Workshop on AQFT, Modular Techniques, and Rényi Entropy

This workshop will focus on the applications of algebraic quantum field theory (AQFT), modular techniques, and Rényi entropy in AdS/CFT and black holes. The workshop is hosted by the Gravity, Quantum Fields and Information group and will take place at the AEI in Potsdam from Monday, October 1st to Friday, October 5th, 2018. 

Schedule:

The schedule of talks is below, with ample time allotted for informal discussions. Note that October 3rd is German Unity Day, so shops and administration will be closed. Rather than schedule any official talks, we have elected to give participants a day for quiet work or informal discussion/collaboration.

Workshop schedule

Invited participants:

Raul Arias
Alex Belin
Tom Faulkner (virtual talk)
Christopher Herzog
Stefan Hollands
Nabil Iqbal
Ali Mollabashi
Natascia Pinzani-Fokeeva
Misha Smolkin
Tomonori Ugajin
Erik Verlinde

Abstracts:

Raul Arias: Local temperatures and modular hamiltonians
I will introduce the notion of modular hamiltonian and relating it to the relative entropy I will give a definition of local temperatures. In the second part of the talk I will show you how to compute it and some simple examples where analytic solutions were found.

Alex Belin: Holographic symplectic forms and a CFT prescription to compute extremal volumes
In this talk, I will present a new entry in the AdS/CFT dictionary: the bulk symplectic form is dual to a quantum Kahler form on the space of CFT sources. I will derive this relation and discuss one particular application of it: a CFT prescription to compute extremal volumes in the bulk. This talk will be based on arXiv:1806.10144 as well as work in progress.

Tom Faulkner: Into the bulk with modular flow
I will discuss modular flow in AdS/CFT as a useful tool to reconstruct the bulk. As a simple example I will discuss how to prove entanglement wedge nesting directly in the boundary theory.

Christopher Herzog: Graphene and boundary conformal field Theory
I will discuss boundary contributions to the anomaly in the trace of the stress tensor in boundary conformal field theory. While largely unstudied, these boundary charges hold out the tantalizing possibility of being as important in the classification of quantum field theory as the bulk central charges “a” and “c”. I will show how these charges can be computed from displacement operator correlation functions. I will also demonstrate a boundary conformal field theory in four dimensions — a relative of graphene — with an exactly marginal coupling where these boundary charges depend on the marginal coupling. The talk is based on arXiv:1707.06224, arXiv:1709.0743, and arxiv:1807.01700.

Stefan Hollands: Entanglement measures and modular theory
In this talk I first recall the characterization of an entanglement measure as a way to measure how far a given state of a bipartite system is from a separable state (no entanglement). I will then give several examples of such measures. Some of them are, by definition, related directly to the modular theory of Tomita and Takesaki, and others indirectly so. In the last part, I present concrete results and applications in the context of algebraic quantum field theory.

Nabil Iqbal: Applications of higher form symmetries
Just as ordinary global symmetries are associated with a conserved particle number, quantum field theories with generalized global symmetries have a conserved density of higher-dimensional objects (such as strings, branes, etc.). I will discuss the emergence of gapless Goldstone modes when such a symmetry is spontaneously broken and will review how such a generalized symmetry plays an important role in characterizing the long-distance physics of familiar Maxwell electrodynamics in four dimensions. Many structures of ordinary symmetries admit a higher-form generalization; I will discuss some of these, focusing on the 4d analogues of familiar 2d concepts such as bosonization and (Abelian) Kac-Moody algebras. If time permits I will discuss how the holographic realizations of such higher-form symmetries.

Ali Mollabashi: Dynamics of Entanglement in Lifshitz-type quantum field theories
I will introduce Lifshitz harmonic lattice models as a family of simplest many-body models to study entanglement in free Lifshitz field theories. Using this model in the first part I will discuss about the leading divergence of entanglement entropy in the vacuum state. Also extending the study to thermal states I will report some results about the 'shared area' law for logarithmic negativity in 1+1 and 2+1 dim. In the second part I will discuss about propagation of entanglement in such a model after a mass quench.

Natascia Pinzani-Fokeeva: Schwinger-Keldysh effective field theories
I will discuss novel effective field theory constructions valid for thermal states, as opposed to the canonical Wilsonian effective approach in vacuum. In particular, I will show how the relevant symmetries of the problem can be efficiently implemented using two anticommuting BRST charges and superspace techniques.

Tomonori Ugajin:
First talk: Modular hamiltonians of excited states, OPE blocks and emergent bulk fields
We study the entanglement entropy and the modular Hamiltonian of slightly excited states reduced to a ball shaped region in generic conformal field theories. We set up a formal expansion in the one point functions of the state in which all orders are explicitly given in terms of integrals of multi-point functions along the vacuum modular flow, without a need for replica index analytic continuation. We show that the quadratic order contributions in this expansion can be calculated in a way expected from holography, namely via the bulk canonical energy for the entanglement entropy, and its variation for the modular Hamiltonian. The bulk fields contributing to the canonical energy are defined via the HKLL procedure. In terms of CFT variables, the contribution of each such bulk field to the modular Hamiltonian is given by the OPE block corresponding to the dual operator integrated along the vacuum modular flow. These results do not rely on assuming large N or other special properties of the CFT and therefore they are purely kinematic.

Second talk: Towards an entanglement measure for mixed states in CFTs based on relative entropy
Relative entropy of entanglement (REE) is an entanglement measure of bipartite mixed states on disjoint subsystems AB , defined by the minimum of the relative entropy between a given mixed state and an arbitrary separable state . The REE is always bounded by the mutual information IAB because the latter measures not only quantum entanglement but also classical correlations. In this paper we address the question of to what extent REE can be small compared to the mutual information in conformal field theories (CFTs). For this purpose, we perturbatively compute the relative entropy between the vacuum reduced density matrix on disjoint subsystems AB and arbitrarily separable state in the limit where two subsystems A and B are well separated, then minimize the relative entropy with respect to the separable states. We argue that the result highly depends on the spectrum of CFT on the subsystems. When we have a few low energy spectrum of operators as in the case where the subsystems consist of a finite number of spins in spin chain models, the REE is considerably smaller than the mutual information. However in general our perturbative scheme breaks down, and the REE can be as large as the mutual information.

Erik Verlinde: TBA

Practical information:


Invited participants will be housed in the on-campus guesthouse, the keys for which may be picked up upon arrival at the reception desk in the central building. The reservation and payment will be taken care of on our end; you don't need to do anything. Additionally, all participants will receive a desk at the institute, and wifi is available throughout the campus.

The easiest way to reach the AEI is by taking one of the trains from Berlin to Golm, from which the institute is a short 5-10 minute walk. Note that depending on the time of day, it may be necessary to change trains in Potsdam Hbf. There are frequent trains between Potsdam and Golm, in addition to a (slower but more frequent) bus service (lines 605 & 606) that stops directly at the campus. More details, including a map of the Max Planck campus, can be found here.

Breakfast and lunch will be available in the on-campus cafeteria, located in the central building. For dinner, there are a wide variety of restaurants in Potsdam. Additionally, there is a REWE supermarket just across the train tracks from the guesthouse, and the latter is equipped with a kitchen if you wish to prepare some basic meals yourself. However, be aware that both the supermarket and the on-campus cafeteria will be closed on Wednesday the 3rd!

If you have further questions, please do not hesitate to contact the organizers: Diptarka Das and Ro Jefferson.