Scientific Series

I discuss a new proposal for nonperturbatively defining chiral gauge theories, something that has resisted previous attempts. The proposal is a well defined field theoretic framework that contains mirror fermions with very soft form factors, which allows them to decouple, as well as ordinary fermions with conventional couplings.  The construction makes use of an extra dimension, which localizes chiral zeromodes on the boundaries, and a four dimensional gauge field extended into the bulk via classical gradient flow.  After explaining how this setup works, I consider open questions concerning the flow of topological gauge configurations, as well as possible exotic phenomenology in the Standard Model lurking at the low energy frontier.

I will present a new area law in General Relativity. This new area law holds on local analogues of event horizons that have an independent thermodynamic significance due to the Bousso bound. I will also discuss a quantum generalization of this more local notion of thermodynamics.

We introduce the spectrum bifurcation renormalization group (SBRG) as an improvement of the excited-state real space renormalization group (RSRG-X) for qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the full MBL phase. As a Hilbert-space preserving RG, the SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.

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 compute the scaling dimensions of a large class of disorder operators ("monopoles") in the planar limit of CS-fermion theories.  The lightest such operator is shown to have dimension (2/3) k^{3/2}, where k is the CS level.  The computation is based on recently developed techniques for solving CS-matter at all 't Hooft couplings, and the operator dimensions are obtained by finding complex saddles in the low-temperature phase of the CS-fermion path integral in a monopole background.  We will also discuss the implications of this result to 3D bosonization dualities.

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.

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.