ADS/CFT: String Theory to Cold Atoms

Subir Sachdev A

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The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier–Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.

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Tadashi Takayanagi

In this talk we would like to review developments of AdS/CFT correspondence, which plays significant roles in the developments of string theory. In particular, we will focus on the recent active subjects on the connection of AdS/CFT and quantum information, which leads to the idea of emergence space from quantum entanglement.

João C. Pinto Barros, Michele Burrello, Andrea Trombettoni

M. Botta Cantcheff, A. L. Gadelha, Dáfni F. Z. Marchioro +1 more

Based on Maldacena's description of an eternal anti--de Sitter (AdS) black hole, we reassess the thermo field dynamics (TFD) formalism in the context of the AdS/CFT correspondence. The model studied here involves the maximally extended AdS-Schwarschild solution and two (noninteracting) copies of the conformal field theory (CFT) associated to the global AdS spacetime, along with an extension of the string by imposing natural gluing conditions in the horizon. We show that the gluing conditions in the horizon define a string boundary state which is identified with the TFD thermal vacuum, globally defined in the Kruskal extension of the AdS black hole. We emphasize the connection of this picture with unitary $SU(1,1)$ TFD formulation, and we show that information about the bulk and the conformal boundary is present in the $SU(1,1)$ parameters. Using the unitary $SU(1,1)$ TFD formulation, a canonical prescription for calculating the world sheet real time thermal Green's function is made, and the entropy associated with the entanglement of the two CFT's is calculated.