Talks

The construction of soluble lattice toy models is an important theoretical approach in the study of strongly interacting topological phases of matter. On the other hand, the primary experimental probe to such systems is via electromagnetic response. Somewhat unsatisfactorily, the current systematic construction of the lattice toy models focuses on braiding statistics and does not admit coupling to an electromagnetic background. Thus there is a mismatch between our theoretical approach and experimental probe. In this talk I introduce how to systematically incorporate electromagnetic response into the soluble lattice toy models, for a large class of abelian topological phases. [Reference: 1902.06756] 

Despite intensive theoretical research for several decades, the theory of quantum gravity remains elusive. I will review the obstacles that prevent from reconciling the principles of general relativity with those of quantum mechanics. It is plausible that an eventual ultraviolet completion of general relativity will require sacrificing some of these principles. I will then focus on the class of theories where the abandoned property is local Lorentz invariance, replaced by an approximate anisotropic scaling symmetry in deep ultraviolet. At low energies these theories reduce to a special type of scalar — tensor gravity. I will show that this approach allows us to construct renormalizable gravitational theories in any number of spacetime dimensions. The study of a (2+1) dimensional model reveals its asymptotic freedom and suggests that this property may be generic for gravity with anisotropic scaling. Relevance of these results for gravity in the real world will be discussed.

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.

In a synthetic approach to geometry and physics, one attempts to formulate an axiomatic system in purely logical terms, abstracting away from irrelevant "implementation details". In this talk, I will explain how intuitionistic logic and topos theory provide a synthetic theory of space, and then consider a (naive version of) Euclidean QFTs in terms of a conjectural elegant synthetic reformulation: a Euclidean QFT is nothing but a probability space in intuitionistic logic, extended by suitable modalities formalizing compact regions of space. Time permitting, I will sketch how this approach is roughly dual to AQFT, and/or how to define vacua in terms of the DLR equations. I am also hoping for feedback on how naive this approach really is in the light of renormalization.