Edge modes in gauge theories and gravitational theories
ABSTRACT
The presence of boundary and its boundary condition constrain the possible gauge transformation or diffeomorphism, leading to the emergence of physical degrees of freedom known as edge modes. This talk presents several illustrative examples highlighting the crucial role of edge modes: the sewing of Chern-Simons theory, the non-factorizable Hilbert space of gauge theory, edge mode contributions to entanglement entropy, and boundary charges in gravitational systems. After these whizzing examples, I will provide a gentle introduction to covariant phase space formalism in the presence of boundary, pointing out its subtleties. Noether’s 1st and 2nd theorem will be revisited in the presence of boundary and discuss the boundary symplectic form and boundary charges through concrete examples. These systems would universally require an extension of the phase space to accommodate additional physical degrees of freedom: edge mode.