Scientific Series

The covariant (spinfoam) formulation of loop gravity is a tentative physical quantum theory of gravity with well defined transition amplitudes.  I give my current understanding of the state of the art in this research direction, the issues that are open and need to be explored, and the current attempts to use the theory to compute quantum effects in the early universe and in black hole physics.

While it is considered to be one of the most promising hints of new physics beyond the Standard Model, dark matter is as-yet known only through its gravitational influence on astronomical and cosmological observables. I will discuss our current best evidence for dark matter's existence as well as the constraints that astrophysical probes can place on its properties, while highlighting some tantalizing anomalies that could indicate non-gravitational dark matter interactions. Future observations, along with synergies between astrophysical and experimental searches, have the potential to illuminate dark matter's fundamental nature and its influence on the evolution of matter in the cosmos from the first stars and galaxies to today.

We look at the interior operator reconstruction from the point of view of Petz map and study its complexity. We show that Petz maps can be written as precursors under the condition of perfect recovery. When we have the entire boundary system its complexity is related to the volume / action of the wormhole from the bulk operator to the boundary. When we only have access to part of the system, Python's lunch appears and its restricted complexity depends exponentially on the size of the subsystem one loses access to.

It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries (Lorentz symmetries) parametrized by the value of the cosmological constant. They appear as some kind of regularization either through the quantization of the Chern-Simons formulation (Fock-Rosly formulation/combinatorial quantization, path integral quantization) or the state sum approach (Turaev-Viro model). Such deformation might be perplexing from a classical picture since the action is defined in terms of plain/undeformed gauge symmetry. I would like to present here a novel way to derive/justify such quantum group deformation, starting from the classical action.

I will review the construction of Coulomb branches in 3D gauge theory for a compact Lie group G and a quaternionic  representation E. In the case when E is polarized, these branches are determined by topological boundary conditions built from the gauged A-model of the two polar halves of E. No analogue of this is apparent in the absence of a polarization, nonetheless the Coulomb branch can be defined by the use of a ‘quantum’ square root of E (related to the Spin representation). These branches ought to be part of a 3D topological field theory, but that is only apparent in special cases.

We discuss several numerical and analytical studies of the modified gravity theory Einstein dilaton Gauss-Bonnet (EdGB) gravity. This class of modified gravity theories admit scalarized black hole solutions. The theory may then provide significantly different gravitational wave signatures during binary black hole merger as compared to general relativity, so that gravitational wave observations may provide new stringent constraints on EdGB gravity. The theory is also an important member of the Horndeski theories, which have been used to model theories of the early universe, including inflation and ekpyrosis. We describe our investigations of the self-consistency of EdGB gravity for spherically symmetric solutions that differ significantly from those in GR, including scalarized black hole solutions, and find that for solutions where the Gauss-Bonnet corrections to general relativity are not small, the theory no longer admits hyperbolic evolution. We discuss how an effective field theory interpretation of the equations of motion though should always guarantee (locally) hyperbolic evolution for the theory.

In the 1980’s, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to ‘baby universes’ and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore this structure in detail in simple topological models of the bulk that allow us to compute the full spectrum of associated boundary theories. We also argue that similar properties must hold in any consistent gravitational path integral.

Hosted By: Stanford University  Footage Courtesy: Simons Foundation for Mathematics and Physical Sciences

There has been tremendous progress in the many layers needed to realize large-scale quantum computing, from the hardware layers to the high level software. There has also been vastly increased exploration into the potentially useful applications of quantum computers, which will drive the desire to build quantum computers and make them available to users. I will describe some of my research in quantum algorithmics and quantum compiling.

The knowledge and tools developed for these positive applications give us insight into the cost of implementing quantum cryptanalysis of today's cryptographic algorithms, which is a key factor in estimating when quantum computers will be cryptographically relevant (the "collapse time"). In addition to my own estimates, I will summarize the estimates of 22 other thought leaders in quantum computing.

What quantum cryptanalysis means to an organization or a sector depends not only on the collapse time, but also on the time to migrate to quantum-safe algorithms as well as the shelf-life of information assets being protected. In recent years, we have gained increasing insight into the challenges of a wide-scale migration of existing systems. We must also be proactive as we deploy new systems. Open-source platforms, like OpenQuantumSafe and OpenQKDNetwork, are valuable resources in helping meet many of these challenges.

While awareness of the challenges and the path forward has increased immensely, there is still a long road ahead as we work together with additional stakeholders not only to prepare our digital economy to be resilient to quantum attacks, but also to make us more resilient to other threats that emerge.

I describe a novel way to produce states associated to geodesic motion for classical particles in the bulk of AdS that arise from particular operator insertions at the boundary

at a fixed time. When extended to black hole setups, one can understand how to map back the geometric information of the geodesics back to 

the properties of these operators. In particular, the presence of stable circular orbits in global AdS are analyzed. The classical Innermost Stable Circular Orbit 

(ISCO) play an important role separating metastable state excitations from those that quickly  fall in the horizon of  black hole. In the dual CFT, this metastability effect must be a non-perturbative effect due to the curvature on the boundary.

In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand  the  Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux  and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes. This leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. Taking a finite dimensional truncation of this quantization yields states of quantum geometry,  dubbed `Poincaré charge networks’, which carry a representation of the 3D diffeomorphism boundary charges on top of the SU(2) fluxes and gauge transformations. This opens the possibility to have for the first time a framework where spatial diffeomorphism are represented at the quantum level. Moreover, our construction leads naturally to the picture that the relevant geometrical degrees of freedom live on boundaries, that their dynamics and the fabric of quantum space itself is encoded into their entanglement, and it is designed to offer a new setting to study the coarse-graining of gravity both at the classical and the quantum levels.

As of late March 2020, Covid-19 has already secured its status among the most expansive pandemics of the last century. Covid-19 is caused by a coronavirus--SARS-CoV-2--that causes a severe respiratory disease in a fraction of those infected, and is typified by several important features: ability to infect cells of various kinds, contagiousness prior to the onset of symptoms, and a widely varying experience with disease across patient demographics.

In this seminar, I discuss the many lessons that the scientific community has learned from Covid-19, including insight from molecular evolution, cell biology, and epidemiology. I discuss the role of mathematical and computational modeling efforts in understanding the trajectory of the epidemic, and highlight modern findings and potential research questions at the interface of virology and materials science. I will also introduce areas of inquiry that might be of interest to the physics community.

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem: 
(C) Which gauge invariant degrees of freedom are associated to a region with boundaries? 
(S) Do the gauge invariant degrees of freedom in two complementary regions R and R’ unambiguously comprise *all* the gauge-invariant degrees of freedom in M = R ∪ R’ ? Or, do new “boundary degrees of freedom” need to be introduced at the interface S = R ∩ R’ ?
In this talk, I will address and answer these questions in the context of Yang-Mills theory. The analysis is carried out at the level of the symplectic structure of the theory, i.e. for linear perturbations over arbitrary backgrounds. I will also discuss how the ensuing results translate into a quasilocal derivation of the superselection of the electric flux through the boundary of a region, and into a novel gluing formula which constructively proves that no ambiguity exists in the gluing of regional gauge-fixed configurations.
Time allowing I will also address how the formalism generalizes the “Dirac dressing” of charged matter fields, and how, in the presence of matter, quasi-local “global” charges (as opposed to gauge charges) emerge at special (i.e. reducible) configurations.

This talk is based on arXiv:1910.04222, with H. Gomes (U. of Cambridge, UK).
See also arXiv:1808.02074, with H. Gomes and F. Hopfmüller (Perimeter)