Scientific Series

In the context of class S theories and 4D/2D duality relations there, we discuss the skein

relations of general topological defects on the 2D side which is expected to be counterparts

of composite surface-line operators in 4D class S theory. Such defects are geometrically

interpreted as networks in a three dimensional space. We also propose a conjectural com-

putational procedure for such defects in two dimensional SU(N) topological q-deformed

Yang-Mills theory by interpreting it as a statistical mechanical system associated with

ideal triangulations.

This talk is based partly on arXiv:1504.00121 with Yuji Tachikawa (Phys.Univ.Tokyo) and much on a forthcoming paper in arXiv.

The Weak Gravity Conjecture (WGC), in its original form, says that given an abelian gauge theory there should be at least one charged particle whose charge is bigger than its mass in Planck units. This has surprisingly powerful implications for the possibility of large-field inflation. In this talk I will explore some of the arguments linking the WGC to inflation before taking a closer look at a different question: which version of the WGC should we be trying to prove? I suggest that the right version to focus on is much stronger than the original WGC, and requires a sufficiently light particle to exist in every representation of the gauge group. I will present some evidence for this statement from both weakly-coupled string theory and semiclassical GR. This talk is based on work with Ben Heidenreich and Tom Rudelius (arXiv:1506.03447, 1509.06374, and further work in progress).

We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap method. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks of c = 6 and bosonic Virasoro conformal blocks of c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum are obtained in the K3 CFT as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and find numerically an upper bound on this gap that is saturated by the A1 N = 4 cigar CFT. 

Axions, having a perturbative shift symmetry, can have masses much smaller than other types of particles in a technically natural way. Ultralight axions (ULAs) with m~10^{-22} eV are attractive dark matter candidates with novel properties that distinguish them from cold dark matter (CDM). A single ULA with a GUT scale decay constant provides the correct relic density without fine-tuning. Quantum gravitational effects are expected to break continuous global symmetries, and may spoil the axion potential. However, if the axion global symmetry is an accidental symmetry descending from an exact discrete symmetry, then the problematic higher dimensional operators can be forbidden to very high order. I will discuss the astrophysical and cosmological phenomenology of ULAs that makes them attractive, and methods to distinguish them from CDM observationally. I will also discuss a two-axion model which solves the strong CP problem and in addition possesses a ULA that may be detectable via ~month period nuclear spin precession in an experiment such as CASPEr-Wind. Given time, I may discuss other experimental searches for axion-like particles.

The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions. With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. 

In the past years, much progress has been made for certain spin, bosonic, and even fermionic quantum many-body systems. However, a large class of interacting models is thought to be exempt from numerical studies due to the fermion sign problem. At its heart, it occurs when the statistical weights in the simulation are positive and negative resulting in an exponential scaling of the algorithm instead of a polynomial one. In this work, we study the connection of the sign problem and the entanglement entropy using Determinantal Quantum Monte Carlo, the method of choice for unbiased, large-scale simulations of fermionic systems. We show that there is a strong correlation between the behavior of the entanglement entropy and the sign problem and that the particular structure of the ‘observable’ entanglement entropy to some extent allows to handle the sign problem much better than for usual correlation functions.

Bell inequalities bound the strength of classical correlations arising between outcomes of measurements performed on subsystems of a shared physical system. The ability of quantum theory to violate Bell inequalities has been intensively studied for several decades. Recently, there has been an increased interest in studying physical correlations beyond the scenario of Bell inequalities, to more general network structures involving many sources of physical states and observers that may be measuring on subsystems of independent states. Much less is known about the nature of physical correlations in networks as compared to standard Bell inequalities. In this talk we will discuss the motivation and interest for studying such network correlations, review the recent progress in understanding such networks, and discuss the many open questions and new possible directions for research on this topic.

I will discuss ongoing work developing Hamiltonian truncation methods for studying strongly-coupled IR physics originating from a perturbed UV conformal field theory. This method uses a UV basis of conformal Casimir eigenstates, which is truncated at some maximum Casimir eigenvalue, to approximate the low energy spectrum of the IR theory. So far, such methods have been limited to theories in 2D, and I will present a new framework for generalizing this approach to higher dimensions. Focusing specifically on the case of scalar fields in 3D, I will then show tests of this framework by comparing with known analytic results at weak coupling and in the O(N) model at large-N, before discussing the possible application to strongly-coupled systems like the 3D Ising model.

The Advanced LIGO observatories have successfully completed their first science run. Data were collected from September 2015 to January 2016, with a sensitivity a few times better than initial instruments in the hundreds of Hertz band. In this talk I will describe the searches for gravitational-wave transients performed during the first few weeks of the science run. Furthermore, I will describe the methods devised to characterize transient gravitational-wave sources and their applications in the advanced gravitational-wave detector era.