Scientific Series

Renormalized perturbation theory for QFTs typically produces divergent series, even if the coupling constant is small, because the series coefficients grow factorially at high order. A natural, but historically difficult, challenge has been how to make sense of the asymptotic nature of perturbative series.  In what sense do such series capture the physics of a QFT, even for weak coupling?   I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs - that is, perturbation theory - yields well-defined answers once the implications of  resurgence theory are taken into account.   Resurgence theory relates expansions around different saddle points of a path integral to each other, and has the striking practical implication that the high-order divergences of perturbative series encode precise information about the non-perturbative physics of a theory.  These ideas will be discussed in the context of a QCD-like toy model theory, the two-dimensional principal chiral model, where resurgence theory appears to be capable of dealing with the most difficult types of divergences, the renormalons.  Fitting a conjecture by ’t Hooft, understanding the origin of renormalon divergences allows us to see the microscopic origin of the mass gap of the theory in the semiclassical domain.

The cosmological model based on cold dark matter (CDM) and dark energy has been hugely successful in describing the observed evolution and large scale structure of our Universe.  However, at small scales (in the smallest galaxies and at the centers of larger galaxies), a number of observations seem to conflict with the predictions CDM cosmology, leading to recent interest in Warm Dark Matter (WDM) and Self-Interacting Dark Matter (SIDM) models. These small scales, though, are also regions dominated by the influence of baryons. I will present results from high resolution cosmological galaxy simulations that include both baryons and dark matter to show that baryonic physics can significantly alter the dark matter structure and substructure of galaxies, revolutionizing our expectations for galaxy structure and influencing our interpretation of the Dark Matter model.

We propose a new way to search for (hidden) cool molecular hydrogen H2 in the Galaxy through diffractive and refractive effects: Stars twinkle because their light crosses the atmosphere. The same phenomenon is expected on a longer time scale when the light of a remote star crosses an interstellar turbulent molecular cloud, but it has never been observed at optical wavelengths. Our simulations and test observations show that in favorable cases, the light of a background star can be subject to stochastic fluctuations on the order of a few percent at a characteristic time scale of a few minutes.

We  searched for scintillation caused by molecular gas within visible dark nebulae as well as by hypothetical halo clumpuscules of cool molecular hydrogen (H2-He) with the ESO-NTT telescope. Within a few thousands of densely sampled light-curves, we found one candidate that shows variabilities compatible with a strong scintillation effect through a turbulent structure of the B68 nebula. Furthermore, since no candidate has been found toward the SMC, we were also able to establish upper limits on the contribution of gas clumpuscules to the Galactic halo mass.

I will discuss the perspectives of synchronized observations with two large distant telescopes, to observe the time decorrelation between the light curves, an undisputable signature of the scintillation process. I will then show that a few nights of observation using the so-called « movie-mode » of LSST should allow one to significantly constrain the last unknown baryonic contribution to the Galactic mass.

I offer a personal perspective on the causal dynamical triangulations approach to the construction of quantum theories of gravity. After briefly introducing the approach's formalism and results, I illuminate this perspective with 3+1 vignettes of recent and ongoing research. Specifically, I review attempts to locate an ultraviolet fixed point through renormalization group analyses; I report measurements of the homogeneity of the approach's quantum geometries; I discuss efforts to determine the large scale effective action in the case of 2+1 dimensions; and I suggest a speculative possibility for reviving the Euclidean dynamical triangulations approach.

One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background. We also consider as a concrete example linearized metric perturbations of a five-dimensional AdS-Schwarzschild black brane and show that a spurious excitation appears in the long-wavelength response that is only removed from the spectrum when the membrane paradigm is replaced by ingoing boundary conditions at the event horizon. We interpret this excitation in terms of an additional Goldstone boson that appears due to symmetry breaking by the classical solution ending on the stretched horizon rather than the event horizon.

