Scientific Series

The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry.  The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon.  From a modern point of view, topological defects generalize the notion of global symmetries.  We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry. The duality defect extends the Monster group to a larger category of topological defects that contains an Ising subcategory.  We introduce the defect McKay-Thompson series defined as the Monster partition function twisted by the duality defect, and find that it is invariant under the genus-zero congruence subgroup 16D0 of PSL(2,Z).

The central idea of the bootstrap philosophy is to constrain observables directly from consistency conditions alone, bypassing the intricacies of the Lagrangian formalism. In this talk, I will adopt this viewpoint and describe a boundary-centric approach to determine cosmological correlators, following a perspective familiar from the modern studies of scattering amplitudes. Specifically, I will describe the symmetries and singularities of three- and four-point functions in de Sitter space and inflation, and explain how these principles can be used to fully determine the final answer without reference to bulk time evolution. I will also highlight spectroscopic features encoded in these correlators, relevant for the search of primordial non-Gaussianity in future cosmological observations.

Maps of the mass density field can be used to predict peculiar velocities point-by-point. The comparison of these predictions to peculiar velocity data can be used to determine the cosmological parameter combination f sigma_8. I will briefly discuss the history of this field, present some of our recent results as well as other applications to calibrating the Hubble constant via SNe and gravitational waves, and discuss ongoing work to improving these measurements, through better modelling and, more importantly, acquiring more peculiar velocity data.

I will briefly review the pseudogap phenomenology in high Tc cuprate superconductor, especially the recent experiments, and propose a unified picture of the phenomenology under only one assumption: the fluctuating pair density wave. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

We derive general results relating revivals in the dynamics of quantum
many-body systems to the entanglement properties of energy eigenstates.
For a D-dimensional lattice system of N sites initialized in a
low-entangled and short-range correlated state, our results show that a
perfect revival of the state after a time at most poly(N) implies the
existence of "quantum many-body scars", whose number grows at least as
the square root of N up to poly-logarithmic factors. These are energy
eigenstates with energies placed in an equally-spaced ladder and with
Rényi entanglement entropy scaling as log(N) plus an area law term for
any region of the lattice. This shows that quantum many-body scars are a
necessary condition for revivals, independent of particularities of the
Hamiltonian leading to them. We also present results for approximate
revivals, for revivals of expectation values of observables and prove
that the duration of revivals of states has to become vanishingly short
with increasing system size.

Work in collaboration with Henrik Wilming (ETH)

I will describe how current and upcoming 21-cm measurements during cosmic dawn can probe a plethora of dark-matter and dark-energy models. This era saw the formation of the first stars, which coupled the spin temperature of hydrogen to its kinetic temperature---producing 21-cm absorption. The depth of this absorption acts as a thermostat, allowing us to constrain exotic cooling or heating due to dark matter. Additionally, the timing of the 21-cm signal strongly depends on the abundance of the small minihalos that hosted the first stars, allowing us to tightly constrain dark-matter models with suppressed power, such as warm or fuzzy dark matter. Finally, I will describe how in LCDM the acoustic physics of recombination are imprinted onto the 21-cm power spectrum during cosmic dawn, resulting in robust velocity-induced acoustic oscillations (VAOs). These act as a new standard ruler at z~20, opening up searches for early dark energy and perhaps resolving the H0 tension.

 In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of quantum corrected version of the Fokker–Planck equation without dissipation and its fourth-order corrected analytical solution for the probability distribution profile responsible for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker–Planck equation describes the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss Itô, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion of particle production phenomena to describe the quantum description of randomness involved in the dynamics. We also present computation to derive the expression for the measure of the stochastic nonlinearity (randomness or chaos) arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of random matrix theory (RMT). Finally, we discuss the role of out of time order correlation function (OTOC) to describe quantum chaos in early universe cosmology. 

It has recently been shown that quenched randomness, via the phenomenon of many-body localization, can stabilize dynamical phases of matter in periodically driven (Floquet) systems, with one example being discrete time crystals. This raises the question: what is the nature of the transitions between these Floquet many-body-localized phases, and how do they differ from equilibrium? We argue that such transitions are generically controlled by infinite randomness fixed points. By introducing a real-space renormalization group procedure for Floquet systems, asymptotically exact in the strong-disorder limit, we characterize the criticality of the periodically driven interacting quantum Ising model, finding forms of (multi-)criticality novel to the Floquet setting. We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.

We present a plausible counterexample to the weak cosmic censorship conjecture in four-dimensional Einstein-Scalar theory with asymptotically flat boundary conditions. Our setup stems from the analysis of the massive Klein-Gordon equation on a fixed Kerr black hole background. In particular, we construct the quasinormal spectrum numerically, and analytically in the WKB approximation, then go on to compute its backreation on the Kerr geometry. In the regime of parameters where the analytic and numerical techniques overlap we find perfect agreement. We give strong evidence for the existence of a nonlinear instability at late times.

We show that a generic many-body Hamiltonian can be uniquely reconstructed from a single pair of initial-final states under the unitary time evolution. Interesting it is, this method is not practical due to its high complexity. We then propose a practical method for Hamiltonian reconstruction from multiple pairs of initial-final states. The stability of this method is mathematically proved and numerically verified.

This work is joint with Liujun Zou and Timothy Hsieh.

Recently they have been generalized to other 3d homogeneous spaces, namely 3d anti de Sitter space and half-pipe space, a 3d homogeneous space with a degenerate metric.

We show that generalized ideal tetrahedra correspond to dual tetrahedra in 3d Minkowski, de Sitter and anti de Sitter space. They are those geodesic tetrahedra whose faces are all lightlike.

We investigate the geometrical properties of these dual tetrahedra in a unifi ed framework.  We then apply these results to obtain a volume formula for generalised ideal tetrahedra and their duals, in terms of their dihedral angles and their edge lengths.

This is joint work with Dr Carlos Scarinci, KIAS.

It has been realized that anomalies can be classified by topological phases in one higher dimension. Previous studies focus on ’t Hooft anomalies of a theory with a global symmetry that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this talk, I will introduce an anomaly that appears on the boundaries of (non-invertible) topological order with anyonic excitations [1]. The anomalous boundary theory is no longer invariant under a re-parametrization of the same spacetime manifold. The anomaly is matched by simple universal topological data in the bulk, essentially the statistics of anyons. The study of non-invertible anomalies opens a systematic way to determine all gapped and gapless boundaries of topological orders, by solving simple eigenvector problems. As an example, we find all conformal field theories (CFT) of so-called ``minimal models’’, except four cases, can be the critical boundary theories of Z_2 topological order (toric code). The matching of non-invertible anomaly have wide applications. For example, we show that the gapless boundary of double-semion topological order must have central charge c_L=c_R >= 25/28. And the gapless boundary of the non-Abelian topological order described by S_3 topological quantum field theory can be three-state Potts CFT, su(2)_4 CFT, etc. [1] WJ, Xiao-Gang Wen, arXiv: 1905.13279, Phys. Rev. Research 1,033054