Date : November 30, 2021, 16:00 CET

Andrew O’Bannon (U. of Southampton)


Title: Central Charges of Conformal Boundaries and Defects

Abstract:  In a 2d conformal field theory (CFT) the central charge is defined from the Virasoro algebra. Crucially, the central charge obeys the c-theorem, a powerful, universal, non-perturbative constraint: the central charge must decrease under renormalization group flows. The central charge appears in many other places too, such as stress tensor two-point functions, thermal entropy, entanglement entropy, and more. All of these indicate that the central charge counts CFT degrees of freedom. However, what happens with a 2d boundary of a 3d CFT, or a 2d conformal defect in a higher-dimensional CFT? Generically in these cases no Virasoro algebra is present. Can we still define a central charge? If so, in what quantities does it appear? Can we prove a c-theorem? These questions may be crucial for graphene with a boundary, surface operators in CFTs, and many other systems. In this talk I will summarize the state of the art in this area, including examples and open questions.