Scientific Series

The Large Hadron Collider (LHC) is now running (after a rocky start). This talk reviews why the start was rocky and how this constrains the physics program over the next few years. I will briefly survey how 'naturalness' arguments argue why something should be discovered, and why theoretical proposals fall into three main categories. If time permits I will close by telling you why I think the cosmological constant problem implies the LHC will strike paydirt and make quantum gravity an experimental science.

We perform an exact localization calculation for the expectation value of Wilson-'t Hooft line operators in N=2 gauge theories on S^1 x R^3. The expectation values form a quantum mechanically deformed algebra of functions on the Hitchin moduli space by Moyal multiplication. We demonstrate that these expectation values are the Weyl transform of the Verlinde operators, which acts on conformal blocks as difference operators. Our results are also in exact match with the predictions from wall-crossing in the IR effective theory.

We investigate the entanglement spectra of topological insulators which have gapless edge states on their spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a `trace index'. We find that any free-fermion topological insulator that exhibits spectral flow has a non-vanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the single-particle and many-body entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics in translationally invariant and disordered systems.

Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes. In 2 dimensions, one example of this is the fractional spin Hall insulator (essentially a spin-up and spin-down copy of a fractional quantum Hall insulator, with opposite effective magnetic fields for each spin). I will discuss another family of strongly interacting insulators, which exist in both 2 and 3 dimensions, that can have time-reversal protected edge modes. This gives a new set of examples of `fractional' topological insulators.

Cosmology and quantum gravity have not always had the smoothest of interactions. As a case in point I'll summarize the calculation behind the prediction of tensor modes in inflationary universes and discuss the difficulties found in recasting this calculation in terms of Ashtekar-Barbero-Immirzi variables. Contrary to the belief that ``inflation is shielded from quantum gravity'', novelties are found, leading to the interesting prediction of a chiral signature in the gravitational wave background, proportional to the imaginary part of the Immirzi parameter. This would leave a distinctive imprint in the polarization of the cosmic microwave background. On a more theoretical level, our remarks shed light on matters permeating quantum gravity, such as the inner product, the ground state (which we prove is NOT the Kodama state) and ordering issues.

In recent years there has been a lot of interest in F-Theory GUTs, mostly considering local models. In this talk I first consider an SU(5) GUT locally at the "point of E_8". The requirements of proton stability and reasonable flavour structure single out exactly two models. However, both models cannot be embedded in a semilocal construction (via the spectral cover approach). This casts doubts on the predictivity of local models.

I will discuss the phenomenologically interesting scenario of matter inflation in supersymmetric hybrid inflation models. The inflaton resides in a gauge non-singlet matter multiplet and the eta-problem is solved by a "Heisenberg" symmetry. This symmetry relates the inflaton with a modulus field and we stabilize this modulus via corrections to the Kähler potential. The Heisenberg symmetry arises naturally for the untwisted matter fields in heterotic orbifolds. A way to embed matter inflation into heterotic orbifold compactifications is suggested and moduli stabilization in the extended setup is discussed. I argue that the corrections from moduli stabilization may not spoil the flatness of the inflaton potential at large radius.

I will first summarize recent exact localization computations of supersymmetric gauge theories, and then discuss curious connections between SUSY/non-SUSY theories coming from 6d (2,0) theories. I particular, I will focus on our recent proposal relating 3d N=2 theories and 3d SL(2,R) Chern-Simons theories (or more mathematically, geometry of 3-manifolds).

Strongly correlated electron systems are play grounds for exotic quantum states such as high Tc superconductivity, quantum spin liquids, non-fermi liquids and so on. Recently high Tc superconductivity has been observed in an iron based compound K2Fe4Se5. I will present a model and outline an effective theory [1] that describes physics of this complex system - a non linear O(3) sigma model in 2 + 1 dimensions coupled to Dirac fermions. Topological solitons and induced quantum numbers are well known in Skyrme model for protons and neutrons. In our context, we get topological baby Skyrmions with an induced charge 2e. Baby Skyrmions conduct themselves `super'.

The hierarchy of the Yukawa couplings is an outstanding problem of the standard model. We present a class of models in which the first and second generation fermions are SUSY partners of pseudo-Nambu-Goldstone bosons that parameterize an E_7/SO(10) Kahler manifold, explaining the small values of these fermion masses relative to those of the third generation. We consider experimental constraints on this scenario, and find that the simplest model with universal gaugino masses is already ruled out by the LHC. However, models with non-universal gaugino masses will likely be excluded only by direct dark matter searches.

I will outline our recent approach to a theory of quantum networks, which we base on the graphical tensor calculus of Penrose. We aim to use this approach as a means to unite quantum computation, condensed matter physics and tensor network states with a long history of existing methods and techniques. I will sketch the status of our approach and focus on methods we have developed to reason and control the states created by specific networks of contracted tensors, as well as tensor contractions capturing the key properties of algebraic invariants of operators and states.