Scientific Series

I will demonstrate that SL(2,Z) duality is a property of all low-energy effective Abelian theories with electric or magnetic charges  The duality will be verified at one loop by comparing the amplitudes in the case of an electron and the dyon that is its SL(2,Z) image, and I will show that it can be extended order by order in perturbation theory.  I will discuss how the duality generically breaks down at high energies, and show how the results apply to the Seiberg-Witten theory.

In this talk I discuss the effects of nonlinear backreaction of small scale density inhomogeneities in general relativistic cosmology. It has been proposed that in an inhomogeneous universe, nonlinear terms in the Einstein equation could, if properly averaged and taken into account, affect the large scale Friedmannian evolution of the universe. In particular, it was hoped that these terms might mimic a cosmological constant and eliminate the need for dark energy. After reviewing some of these approaches, and some of their flaws, I will describe a perturbative framework (developed with R. Wald) designed to properly take into account these effects. In our framework, we assume that the spacetime metric is "close"---within 1 part in 10^4, except near strong field objects---to a background metric of FLRW symmetry, but we do not assume that the background metric satisfies the Friedmann equation. We also do not require that spacetime derivatives of the metric be close to derivatives of the background metric. This allows for significant deviations in geodesics, and very large curvature inhomogeneities. A priori, this framework also allows for significant backreaction, which would take the form of new effective matter sources in the Friedmann equation. Nevertheless, we prove that if the matter stress-energy tensor satisfies the weak energy condition, then large matter inhomogeneities on small scales cannot produce significant backreaction effects on large scales, and in particular cannot account for dark energy. As I will also review here, with a suitable ‘dictionary,’ Newtonian cosmologies provide excellent approximations to cosmological solutions to Einsteinʼs equation (with dust and a cosmological constant) on all scales. Our results thereby provide strong justification for the mathematical consistency and validity of the LCDM model within the context of general relativistic cosmology. While our rigorous framework makes use of 1-parameter families and weak limits, in this talk I will provide a simple heuristic discussion that places emphasis on the manner in which "averaging" is done, and the fact that one is solving the Einstein equation.

In any quantum field theory, the energy flux at a point of spacetime can be negative.  This would produce a repulsive gravitational field causing nearby light rays to defocus.  This in turn threatens to produce a variety of exotic phenomena including traversable wormholes, warp drives, time machines, and evasion of singularity theorems.  I will describe a new "quantum focusing conjecture" that prevents such pathologies.  In the flat spacetime limit it reduces to a novel lower bound on the energy density, which can be proven for several classes of field theories.

In this talk, I discuss several application of semileptonic B-meson form factors.  Topics include the determination of $|V_{ub}|$ and $|V_{cb}|$, hints for new physics in semitauonic decays, and Standard-Model predictions for flavor-changing-neutral-current processes: $B\to P\nu\bar{\nu}$ and $B\to P\ell^+\ell^-$, where $P$ denotes a pion or kaon.
I will also cover some details of the underlying lattice-QCD calculations at a nontechnical level.

Alternative theories of gravity are popular alternatives to the LCDM model because they can self-accelerate without a cosmological constant. On smaller scales, consistency with solar system tests of gravity is achieved by utilising screening mechanisms, which act to hide fifth-forces locally. This makes them difficult to distinguish from general relativity. In this talk I will describe recent work using astrophysical objects---stars, galaxies, and clusters---as new and novel probes of alternative gravity theories.

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.