Scientific Series

In this talk first I will introduce and motivate the problem of finding finite energy Yang-Mills instantons on curved backgrounds.  

After the historical introduction, I will focus the example of the Euclidean Schwarzschild (ES) manifold from Quantum gravity. The ES manifold was first introduced by Hawking in the late 70's. It is an asymptotically locally flat solution of the Euclidean Einstein equation, but not hyper-Kahler, which makes instanton theory harder. Throughout the past four decades, related results have been sporadic: there have been only finitely many (at most 2) known solutions for each energy value.

In our work, making use of an old idea of Witten, and subsequently Taubes and Garcia-Prada, we produce infinitely many unit energy solutions, and also solutions of continuously varying energy, a feature (seemingly) unique to asymptotically locally flat spaces. These instantons describe vortex-like pseudoparticles; at the end of the talk I will present an intuitive picture in terms of planar (Ginzburg-Landau) vortices.

This is joint work with Gonçalo Oliveira (IMPA).

We suggest that two-to-two dark matter fusion may be the relaxation process that resolves the small-scale structure problems of the cold collisionless dark matter paradigm. In order for the fusion cross section to scale correctly across many decades of astrophysical masses from dwarf galaxies to galaxy clusters, we require the fractional binding energy released to be greater than v^n ~ [10^{-(2-3)}]^n, where n=1,2 depends on local dark sector chemistry. The size of the dark-sector interaction cross sections must be sigma ~ 0.1-1 barn, moderately larger than for Standard Model deuteron fusion, indicating a dark nuclear scale Lambda ~ O(100 MeV). Dark fusion firmly predicts constant sigma v below the characteristic velocities of galaxy clusters. Observations of the inner structure of galaxy groups with velocity dispersion of several hundred kilometer per second, of which a handful have been identified, could differentiate dark fusion from a dark photon model.

"Recently, exactly solvable 3D lattice models have been discovered for a new kind of phase, dubbed fracton topological order, in which the topological excitations are immobile or are bound to lines or surfaces. Unlike liquid topologically ordered phases (e.g. Z_2 gauge theory), which are only sensitive to topology (e.g. the ground state degeneracy only depends on the topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice. This geometry dependence allows for remarkably new physics which was forbidden in topologically invariant phases of matter.

In this talk, I will review the X-cube model [1] of fracton order. I will then explain how geometry dependence allows for braiding of point-like particles in this 3D phase. I'll summary how the X-cube model can be described by a quantum field theory, which is analogous to a topological quantum field theory (TQFT). [3] We will see that the gauge invariance of the field theory results in the mobility restrictions of the topological excitations by imposing a new kind of geometric charge conservation. I will conclude by briefly discussing current work on the remarkable geometry-dependent phenomenology of fracton order. For example, I will explain why even on a manifold with trivial topology, spatial curvature can induce a robust ground state degeneracy.

[1] Vijay, Haah, Fu 1603.04442

[2] Slagle, Kim 1704.03870"

In this talk, I will show that light cones in MInkowski spacetime are a beautiful analoue of black hole horizons in curved spacetime. To do so, I will prove the analogue of the four laws of black hole thermodynamics in this setting. This is what we called light cone thermodynamics. More precisely, I will consider null surfaces defined by the out-going and in-falling wave fronts emanating from and arriving at a sphere in Minkowski spacetime. Such null surfaces, made of pieces of light cones, are bifurcate conformal Killing horizons for suitable conformally stationary observers. They can be extremal and non-extremal depending on the radius of the shining sphere. Such conformal Killing horizons have a constant light cone (conformal) temperature, given by the standard expression in terms of the surface gravity. Considering exchanges of conformally invariant energy across the conformal horizon, one can prove, in perturbation theory, a first law where entropy changes are given by 1/4 of the changes of the area of the bifurcate surface in Planck units. In the extremal case they become light cones associated with a single event; these have vanishing temperature as well as vanishing entropy. I will conclude with possible generalisations and applications of such results.

The construction of trial wave functions has proven itself to be very useful for understanding strongly interacting quantum many-body systems. Two famous examples of such trial wave functions are the resonating valence bond state proposed by Anderson and the Laughlin wave function, which have provided an (intuitive) understanding of respectively spin liquids and fractional Quantum Hall states. Tensor network states are another, more recent, class of such trial wave functions which are based on entanglement properties of local, gapped systems. In this talk I will discuss the use of tensor network states for topological phases, and what we can learn from this approach. I will consider one- and two-dimensional systems, consisting of both spins and fermions. The focus will be on the different connections that can be made using tensor networks, such as connecting theory to numerics, and physical properties to ground state entanglement.

