Topic: Generalized conformal geometry, CFT conservation laws and holography

Speaker: Assoc. Prof. Zhao-Long Wang

Coordinates: PCFT C1124, 16:00, Tuesday, October 31

Abstract: Inspired by the $SO(2,d)$ gauge theory formalism of AdS gravity, the corresponding $SO(2,d)$ background ruler and gauge field are introduced on the dual CFT side. In addition to the metric $g_{\mu\nu}$, another background 2-tensor $f_{\mu\nu}$ appears in this formalism. $f_{\mu\nu}$ can be viewed as a natural generalization of the Schouten tensor and thus we get a generalized version of conformal geometry. For a CFT coupled to the generalized conformal geometry, $f_{\mu\nu}$ contributes additional terms in the diffeomorphism and Weyl conservation laws. In the presence of these additional terms, the bulk Hamiltonian constraints of AdS gravity is explicitly reproduced by the CFT conservation laws. Besides, the radial evolution equation of the bulk gravity is naturally identified with the Callan-Symanzik equation of the theories coupled to generalized conformal geometry.