Based on arXiv:1405.4243

Quantum Adiabatic Optimization proposes to solve discrete optimization problems by mapping them onto quantum spin systems in such a way that the optimal solution corresponds to the ground state of the quantum system. The standard method of preparing these ground states is using the adiabatic theorem, which tells us that quantum systems tend to remain in the ground state of a time-dependent Hamiltonian which transforms sufficiently slowly. In this talk I'll show that alternative strategies using non-adiabatic effects can in some cases be dramatically faster for instances which are hard for the traditional adiabatic method.

I will also discuss Simulated Quantum Annealing (SQA), which is a classical simulation of adiabatic optimization at non-zero temperature based on Path-Integral Quantum Monte Carlo. SQA is widely used in practice to study adiabatic optimization, but relatively little is known about the rate of convergence of the markov chain that underlies the algorithm. By focusing on a family of instances which adiabatic optimization solves in polynomial time, but require exponential time to solve using classical (thermal) simulated annealing, I will present numerical evidence as well as a work-in-progress proof that SQA can be exponentially faster than classical simulated annealing.

In (relatively) recent years some philosophers of physics have developed and advocated a new view about how to understand spatiotemporal structures posited in theories such as classical mechanics, relativistic theories and GR; it is called the 'dynamical approach' to spacetime (H. Brown 2005, Physical Relativity).  The dynamical approach (DA) holds that spacetime structure should not be thought of as conceptually prior to the laws of nature, or as constraining the forms that the laws may have. Instead, the DA approach says that the laws of nature are prior, and spacetime structures are no more than a reflection, or codification, of facts (especially symmetry facts) about the dynamical laws in our world. In my talk I will explore the motivations and arguments given in support of the dynamical approach, and raise doubts about whether they are coherent and compelling. Although no-one should come away from my talk with a perfect understanding of the nature of spacetime (or even just: spacetime as it appears in classical relativistic theories), I hope that all will come to appreciate the difficulty of deciding what even clear and mathematically well-understood physical theories really tell us about basic aspects of physical reality.

In the search for dark matter, neutrino experiments can play a key role by doubling as dark matter production and detection experiments. I will describe how the proposed DAEdALUS decay-at-rest neutrino experiment can be used to search for MeV-scale dark matter, with particular emphasis on dark matter produced through a dark photon in rare neutral pion decays. The fact that the dark photon need not be on-shell opens up a wide range of new possibilities for the experimental program of searching for dark matter at neutrino experiments.

In two spatial dimensions, it is well known that particle-like excitations can come with fractional statistics, beyond the usual dichotomy of Bose versus Fermi statistics. In this talk, I move one dimension higher to three spatial dimensions, and study loop-like objects instead of point-like particles. Just like particles in 2D, loops can exhibit interesting fractional braiding statistics in 3D. I will talk about loop braiding statistics in the context of symmetry protected topological phases, which is a generalization of topological insulators.

The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of computing devices, its implications in other scientific fields have hardly been explored. What if we consider the Church-Turing thesis as a law of nature? In this talk I will present our first results in connection with quantum information theory [1] by showing that computer science laws have profound implications for some of the most fundamental results of quantum theory.  First I will show how they question our knowledge on what a mixed quantum state is, as we identified situations in which ensembles of quantum states defining the same mixed state, indistinguishable according to the quantum postulates, do become distinguishable when prepared by a computer (or any classical system). Then I will introduce a new loophole for Bell-like experiments: if some of the parties in a Bell-like experiment use a computer to decide which measurements to make, then the computational resources of an eavesdropper have to be limited in order to have a proper observation of non-locality.

I will talk about 4d N=2 gauge theories with a co-dimension-two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and N=2* theory, a full surface operator can be described as the 4d gauge theory coupled to a 2d N=(2,2) gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations. In addition, I will show the validity of the orbifold method in one-loop computations when a full surface operator is inserted, and the form of the structure constants with a semi-degenerate field in SL(N,R) WZNW model is predicted from one-loop determinants.