Scientific Series

In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework. If time permits, we finish with a discussion of excitations and the generalization to higher dimensions.

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to Q=716π−−−√≈0.37. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in SU(3) and SU(5) gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to QL≈0.38±0.04.

We investigate the properties of Chern-Simons theory coupled to massive fermions at finite density. In the large N limit, this is solvable to all orders in the coupling and we use this as a playground for investigating the behavior of strongly correlated condensed matter systems. At low temperatures the system enters a Fermi liquid state whose features may be compared to the phenomenological theory of Landau Fermi liquids and our analysis indicates the need to augment this framework to properly characterize parity odd transport. Furthermore, an investigation of the equation of state reveals novel phenomena at strong coupling. As the interaction strength is tuned to infinity, the system exhibits an extended intermediate regime in which the thermodynamics is described by neither Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

The collection of all Dirac operators for a given fermion space defines its space of geometries. 
Formally integrating over this space of geometries can be used to define a path integral and a thus a theory of quantum gravity. 
In general this expression is complicated, however for fuzzy spaces a simple expression for the general form of the Dirac operator exists. This simple expression allows us to explore the space of geometries using Markov Chain Monte Carlo methods and thus examine the path integral in a manner similar to that used in CDT. 
In doing this we find a phase transition and indications that the geometries close to this phase transition might be manifold like.

In the coming years, astrophysical observations of strongly gravitating systems will provide us with exciting new data to study extremely compact objects and Einstein’s theory of general relativity. In particular, gravitational wave observatories will soon reach the sensitivity required to detect merging black holes and neutron stars, while the Event Horizon Telescope is about to observe accretion flows around two supermassive black holes with sub-horizon resolution. Accurate modeling of these systems require complex simulations including general relativistic magnetohydrodynamics, radiation transport, and, for the Event Horizon Telescope, heat conduction and viscosity in a nearly collisionless plasma. In this talk, I will discuss recent results from global general relativistic simulations of these systems. I will mainly focus on our understanding of the gravitational wave and electromagnetic signals powered by binary mergers, and what they may tell us about the properties of neutron-rich nuclear matter and the origin of many heavy elements observed in the Universe today. I will also discuss how to model non-ideal fluids in general relativistic magnetohydrodynamics simulations of accretion disks, and how non-ideal effects may modify the properties of accretion flows around slowly accreting supermassive black holes — including the two targets of the Event Horizon Telescope.

I will review a recent proposal for a top-down approach to AdS/CFT by A. Schwarz, which has the advantage of requiring few assumptions or extraneous knowledge, and may be of benefit to information theorists interested by the connections with tensor networks.  I will also discuss ways to extend this approach from the Euclidean formalism to a real-time picture, and potential relationships with MERA.

In this talk I will sketch the relation between unitary representations of the BMS3 group and three-dimensional, asymptotically flat gravity. More precisely, after giving an exact definition of the BMS group in three dimensions, I will argue that its unitary representations are classified by orbits of CFT stress tensors under conformal transformations. These stress tensors, in turn, can be interpreted as Bondi mass aspects for asymptotically flat metrics. I will also show how one can compute characters of the BMS3 group, which coincide with suitable gravitational one-loop partition functions

We present an effective Z2 gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological Z2 spin liquid (SL) phase, and the 12-site and 36- site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent Z2 gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a different Z2 gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up- and down-triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. Particularly, interesting dimer melting effects are found in the 36-site VBS. We discuss the implications of our findings and also compare the results with a different type of Z2 gauge theory used in previous studies.

In recent years, entanglement has become a new frontier with applications across several fields in physics. Nevertheless, simple conceptual pictures and practical ways to quantify entanglement in many-body systems have remained elusive even for the simplest models. In this talk, I will consider entanglement and Renyi entropies as well as quantum (mutual, tripartite, etc.) information in a quantum field theory. For free field theories, I will show that quantum entropies and information can be computed and understood by analogy with the thermal Casimir effect in one higher dimension. Furthermore, I will introduce a geometrical picture for the quantum (mutual, tripartite) information as a sum over polymers establishing a connection to purely entropic effects that prove useful in deriving information inequalities.  Finally, I will show that similar ideas may be extended beyond free field theories.

In light of the upcoming Generation 2 (G2) direct-detection experiments attempting to record dark matter scattering with nuclei in underground detectors, it is timely to inquire about their ability to single out the correct theory of dark-matter-baryon interactions, in case a signal is observed. I will present a recent study in which we perform statistical analysis of a large set of direct-detection simulations, covering a wide variety of operators that describe scattering of fermionic dark matter with nuclei. I will show that a strong signal on G2 xenon and germanium targets has enough discrimination power to reconstruct the momentum dependence of the interaction, ruling out entire classes of models. However, zeroing in on a correct UV completion will critically depend on the availability of measurements from a wide variety of nuclear targets (including iodine and fluorine) and on the availability of low energy thresholds. This study quantifies complementarity amongst different experimental designs and targets, and provides a roadmap for future data analyses. It also highlights the critical need for bringing in information from all available probes in dark matter studies.

Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a systematic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective thermal behavior generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a universality class in equilibrium thermodynamics. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermal behaviour.

I will review the possible role in Geometric Langlands
of N=4 boundary conditions in four-dimensional supersymmetric Yang Mills theory.
The action of S-duality on such boundary conditions can be understood
in terms of symplectic duality.