Scientific Series

The program of Ben-Zvi--Sakellaridis--Venkatesh connects the construction of L-functions in number theory with S-duality of boundary conditions in 4d. In particular this predicts certain equivalences of categories between equivariant D-modules on the formal loop space of a smooth variety X and equivariant quasi-coherent sheaves on a Hamiltonian manifold. I discuss an extension of this conjecture to certain singular varieties X and the possibility of quantizing the equivalence. I will explain joint work with Yiannis Sakellaridis on computing a certain factorization algebra which plays a role in the story. 

Zoom Link: https://pitp.zoom.us/j/95543248994?pwd=bmZIRnEyLzZnNmlEWW5oNTEwaEhNUT09

This talk is devoted to the geometric approach to supergravity and applications in the framework of loop quantum gravity. Among other things, this approach leads to a reformulation of the theory in which (part of) supersymmetry manifests itself in terms of a gauge symmetry. Using the interpretation of supergravity in terms of a super Cartan geometry, we will derive the Holst variant of the MacDowell-Mansouri action for N=1 and N=2 AdS supergravity in D=4 for arbitrary Barbero-Immirzi parameters. We will show that these actions provide unique boundary terms that ensure local supersymmetry invariance at boundaries. The chiral case is special. The action is invariant under an enlarged gauge symmetry, and the boundary theory is a super Chern-Simons theory. The action also implies boundary conditions that link the super electric flux through, and the super curvature on, the boundary. Applications we have in mind are supersymmetric black holes and loop quantum cosmology. To this end, we will study a class of symmetry reduced models of chiral supergravity. The enlarged gauge symmetry of the chiral theory is essential as it allows for nontrivial fermionic degrees of freedom even if one imposes spatial isotropy. The quantization of the theory yields a natural state space and allows a consistent implementation of the constraint algebra.

Finally, we will give an outlook on applications towards a quantum description of supersymmetric black holes in the context of LQG and possible relations to superstring theory.

In the first half of this talk I will discuss recent developments in Gamma Ray Burst (GRB) afterglows.  GRBs associated with gravitational wave events are, and will likely continue to be, viewed at a larger inclination than GRBs without gravitational wave detections.  Viewing GRBs and their afterglows at large inclination can massively affect the observed electromagnetic emission. I will discuss how we model and reason about GRB afterglows in this new era, and new software tools to aid in this work. With our theoretical tools in hand we will briefly go over some recent applications of these models to both short and long GRBs.

In the second half of this talk I will cover ongoing work on binary black hole accretion with the moving-mesh hydrodynamics code Disco.  Gas accretion may hinder or accelerate the merger of supermassive binary black holes, affecting predicted rates for LISA and PTA targets.  Determining the magnitude and sign of the torque exerted on the black hole binary by surrounding gas is a difficult problem that can only be approached by hydrodynamic simulation.  I will discuss recent simulations with Disco that explore the dependence of this torque on the mass ratio of the binary and temperature of the gas, the latter of which can reverse the sign of the torque.

In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.

Zoom Link: https://pitp.zoom.us/j/99898585189?pwd=NytLaWt2RjFPOTVJOEptMlBBd1BvZz09

I will discuss a set of calculations of dark matter interactions with low threshold semi-conductor detectors such as SENSEI and superCDMS. As a warm-up, I'll show how to rephrase traditional DM-electron scattering calculations in terms of the energy loss function of the material. We will then apply this framework to compute the rate for the Migdal effect in semi-conductor targets. This is needed because the traditional calculations of the Migdal effect do not apply in low threshold semi-conductor detectors, as the delocalized nature of the valence electrons is not taken into account.

Although cold dark matter (CDM) has been established, this is only the case for measurements at large scales, which are larger than galaxy-sized structures. Even though we need to understand the important role of baryonic components, matter distribution at small scales can be the key to distinguishing different particle dark matter candidates. In fact, warm dark matter, self-interacting dark matter, and fuzzy dark matter have been proposed, yielding different matter distributions at sub-galactic scales. These small-scale distributions have been studied with numerical simulations. Whereas very reliable, numerical simulations suffer certain issues. They are limited by both numerical resolution and shot noise. They tend to take a lot of computational time. These might be a bottleneck for surveying through multi-dimensional parameter space of various dark matter models. I present semi-analytic models of small-scale structure, especially dark matter subhalos, which are based on structure formation theory and the tidal evolution of subhalos. Our models for CDM have been well tested against the results of various numerical simulations. The semi-analytic models are free from all the problems of the numerical simulations mentioned above. Therefore, they might be essential ingredients for identifying the particle nature of dark matter through gravitational (lensing, pulsar timing), astrophysical (satellite counts, stellar streams), and astroparticle probes (gamma rays).

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. It also unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior. Remarkably, the physical ISO(2,1) symmetry can be seen as a broken infinite-dimensional symmetry. This is done by reinterpreting the action for the model as a geometric action for the BMS3 group, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors.

Zoom Link: https://pitp.zoom.us/j/99646733321?pwd=U05kYU85V0Q4VCtrZ1BNV2JZbE1DUT09

We consider quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one-loop-resummed exchange diagrams.

The epoch of cosmic reionization can be probed using the secondary anisotropies imprinted on the cosmic microwave background (CMB) temperature and polarization field. I will discuss the imprints of patchy reionization on the kSZ power spectrum and CMB B-mode polarization. I will introduce two new scaling relations to connect the kSZ and secondary B-mode power spectrum with the physics of reionization. I will discuss the advantage of a joint study of the kSZ signal and secondary B-mode polarization from the ongoing/upcoming CMB experiments to get a better understanding of the epoch of reionization.

The inclusion of the cosmological constant is one of the main questions faced by quantum gravity. In three dimensions, non-perturbative approaches to quantum gravity including loop quantum gravity (LQG),  combinatorial quantization and  spinfoam path integrals encode the cosmological constant as a deformation parameter in a quantum group structure. In this talk, I will focus on the LQG approach: I will explain the Poisson-Lie structure of the classical phase space and how its quantization naturally leads to the emergence of quantum groups. I will use the holonomy-flux algebra and its spinorial presentation introduced in the series of work by Bonzom, Dupuis, Girelli, Livine and myself. This allows to construct the Hamiltonian constraint, understand its matrix elements as Turaev-Viro amplitudes. This connects LQG to the other approaches in a unified mathematical setting.