Scientific Series

Modern numerical methods have revolutionized the practice of science, creating a third discipline between traditional theory and experiment. Perhaps the most widely known and successful technique has been the Monte Carlo method in general, and the Metropolis algorithm in particular. In this talk, I will present a new way of performing unbiased Monte Carlo simulations based on highly-accurate tensor network contractions. The resulting technique inherits the legendary precision of tensor networks without any of the variational bias. From a Monte Carlo point-of-view, the method can be seen as an aggressive multi-sampling technique where each sample may account for the vast majority of the entire partition function resulting a a drastic reduction in sample-to-sample variance (in contrast to standard
configuration-based Monte Carlo, where only a small subset of possible configurations are sampled). The presented results are all classical, though applications to quantum systems and the sign problem will be discussed.

Twin Higgs theories attempt to solve the little hierarchy problem - why has the LHC not yet observed new states stabilising the EW scale? - by introducing a SM-neutral twin sector, related to the SM by an approximate Z_2 symmetry. The physical Higgs is then a PNGB mixture from both sectors, and acts as a portal between them. In this talk, I will discuss the cosmology of minimal (“fraternal”) Twin Higgs models. Higgs portal interactions establish thermal equilibrium between the SM and twin sector at high temperatures, giving a thermal history with possibilities for both symmetric dark matter (through a “twin WIMP miracle”), and asymmetric dark matter (from twin QCD states which naturally have GeV-scale masses). More generally, relic abundances of cosmologically stable states place constraints on the parameters of the theory, and twin sector phase transitions need to be considered.

Oscillating signatures in the correlation functions of the primordial density perturbations are predicted by a variety of inflationary models. A theoretical mechanism that has attracted much attention is a periodic shift symmetry as implemented in axion monodromy inflation. This symmetry leads to resonance non-Gaussianities, whose key feature are logarithmically stretched oscillations. Oscillations are also a generic consequence of excited states during inflation and of sharp features in the potential. Oscillating shapes are therefore a very interesting experimental target. 

After giving an overview of the theoretical motivations, I will discuss how to search for these signatures in the CMB. Fast oscillations are difficult to search for with traditional estimation techniques, and I will demonstrate how targeted expansions, that exploit the symmetry properties of the shapes, allow to circumvent these difficulties. As a member of the Planck collaboration, I will discuss the Planck results that have been obtained using these methods in the bispectrum, as well as related results in the power spectrum. Due to their low overlap with other non-gaussian shapes, oscillating bispectrum shapes are not exhaustively constrained and a potential discovery in the CMB is therefore not yet ruled out. 

After a quick review of the Higgs and Coulomb branches of 3d N=4 theories, I'll introduce some simple classes of boundary conditions and explain how they lead to (pairs of) modules for certain (pairs of) quantum algebras. I will focus on abelian theories, for which the relevant boundary conditions/modules can be described using the geometry of (pairs of) hyperplane arrangements. From this, the simplest examples of symplectic-dual modules will arise.

I will introduce the unitarity, a parameter quantifying the coherence of a channel and show that it is useful for two reasons. First, it can be efficiently estimated via a variant of randomized benchmarking. Second, it captures useful information about the channel, such as the optimal fidelity achievable with unitary corrections and an improved bound on the diamond distance.

The orbital angular momentum in a chiral superfluid has posed a paradox for several decades. For example, for the $p+ip$-wave superfluid of $N$ fermions, the total orbital angular momentum should be $N/2$ if all the fermions form Cooper pairs. On the other hand, it appears to be substantially suppressed from $N/2$, considering that only the fermions near the Fermi surface would be affected by the pairing interaction. To resolve the long-standing question, we studied chiral superfluids in a two-dimensional circular well, in terms of a conserved charge and spectral flows. We find that the total orbital angular momentum takes the full value $N/2$ in the chiral $p+ip$-wave superfluid, while it is strongly suppressed in higher-order ($d+id$ etc.) chiral superfluids. This surprising difference is elucidated in terms of edge states.

In order for quantum fluctuations during inflation to be converted to classical stochastic perturbations, they must couple to an environment which produces decoherence. Gravity introduces inevitable nonlinearities or mode couplings. We study their contribution to quantum-to-classical behavior during inflation. Working in the Schrodinger picture, we evolve the wavefunctional for scalar fluctuations, accounting for minimal gravitational nonlinearities.  The reduced density matrix for a given mode is then found by integrating out shorter-scale modes. We find that the nonlinearities produce growing phase oscillations in the wavefunctional, which decohere the single-mode reduced density matrix into a diagonal mixed state. However, the weakness of the coupling delays decoherence until the mode is much longer than the Hubble scale environment modes. In summary, the gravitational coupling of long and short scales is sufficient to produce a mixed state of classical perturbations during inflation.

String theory is starting to provide novel all-loop precision tools for the computation of scattering amplitudes in the high energy (HE) limit of N=4 SYM theory. After a review of some key insights and results for hexagon amplitudes, I will describe ongoing developments addressing higher numbers of external gluons.

I will discuss how to classify (up to discrete identifications) all rigid 4D N=2 supersymmetric backgrounds in both Lorentzian and Euclidean signatures that preserve eight real supercharges. These include backgrounds such as warped S_3×R, warped AdS_3×R, and AdS_2×S^2, as well as some more exotic geometries. I will also address how to construct all supersymmetric two-derivative actions involving hypermultiplets and vector multiplets in these backgrounds.

We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order  even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more `rigid'.  Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.