Scientific Series

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] 

Epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known epistemic ontological models of quantum theory in dimension d ≥ 3, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness. We also discuss hidden Markov models and their relationship to ontological models, demarcating the ways in which one might move ‘outside’ the ontological models formalism.

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.

Hidden sector particles, with masses and couplings below those of the weak interactions, can resolve many of the outstanding questions of the Standard Model, including the identity of dark matter, the origin of the baryon asymmetry, and the physics of neutrino masses. Existing searches at colliders such as the Large Hadron Collider are, however, often insensitive to signals of hidden sectors. Using the well-motivated example of low-scale leptogenesis and neutrino masses, I will demonstrate connections between the cosmology of hidden sectors and their signatures in experiments. I will then present new experimental ideas for how to uncover the existence of hidden sectors at the LHC, as well as my role in founding and leading a joint theory-experiment initiative working to greatly expand sensitivity to long-lived particles  Finally, I will discuss my theoretical and experimental work on low-energy colliders such as B factories, which have an immense and under-utilized potential for discovering hidden particles. Given the many connections between colliders, astrophysics, cosmology, and other terrestrial experiments emerging from the study of hidden sectors, the future is bright for expanding our knowledge of the hidden universe.

Current progress in quantum field theory is largely driven by the conformal bootstrap program, which aims to classify the space and properties of conformal field theories using symmetries and other fundamental constraints. In the context of the AdS/CFT Correspondence, this increasingly sophisticated endeavor doubles as a probe of foundations of quantum gravity. I will describe the current era in the holographic application of conformal field theory methods, with particular focus on the use of the conformal bootstrap to describe the spectrum and dynamics of quantum gravity and string theory beyond the classical regime.

Adiabatic evolution is a common strategy for manipulating quantum states. However, it is inherently slow and therefore susceptible to decoherence. Shortcuts to adiabaticity are methods of achieving faster adiabatic evolution, in order to maintain high fidelity in the presence of decoherence and noise. In this talk I will review recent progress on counter-diabatic (CD) driving for many-body systems. In particular, we will discuss a variational principle that allows to systematically compute approximate CD Hamiltonians. Two recent experiments will be discussed. 

3d quantum gravity is a beautiful toy-model for 4d quantum gravity: it is much simpler, it does not have local degrees of freedom, yet retains enough complexity and subtlety to provide a non-trivial example of dynamical quantum geometry and open new directions of research in physics and mathematics. I will present the Ponzano-Regge model, introduced in 1968, built from tetrahedra “quantized" as 6j-symbols from the theory of recoupling of spins. I will show how it provides a discrete path integral for 3d quantum gravity, related to topological invariants and loop quantum gravity and other approaches to quantum gravity. It is also a perfect arena to investigate boundary theories and holographic dualities, with a beautiful duality with the 2d Ising model realized through a supersymmetry, and more.

Experiments with ultracold fermionic gases are thriving and continue to provide us with valuable insights into fundamental aspects of physics. A special system of interest is the so-called unitary Fermi gas (UFG) situated right in the "middle" of the crossover between Bardeen-Cooper-Schrieffer superfluidity and Bose-Einstein condensation. However, the theoretical treatment of these gases is highly challenging due to the absence of a small expansion parameter as well as the appearance of the infamous sign problem in the presence of, e.g., finite spin polarizations. In this talk, I will discuss the concept of stochastic quantization and motivate the complex Langevin (CL) method for non-relativistic fermions as an alternative to conventional Monte Carlo approaches. In particular, I will show how the CL approach can be employed to study the spin-polarized UFG. In the unpolarized limit, our results for the EOS are in excellent agreement with the existing state-of-the-art results from other ab-initio approaches as well as with experimental data. For the polarized case, our results for the EOS and other thermodynamic quantities represent experimentally testable predictions, already providing us with some insight into the underlying phase diagram.

I will give an overview of recent results on three-dimensional N=2 supersymmetric gauge theories placed on arbitrary half-BPS geometries. In particular, I will explain an explicit computation of the supersymmetric partition function on any Seifert three-manifold; such manifolds can have very intricate and interesting topology (for instance, a nice example is the Poincaré sphere) and can provide new interesting observables in 3d SCFTs. I will also discuss to which extent these results exhibit a generalisation of the 3d TQFT structure of Chern-Simons theory to non-topological (but supersymmetric) theories.