Entanglement, free energy and C-theorem in DCFT

          @misc{ pirsa_PIRSA:19080063,
            doi = {10.48660/19080063},
            url = {https://pirsa.org/19080063},
            author = {Nishioka, Tatsuma},
            keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Information},
            language = {en},
            title = {Entanglement, free energy and C-theorem in DCFT},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {aug},
            note = {PIRSA:19080063 see, \url{https://pirsa.org}}
          }
          

Abstract

The g-theorem is a prominent example of C-theorems in two-dimensional boundary CFT and the extensions are conjectured to hold in higher-dimensional BCFTs. On the other hand, much less is known for C-theorems in a CFT with conformal defects of higher codimensions. I will investigate the entanglement entropy across a sphere and sphere free energy as a candidate for a C-function in DCFT, and show they differ by a universal term proportional to the vev of the stress tensor. Based on this relation, I will propose to use the sphere free energy as a C-function in DCFT. This proposal unifies the previously known theorems and conjectures, and passes several checks, including a few examples in field theories and a holographic proof in simple gravity dual models of DCFTs.