The observations of gravitational waves from the mergers of compact binary sources opens a new way to learn about the universe as well as to test General Relativity in the limit of strong gravitational interactions – the dynamics of massive bodies traveling at relativistic speeds in a highly curved space-time. The lecture will describe some of the difficult history of gravitational waves proposed about 100 years ago.  The concepts used in the instruments and the methods for data analysis that enable the measurement of gravitational wave strains of 10-21 and smaller will be presented. The results derived from the measured waveforms, their relation to the Einstein field equations and the astrophysical implications are discussed. The talk will end with a vision for the future of gravitational wave astronomy.

From a quantum information perspective, we will study universal features of chaotic quantum systems. Recent progress has made evident that quantifying chaos is a useful way to gain insight into strongly-coupled field theories, quantum many-body systems, as well as the quantum nature of black holes. We will derive relations between different diagnostics of chaos and scrambling (OTOCs, spectral functions, and frame potentials) and define a quantity to capture the onset of a random matrix description. We will review and use tools from quantum information and random matrix theory, but our goal will be to understand strongly-interacting systems.

We discuss the role of contextuality within quantum fluctuation theorems, in the light of a recent no-go result by Perarnau et al. We show that any fluctuation theorem reproducing the two-point measurement scheme for classical states either admits a notion of work quasi-probability or fails to describe protocols exhibiting contextuality.

Conversely, we describe a protocol that smoothly interpolates between the two-point measurement work distribution for projective measurements and Allahverdyan's work quasi-probability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.

Gravitational shockwaves may signal the breakdown of effective field theory near black hole horizons. Motivated by this, I will revisit the Dray-‘t Hooft solution and explain how to generalize it to the Kerr-Newman background. In doing so I will emphasize the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).

Primordial black hole (PBH), which can be naturally produced in the early universe, remains a promising dark matter candidate . It can merge with a supermassive black hole (SMBH) in the center of a galaxy and generate gravitational wave (GW) signals in the favored frequency region of LISA-like experiments. In this work, we initiate the study on the event rate calculation for such extreme mass ratio inspirals (EMRI). Including the sensitivities of various proposed GW detectors, we find that such experiments offer a novel and outstanding tool to test the scenario where PBH constitutes (fraction of) dark matter. The PBH energy density fraction of DM (fPBH) could potentially be explored as small as 10^−3∼10^−4. Further, LISA has the capability to search for PBH mass upto 10^−2∼10^−1 solar mass. Other proposed GW experiments can probe lower PBH mass regime.

Extending the EFT of Inflation by adding marginal operators in unitary gauge that can affect the equation of motion for scalar perturbations, we unravel new inflationary models in which the dispersion relations is a sixth order polynomial. In particular we focus on the healthy marginal operators that do not infiltrate ghosts into the equations of motion and allow for gravity to decouple from the Goldstone boson above some energy scale. Various scenarios can arise depending on the parameters in the original theory. In particular, one can consider scenarios in which the mode becomes tachyonic while still it is inside the horizon. More conservatively, one can consider models in which the group velocity of the propagation becomes negative. In these inflationary models, the amplitude of scalar power spectrum gets a modulation factor, which in majority of the cases is much bigger than one.  We also show that these marginal operators leave the tensor perturbations intact, and hence the form of tensor power spectrum remains resilient even in the marginally extended EFT of inflation.  Due to the enhancement of the scalar power spectrum,  the tensor-to-scalar ratio is suppressed by a huge factor..

The Hecke category is a certain monoidal category of constructible sheaves on a flag variety that categorifies the Hecke algebra and plays an important role in geometric representation theory. In this talk, I will discuss a monoidal Koszul duality relating the Hecke category of Langlands-dual (Kac–Moody) flag varieties, categorifying a certain involution of the Hecke algebra. In particular, I will try to explain why one needs to introduce a monoidal category of "free-monodromic tilting sheaves" to formulate this duality. (Joint with P.N. Achar, S. Riche, and G. Williamson.)