In this talk, I will discuss a formulation of holography as approximate quantum error correction using a large code subspace consisting of multiple background geometries. We find corrections to the JLMS formula in novel regimes and explain the presence of such corrections in an approximate error correcting code. The large code subspace allows us to discuss the bulk dual of modular flow which affects the background geometry in a non-trivial manner. We discuss situations where modular flow can be well approximated by classical flow by the HRT area operator, and using the Peierls bracket technique, derive the fact that modular flow approximately acts by a kink transform. These results generalize to higher derivative theories and constitute a new Lorentzian derivation of the geometric entropy.

Bio：Pratik Rath is a postdoctoral researcher in high energy physics at the University of California, Santa Barbara, co-sponsored by the It From Qubit (Simons) Collaboration grant and a MURI Collaboration grant on Tensor Networks and Holography. Pratik completed his Ph.D. at UC Berkeley in 2020, under the supervision of Yasunori Nomura, about Aspects of Holography and Quantum Error Correction. He did the PSI masters program at Perimeter Institute under the supervision of Robert Myers, working on Holographic Complexity.

Contact: Wu Jieqiang