Quantum Fields and Strings

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are highly complex. Our procedure for reconstructing this "simple wedge" is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python's lunches. An efficient quantum circuit converts this coarse-grained state into a "simple state" that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.

The quantum gravity path integral involves a sum over topologies. Superficially, this feature is similar to Feynman diagrams of quantum field theory and the genus expansion of worldsheet string theory. There are however some key differences. While the standard construction leads to the non-abelian algebra of quantum fields, the quantum gravity path integral has been argued to define an abelian algebra associated with partition function type observables. We will discuss these issues and argue that one needs to make certain discrete choices to construct a Hilbert space from path integrals that sum over topologies. In particular, the natural choices for quantum gravity differ from those used to construct QFTs as we shall illustrate in the context of one-dimensional models.

The last decade has seen significant progress in our understanding of scattering in anti-de Sitter (AdS) space. Through the AdS/CFT correspondence, we can reformulate scattering processes in AdS in terms of correlation functions in Conformal Field Theory (CFT), which are sharply defined by the requirements of Conformal Symmetry, Unitarity and a consistent Operator Product expansion. Accordingly, numerous highly effective techniques for the study of scattering in AdS have been developed. This has been driven largely by the Conformal Bootstrap programme, which aims to carve out the space of consistent CFTs (and, in turn, quantum gravities in AdS space) principally through the three basic consistency requirements above. In this talk I will describe some steps towards extending some of these techniques and results to boundary correlators in de Sitter (dS) space. Compared to AdS, we have little grasp of the properties required of consistent correlation functions in Euclidean CFTs dual to physics in dS. The boundaries at infinity in dS are space-like with no standard notion of locality and time, so the basic criteria that underpin the Conformal Bootstrap programme do not directly apply to the corresponding programme in dS, the so-called Cosmological bootstrap. I will show how boundary correlators in AdS and dS can be placed on a similar footing by introducing a Mellin-Barnes representation in momentum space, providing a framework that could facilitate bridging the gap between the Conformal and Cosmological bootstrap programmes. I will then discuss how the Mellin-Barnes representation itself can be a useful tool to study boundary correlators both in AdS and dS.

In recent years quantum error correction(QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error-correcting properties of the fermionic sector of various large N theories. Specifically, we examine SU(N) matrix quantum mechanics and 3-rank tensor O(N)^3 theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error-correcting code. Our considerations are based purely on large N analysis and do not appeal to a particular form of Hamiltonian or holography. Based on: arXiv: 2008.12869

Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories.