Scientific Series

In this talk, I will discuss: (1) the new BGG-type resolutions of finite dimensional representations of simple Lie algebras that lead to BGG-relations expressing finite-dimensional transfer matrices via infinite-dimensional ones, (2) the factorization of infinite-dimensional ones into the product of two Q-operators, (3) the construction of a large family of rational Lax matrices from antidominantly shifted Yangians. This talk is based on the joint works with R.Frassek, I. Karpov, and V.Pestun.

I will discuss electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments.  Experiments designed for the detection of axion dark matter only need to reanalyze existing data to search for GWs in the GHz range with strains as small as h ∼ 10^{−22} − 10^{−21}. This is still far from the BBN bound on primordial sources, but it is the best direct constraint that we can currently obtain in the laboratory. To get to this result I will correct some long standing misconceptions present in the literature.

Zoom Link: https://pitp.zoom.us/j/94313100053?pwd=bWk1eHh3NWM3NnB1TjR5d0xrY3BIUT09

I will present an argument that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis. I will argue in particular that an apparent alternative to causal sets, viz. a certain sort of discrete Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way. For it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.

Zoom Link: https://pitp.zoom.us/j/96897602807?pwd=VkJ3VTAwYjhaTnJ3Z2ZVclZFYXErZz09

The gravitational radiation from the ringdown of a binary black hole merger is described by the solution of the Teukolsky equation, which predicts both the temporal and angular dependence of the emission. Many studies have explored the temporal feature of the ringdown wave through black hole spectroscopy. In this work, we further study the spatial distribution, by introducing a global fitting procedure over both temporal and spatial dependences, to propose a more complete test of General Relativity. We show that spin-weighted spheroidal harmonics are the better representation of the ringdown angular emission patterns compared to spin-weighted spherical harmonics. The differences are distinguishable in numerical relativity waveforms. We also study the correlation between progenitor binary properties and the excitation of quasinormal modes, including higher-order angular modes, overtones, prograde and retrograde modes. Specifically, we show that the excitation of retrograde modes is dominant when the remnant spin is anti-aligned with the binary orbital angular momentum. This study seeks to provide an analytical strategy and inspire the future development of ringdown test using real gravitational wave events.

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multi-body couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms. If time allows, I will also present some of our more recent progress on fractons.

Reference: arXiv:2112.05122.

Zoom Link: https://pitp.zoom.us/j/97053396111?pwd=Ny9tK295dGVacENJMzg0aHRObjZEZz09

Since the advent of holography, a lot of progress has been made in our understanding of quantum gravity in AdS. However less is known of its flat space counterpart, even though quantum gravity was certainly first formulated in flat space. Various programs have emerged since, like Celestial Holography or Carrollian Holography, both formulated in four and higher dimensions which is the closest to reality but makes the computation of highly quantum quantities difficult. I will present a 2d model of flat space gravity in which these difficulties can be tackled. This model is dubbed the "Cangemi — Jackiw model" after the authors of arXiv:9203056. It is a model of flat space gravity that can be reformulated in terms of a boundary action whose solutions are Rindler patches. I will explain how this “boundary graviton” reformulation gives access to fully quantum Euclidean results. In particular we will compute the exact spectrum of the Bondi Hamiltonian and show that it can be non-perturbatively completed by a matrix model. I will also comment on scrambling in flat space.

Based on “From black holes to baby universes in CGHS gravity” with Victor Godet (https://arxiv.org/abs/2103.13422) and an upcoming paper with Arjun Kar, Lampros Lamprou and Felipe Rosso.

Zoom Link: https://pitp.zoom.us/j/95709808325?pwd=QVdFUFZiTHVvMWlDb211U3kxQ0ZkZz09

Primordial black holes are a fascinating candidate for the dark matter in the universe. We discuss about their formation in the early universe and evolution across the cosmic history, and focus on their possible detectability at present and future gravitational wave experiments.

21-cm emission from neutral hydrogen atoms provides a unique window into galaxy formation and cosmology in the first billion years of cosmic history. As the first galaxies form after the Big Bang, they generate intense ultraviolet and X-ray radiation fields, which ionize and heat their otherwise neutral surroundings. The resulting modulations in the brightness of 21-cm emission relative to the background can be detected in principle by a single, well-calibrated dipole receiver, as features in the sky-averaged radio spectrum below ~200 MHz. Spatial fluctuations in the 21-cm background are expected also, and can in principle be detected statistically with the current generation of interferometers. In just the last few years, enormous progress has been made on both fronts. The sky-averaged 78 MHz feature reported by the EDGES collaboration in 2018 caused a flurry of activity, largely aimed at explaining its anomalous amplitude. Since then, the MWA, LOFAR, and HERA have all reported upper limits on the 21-cm power spectrum. In this talk, I will focus in particular on the first limits from HERA -- the most stringent limits reported to date -- and describe their implications for galaxy formation and cosmology. I will also discuss the ongoing EDGES controversy, and how JWST and SPHEREx can provide independent tests of astrophysical scenarios that produce EDGES-like 21-cm absorption troughs at frequencies below ~100 MHz.

Twisted interfaces between stacked van der Waals Cuprate crystals enable tunable Josephson coupling, utilizing anisotropic superconducting order parameters. Employing a novel cryogenic assembly technique, we fabricate high-temperature Josephson junctions with an atomically sharp twisted interface between Bi_2Sr_2CaCu_2O_{8+x} crystals. The critical current density J_c sensitively depends on the twist angle. While near 0 degree twist, J_c nearly matches that of intrinsic junctions, it is suppressed almost 2-orders of magnitude but remained finite near 45 degree. J_c also exhibits non-monotonic behavior versus temperature due to competition between two supercurrent contributions from nodal and anti-nodal regions of the Fermi surface. Near 45 degree twist angle, we observe two-period Fraunhofer interference patterns and fractional Shapiro steps at half integer values, a signature of co-tunneling Cooper pairs necessary for high temperature topological superconductivity.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

Nakajima’s quiver varieties play important roles in mathematical physics and representation theory. They are defined as symplectic reduction of the space of representations of the doubled quivers, and they are equipped with natural scheme structures. It is not known in general whether this scheme is reduced or not, and the reducedness issue does show up in certain scenario, for example the integration formula of the K-theoretic Nekrasov’s partition function. In this talk I will show that the quiver variety is reduced when the moment map is flat, and I will also give some applications of this result. This talk is based on my work arXiv: 2201.09838.

Zoom Link: https://pitp.zoom.us/j/97405405211?pwd=dEtVeHhQVjNrdGN4Vkh0ZlRrbEpVQT09

In this talk I will outline recent attempts to probe black holes in the strong gravity regime. The access to gravitational wave emission from binary black hole mergers and images of supermassive black holes allow for new tests of general relativity. After reviewing recent activities, I will outline how quasi-normal modes and shadow images can be used to study possible deviations from general relativity. Finally, I will discuss open problems that need to be addressed in the future.

Cosmic inflation is an important paradigm of the early Universe which is so far developed in two equivalent ways, either by geometrical modification of Einstein's general relativity (GR) or by introducing new forms of matter beyond the standard model of particle physics. Starobinsky's R+R^2 inflation based on a geometric modification of GR is one of the most observationally favorable models of cosmic inflation based on a geometric modification of GR. In this talk, I will discuss in detail the fundamental motivations for Starobinsky inflation and present how certain logical steps in the view of its UV completion lead to the emergence of a gravity theory that is non-local in nature. Then I will establish how one can perform studies of the early Universe in the context of non-local gravity and what are the observational consequences in the scope of future CMB and gravitational waves. I will discuss in detail how non-local R^2-like inflation can be observationally distinguishable from the local effective field theories of inflation.