Quantum Fields and Strings

The Ryu Takayanagi formula identifies the area of  extremal surfaces in AdS with the entanglement entropy of the boundary CFT. However the bulk microstate interpretation of the extremal area remains mysterious. Progress along this direction requires understanding how to define entanglement entropy in the bulk closed string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A model in the context of Gopakumar Vafa duality. We give a self consistent factorization of the closed string Hilbert space which leads to string edge modes transforming under a q-deformed surface symmetry group. Compatibility with this symmetry requires a q-deformed definition of entanglement entropy. Using the topological vertex formalism, we define the Hartle Hawking state for the resolved conifold and compute its q-deformed entropy directly from the closed string reduced density matrix.  We show that this is the same as the generalized entropy, defined by prescribing a contractible replica manifold for the closed string theory on the resolved conifold.  We then apply the Gopakumar Vafa duality to reproduce the closed string entropy from Chern Simons dual  using the un-deformed definition of entanglement entropy. Finally we relate non local aspects of our factorization map to analogous phenomenon recently found in JT gravity.

Dilaton-gravity models are integrable in two dimensions and admit a holographic description. In this talk, the holographic description of the Dilaton-gravity in flat spacetime is discussed. Using the gauge theory formulation of the model we obtain the boundary action which under certain boundary conditions is of the Warped-Schwarzian type. We calculate the 1-loop partition function of the model as the coadjoint orbit of the warped Virasoro group.

I will review the numerical approach to testing gauge/gravity duality using matrix models. This will lead to a summary of recent results from the BFSS, BMN and Berkooz-Douglas matrix models and a strong non-perturbative test of gauge/gravity duality.

There is a deep relation between classical error-correcting codes, Euclidean lattices, and chiral 2d CFTs. We show this relation
extends to include quantum codes, Lorentzian lattices, and non-chiral CFTs. The relation to quantum codes provides a simple way to solve
modular bootstrap constraints and identify interesting examples of conformal theories. In particular we construct many examples of physically distinct isospectral theories, examples of "would-be" CFT partition function -- non-holomorphic functions satisfying all constraints of the modular bootstrap, yet not associated with any

known CFT, and find theory with the maximal spectral gap among all Narain CFTs with the central charge c=4. At the level of code theories the problem of finding maximal spectral gap reduces to the problem of finding optimal code, leading to "baby bootstrap" program. We also discuss averaging over the ensemble of all CFTs associated with quantum codes, and its possible holographic interpretation. The talk is based on arXiv:2009.01236 and arXiv:2009.01244.

I will study quantum error correcting codes that model aspects of the AdS/CFT correspondence. In an algebraic approach I will demonstrate the existence of a consistent assignment, to each boundary region, of conditional expectations that preserve the code subspace. This allows us to give simple derivations of well known results for these holographic code, and also to derive a few new results. 

I will also make a connection to the theory of QFT super-selection sectors.