Entanglement and geometry from subalgebras of the Virasoro algebra

Abstract

In this work we study families of generalised coherent states constructed from SL(2,R) subalgebras of the Virasoro algebra in two-dimensional conformal field theories. We derive the energy density and entanglement entropy and discuss their equivalence with analogous quantities computed in locally excited states. Moreover, we analyze their dual, holographic geometries and reproduce entanglement entropies from the Ryu-Takayanagi prescription. Finally, we outline possible applications of this universal class of states to operator growth and inhomogeneous quenches.

Krylov complexity in a natural basis for the Schrödinger algebra

“…Due to its relevance in AdS/CFT this group has been studied extensively and there are some results with regard to complexity that take advantage of the associated geometry and are possibly implicitly related to certain classes of coherent states [59]. Recently there have also been advances in understanding Krylov complexity from a holographic perspective [37,47,63], although there are still many open questions that one would hope to address. Thus, we believe that our work is not only important for a non-relativistic limit of AdS/CFT, but also provides the groundwork for more general considerations.…”

“…While this approach in itself is novel, there have been several works already where an orthonormal basis for the Krylov subspace is not obtained through the Lanczos algorithm and as such the Liouvillian (Hamiltonian) is not tridiagonal. These include [18,37], where (similarly to this work) the symmetry algebra is considered for the full Virasoro group and S L n ( ) respectively. For the former this leads to a block diagonal structure of the Liouvillian and for the latter to a "trivially" non-tridigonal structure along the same lines with S L 2 ( ) which we examine in more detail in the following sections.…”

The overlap of generalized coherent states of any rank one simple Lie algebra and its classical limit

“…In [20], the algebras g k were expressed as copies of sl(2, R) and analyzed for their relevance in holography and the AdS/CFT correspondence. As sl(2, R) is isomorphic to su(1, 1) [57], here we define…”

“…Moreover, GCS allow studying the classical limit of various quantum field theories [15,16], quantum and classical-quantum descriptions of gravity [17], and the emergence of time in quantum mechanics via the Page and Wootters mechanism [18,19]. More recently, GCS have been used to describe semi-classical states in conformal field theory (CFT) [20][21][22], and have been proven to have a well-defined gravitational dual description via the Holographic principle [20,23]. Other applications to quantum gravity include the crucial case of the thermofield double state [24,25], which connects the problem of studying GCS and their classical limit to that of uncovering the semi-classical behavior of quantum black holes [26] and the related information paradox [27][28][29].…”

Brane detectors of a dynamical phase transition in a driven CFT

“…If we choose H to be other linear combinations of conformal generators L p , Lp , it corresponds to a different quantization [72], [73] in the CFT. The corresponding bulk metric will be obtained by mapping it from the AdS 3 coordinates under large diffeomorphism (generated by boundary L p 's) in a specific gauge [74] and then solving for the bulk curve. Let us now discuss this explicitly when p = {0, ±1}.…”