Scientific Series

We examine the interplay of symmetry and topological order in 2+1D topological phases of matter. We define the topological symmetry group, characterizing symmetry of the emergent topological quantum numbers, and describe its relation with the microscopic symmetry of the physical system.

We then derive a general classification of symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a general algebraic theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter with symmetry. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic defects are turned into deconfined quasiparticle excitations, which results in a different topological phase.

I will discuss recent work studying universal properties of gravity in anti-de Sitter (AdS) spacetime from the perspective of conformal field theory (CFT). After reviewing relevant aspects of the AdS/CFT correspondence, I will demonstrate that all CFTs in three or more dimensions possess a spectrum of operators consistent with long-distance locality and Newtonian gravity in AdS. In generalizing these results to two-dimensional CFTs, I will then show that operators with large scaling dimension create classical backgrounds in the limit of large central charge. This result can be directly related to eigenstate thermalization in 2d CFTs and black hole geometries in 3d AdS. I will conclude by discussing methods for going beyond this large central charge limit in 2d and for studying black holes in higher dimensions.

Photometric surveys are often larger and extend to fainter magnitudes than spectroscopic samples, and can therefore yield more precise cosmological measurements. However, photometric data are significantly contaminated by multiple sources of systematics, either intrinsic, observational, or instrumental. These systematics affect the properties of the raw images in complex ways, propagate into the final catalogues, and create spurious spatial correlations. Some of these correlations may also be imprinted in spectroscopic catalogues, since the latter rely on targets selected from imaging data. Therefore, not just precise — but also accurate — cosmological inferences from imaging surveys require careful mitigation of spatially-varying systematics. I will present a new framework of extended mode projection to robustly mitigate the impact of such systematics on power spectrum measurements. I will demonstrate the effectiveness of the technique, showing constraints on primordial non-Gaussianity using the clustering of 800,000 photometric quasars from the Sloan Digital Sky Survey in the redshift range 0.5 < z < 3.5. Finally, I will present a framework to map the observing conditions of the Science Verification data in the Dark Energy Survey (DES) and incorporate them into end-to-end simulations of the DES transfer function. The considerations presented here are relevant to all multi-epoch surveys, and will be essential for exploiting future high-cadence surveys such as the Large Synoptic Survey Telescope (LSST), which will require detailed null-tests and realistic end-to-end image simulations for correct cosmological inferences.

A modified gravity (MOG) theory has been developed over the past decade that can potentially fit all the available data in cosmology and the present universe. The basic ingredients of the theory are described by an action principle determined by the Einstein-Hilbert metric tensor and curvature tensor. An additional massive vector field φµ is sourced by a gravitational charge $Q=\sqrt{\alpha G_N}M$, where $\alpha$ is a parameter, $G_N$ is Newton's gravitational constant and $M$ is the mass of a body. In addition, two scalar fields $G(x)$ and $\mu(x)$ are added to the action principle, where $G(x)$ describes a variable $G_N$ and $\mu$ is the effective mass-range parameter of the the vector field $\phi_\mu$. For a slow moving test particle in a weak gravitational field, a modified Newtonian acceleration law is derived. This acceleration law reduces to the Newtonian acceleration law for distance scales $d << \mu^{-1}$. This acceleration law is applied to predict the rotation curves of galaxies and globular clusters with excellent fits to data for $\alpha=8.89\pm 0.34$ and $\mu=0.042\pm 0.004\,{\rm kpc}^{-1}$ without dark matter. An application to galaxy clusters with the same values of $\alpha$ and $\mu$ results in fits to cluster dynamics data without dark matter. The colliding clusters "bullet cluster" is also explained without dark matter. The vector field $\phi_\mu$ coupling to standard model particles is of gravitational strength and the mass of the vector field is $m_\phi=2.6\times 10^{-28}\,eV$. This makes the vector field undetectable in the present universe. 

For early universe cosmology before the formation of stars and galaxies, the mass $m_\phi$, determined by the scalar field $\mu(x)$, is bigger, $m_\phi >> 2.6\times 10^{-28}\,eV$, and can act as an ultralight cold dark matter photon with gravitational strength coupling to matter. The modified gravity can fit the cosmological data up to the epoch when stars and galaxies are first formed, and when the $\phi_\mu$ field density $\rho_\phi$ is significantly diluted compared to the baryon density $\rho_b$. After the commencement of the star and galaxy formation epoch, the modified gravity without dark matter takes over. A prediction of the matter power spectrum is made of the first formation of galaxies that do not have dark matter halos. The lack of detectability of the gravitationally sourced dark photon can explain why no convincing detection has so far been made of dark matter particles in laboratory and satellite experiments.

The modified gravity theory vacuum field equations with a smooth vector field source energy-momentum tensor are solved to produce a black hole that differs from the Schwarzschild, Kerr and Reissner-Norstr\"om black holes when the parameter $\alpha\neq 0$. A modified gravity solution is also obtained from a nonlinear regular vector field solution that is regular at $r=0$. This solution can describe a black hole with two horizons as well as a no black hole solution with no horizon. The black hole MOG solutions possess a photosphere and they cast a shadow against a bright background. The sizes and deformations of these shadows can be detected by the VLBI and Event Horizon (EHT) project. These observations will be able to test general relativity for strong gravitational fields.  A traversable wormhole can be constructed using the modified gravity theory with a wormhole throat stabilized by the gravitationally sourced repulsive vector field.  

