Physics Group Meeting

In the Friday seminar last week, Jennifer Lin talked about our joint work to characterize gravitational effective theories whose UV completions are dual to CFT’s on the boundary. I will discuss our attempt at its converse: how to characterize CFT’s that can be described by weakly coupled gravitational theories with smooth geometries [1]. I will present a combinatorial method to enumerate and classify entropy inequalities satisfied by the Ryu-Takayanagi formula. In contrast to the situation for generic quantum systems, it turns out that there are only finitely many independent inequalities for a fixed number of entanglement regions. In particular, for 4 or less regions, the strong subadditivity and the monogamy of mutual information [2] give the complete set of inequalities. Discussion items for future work could include generalization to the Hubeny-Rangamani-Takayanagi formula along the line of the paper [3] by Aron Wall and a relation to quantum error corrections discussed by Xi Dong in the Friday seminar a few weeks ago [4].

References:

[1] The Holographic Entropy Cone, http://arxiv.org/abs/1505.07839

[2] Holographic Mutual Information is Monogamous, http://arxiv.org/abs/1505.07839

[3] Maxmin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy, http://arxiv.org/abs/1211.3494

[4] Bulk Locality and Quantum Error Correction in AdS/CFT, http://arxiv.org/abs/1411.7041