solution not only provided a UV complete definition for U(1) Chern-Simons theory, it also deepens our understanding of the theory in the continuum; moreover, the explicitness of the definition and solution on the lattice is good for pedagogical purposes.