There is an analogy between the propagation of fields in the vicinity of astrophysical black holes and the that of small excitations in fluids and superfluids. This analogy allows one to test, challenge and verify, in tabletop experiments, the elusive processes of black hole mass and angular momentum loss.

I will first present a brief overview on analogue black hole experiments, and then discuss in more detail some of my earlier and more recent experimental and theoretical results on the subject.

The discovery of the Higgs boson at the Large Hadron Collider marks the culmination of a decades-long hunt for the last ingredient of the Standard Model. At the same time, this discovery has started a new era in the search for more fundamental physics. In this talk, I will discuss what we have learned from the Higgs discovery about the mechanism of electroweak symmetry breaking and the implications for the existence of additional Higgs bosons. I will then highlight the future prospects of the Higgs boson in shedding light on New Physics and in particular on the nature of Dark Matter.

We will discuss techniques for computing 4-point functions of local operators in 2D conformal field theories, and their implications for semiclassical 3D quantum gravity. For generic 4-point functions, we present new closed-form expansions of the Virasoro conformal blocks. Specializing to correlators of holomorphic operators, these can be efficiently and exactly determined using an analytic implementation of the conformal bootstrap. Applying this method to the sewing construction of 2D CFT partition functions, we compute, via AdS/CFT, the semiclassical expansion of pure 3D quantum gravity around saddle point geometries of genus two; unlike at genus one, this expansion does not truncate at finite loop order.  

More than a decade after its discovery, cosmic acceleration still 
poses a puzzle for modern cosmology and a plethora of models of dark energy 
or modified gravity, able to reproduce the observed expansion history, have 
been proposed as alternatives to the cosmological standard model. In recent 
years it has become increasingly evident that probes of the expansion his- 
tory are not sufficient to distinguish among the candidate models, and that 
it is necessary to combine those with observations that probe the dynamics 
of inhomogeneities. Future cosmological surveys will map the evolution of 
inhomogeneities to high accuracy, allowing us to test the relationships be- 
tween matter overdensities, local curvature, and the Newtonian potential on 
cosmological scales.

I will discuss theoretical issues involved in finding an optimal framework to 
study deviations from General Relativity on cosmological scales, giving an 
overview of recent progress, with a focus on model-independent, parametrized 
approaches. I will summarize where we stand and what are the next steps 
we should take.

The presence of an instability in the Standard Model Higgs potential may have important implications for inflation and the viability of our Universe. In particular, if the Hubble scale during inflation is comparable to (or larger than) the instability scale of the potential, quantum fluctuations in the Higgs field will lead to the Higgs sampling the unstable part of the potential during inflation. However, to correctly study transitions to the unstable regime and determine the significance for the resulting universe requires addressing a number of subtleties. I will discuss these subtleties and a variety of possible approaches to studying Higgs evolution during inflation. By considering both (1) the evolution of Higgs fluctuations in the Gaussian approximation and (2) a perturbative calculation of the fluctuation two-point correlation function, I aim to elucidate how to address these issues in a consistent, physical way. The insight provided by these approaches will set the scene for studying Higgs fluctuations via the Fokker-Planck (FP) approach, which captures the non-Gaussian nature of the field. As such, it provides information about the rare—but, in terms of the fate of our Universe, potentially extremely important—patches that experience particularly large fluctuations.

For isolated quantum systems fluctuation theorems are commonly derived within the two-time energy measurement approach. In this talk we will discuss recent developments and studies on generalizations of this approach. We will show that concept of fluctuation theorems is not only of thermodynamic relevance, but that it is also of interest in quantum information theory. In a second part we will show that the quantum fluctuation theorem generalizes to PT-symmetric quantum mechanics with unbroken PT-symmetry. In the regime of broken PT-symmetry the Jarzynski equality does not hold as also the CPT-norm is not preserved during the dynamics. These findings will be illustrated for an experimentally relevant system ? two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT-symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point. The discussion will be concluded with an alternative approach to fluctuation theorems and quantum entropy production in quantum phase space.

Galileons are higher-derivative effective field theories with curious properties which have attracted much recent interest among cosmologists.  I will review their origins, their properties, their generalizations, and some recent developments.

This talk touches on three questions regarding the ontological status of quantum states using the ontological models

framework: it is assumed that a physical system has some underlying ontic state and that quantum states correspond to probability distributions over these ontic states.

The first question is whether or not quantum states are necessarily real---that is, whether or not the distributions for different quantum states must be disjoint. The PBR theorem proves the reality of quantum states by making assumptions about the ontic structure of bipartite systems, assumptions that have been challenged. Recent work has therefore concentrated on single systems, producing theorems proving the existence of pairs of quantum states whose overlap region on the ontic state space is very small.

The second question is whether the ontology of a quantum system can be macro-realist---that is, can there be "macroscopic" quantities which always have determinate values? The Leggett-Garg inequalities claim to rule out this possibility, but this conclusion has been disputed.

The third question is less familiar: Must quantum superpositions be ontic? That is, for some superposition with respect to some orthonormal basis, must ontic states exist which can be obtained by preparing the superposition, but not by preparing any of the basis states? In other words, can Schrödinger's cat always be either alive xor dead?