Scientific Series

The Lagrangian dynamics of a fluid element within a self-gravitational matter field is intrinsically nonlocal due to the presence of the tidal force. Instead of searching for local approximations, we provide a statistical solution that could decouple the evolution of the fluid parcel from the surrounding environment. Given the probability distribution of the matter field, the method produces a set of ordinary differential equations to be solved locally. Mathematically, it corresponds to the characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Physically, it describes the mean evolution of the element with specific density and shape averaged over various environments. Furthermore, it is guaranteed that the one-point ρPDF would be preserved if one evolves these local, yet nonlinear, curves with the same set of initial data as the real system. This PDF based method, which is well developed in turbulence and other fields, provides a new perspective for understanding the non-linear structure formation in cosmology, e.g. the halo formation and the evolution of cosmic web. For Gaussian distributed dynamical variables, we demonstrate that the localized mean tidal tensor is proportional to the shear tensor, and the coefficient would recover the prediction of Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For Weakly non-Gaussian field, the averaged tidal tensor could then be expressed as polynomial of other variables.  Moreover, one could further generalize this concept of the mean evolution of the fluid element to incorporate some stochastic contributions, which we suggest would be valuable in describing a variety of processes in cosmology, such as the shell-crossing and realistic halo formation.

I will describe a proposal for a generalization of the BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. I describe the computation of canonical charges and show that the associated Ward identities are equivalent to the Cachazo-Strominger subleading soft graviton formula. Based on joint work with Alok Laddha.

Scalar fields are a useful proxy for other complex interactions, but also an attractive extension of General Relativity and a possible dark matter component. I will discuss some aspects of the gravitational interaction of scalar fields, in particular (i) the formation and growth of self-gravitating structures and their interaction with compact stars. and (ii) superradiance around black holes and how it can be used to constraint particle masses.

A new analysis of electron-proton scattering data (those published in 2010 by the Mainz A1 collaboration and previous world compilations) to determine the proton electric and magnetic radii is presented. The analysis enforces model-independent constraints of form factor analyticity and investigates a wide range of possible systematic effects. Employing standard models for radiative corrections, our improved analysis yields proton electric radii for the Mainz and world data sets that are consistent, although a simple combination yields a value r_E = 0.904(15) fm that is 4-sigma larger than the CREMA muonic hydrogen determination. Remaining possible deficiencies are discussed that, if addressed, could reconcile the values from muonic hydrogen spectroscopy and ep-scattering.

In this talk I’ll discuss an exotic theory of gravity known as “partially massless” gravity.  The linear partially massless theory displays many features analogous to those of electromagnetism, including an electric/magnetic duality.  However, the structure of gauge charges is much richer than in E&M.  I’ll present the analogues of electric point charges and Dirac monopoles.

An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.

We hope to find clues about the particle physics of the primordial (inflationary?) universe in the statistics of the cosmological perturbations. However, if the fluctuations are non-Gaussian the statistics we observe can differ significantly from the global, mean predictions of an inflationary model. I will discuss how the conclusions we draw about the primordial degrees of freedom can be affected in interesting ways by the finiteness of our observable universe.

After a short review of the gauge gravity duality, we will discuss black holes.  We will explain what the duality tells us about black holes as viewed from the outside.  We will review some of the puzzles that arise when we try to describe the black hole  interior. We will describe wormholes and their interpretation in the dual field theory as entangled states.

Matrix product operators form a natural language for describing topological quantum order. I will discuss how they arise as symmetries in PEPS, how anyon excitations arise as end points on them, and how the virtual indices of the MPO's provide a tensor product structure for the logical qubits in topological quantum computation.

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions.

Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop.

We study 5d and 6d SCFTs with eight supercharges by using 5-brane web diagrams in Type IIB string theory. There are two important properties of the web diagram. One is that it enables us to compute the exact partition function of the 5d theory on the 5-brane web. Even though the web diagram is not dual to a toric geometry, we develop a technique to compute the partition function by using the topological vertex. The other is that a new class of the 5-brane web diagram is conjectured to imply that the corresponding 5d theory has a 6d superconformal fixed point at high energies. Such a web diagram is called Tao web diagram. By using the Tao web diagram, we conjecture new 5d theories whose UV completion is a 6d SCFT. Moreover, we can show that a brane configuration realizing the 6d SCFT may reduce to the Tao web diagram, giving a direct way of identifying the 6d description of the 5d theory. This construction also indicates various dualities of the 5d theories.

Using the method of flux fusion anomaly test recently developed by M. Hermele and X. Chen (arXiv:1508.00573), we show that the possible ways of fractionalize crystal symmetry is greatly restricted if we assume the spin liquid has an SU(2) spin rotation symmetry and the spinon carries a half-integer spin. For a Z_2 spin liquid, under these assumptions the vison can only take the crystal symmetry fractionalization described by the Ising gauge theory. For a chiral spin liquid these assumptions imply that the spinon must also take fractionalized quantum numbers of crystal symmetries.