IAS Physics Group Meeting

Abstract: In the AdS/CFT correspondence, it is of great importance to understand the emergence of bulk geometry from quantum mechanical degrees of freedom on the boundary. Volumes of spatial subregions are key quantities characterizing the bulk geometry which have recently been proposed to be dual to various notions of complexity in the boundary theory. In this informal talk, I will propose a different boundary dual; namely, that differences between volumes of bulk subregions are related to the index of inclusion for their dual boundary subalgebras. 

I will first review the definition of "index" for an inclusion of arbitrary von Neumann algebras and discuss its properties. I will then compute it in some simple cases before finally arguing that, in the case of von Neumann algebras in holographic field theories, it is related to bulk volume differences.