Talks

Since the Higgs, the LHC has offered no discoveries despite a sweeping hunt for new resonances. However, many well-motivated new physics models would not turn up in resonance searches, but could instead be uncovered in existing and forthcoming LHC data, by searching for novel angular distributions of Standard Model particles. I will show that in the upcoming years at the LHC, (1) through radiative corrections, dark matter can turn up in dilepton scattering angles in the parametric regions where it would elude conventional missing energy-based searches; the scattering patterns can reveal dark matter's mass, self-conjugation property, spin, and chirality of interactions, (2) through tree level interference, leptoquarks may emerge in dilepton scattering angles long before they would in dedicated direct searches; these angular measurements would also overtake the excellent sensitivities of low-energy precision measurements of atomic parity violation, and (3) Higgs Yukawa couplings to light quarks of the size of the bottom Yukawa could be measured using the Higgstrahlung scattering angle.

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions.

I present three possible non-standard additions to cosmology.  First I show that a very long early period of inflation could exist in which parameters evolve, or 'relax', to seemingly fine-tuned values.  Next, I show that even if cosmic inflation existed, a period after inflation with anisotropic stress can dramatically affect super-horizon modes and thus the imprint on the cosmic microwave background.  Finally, I show that cosmological singularities can be avoided by a bounce without using exotic matter that violates the Null Energy Condition, but by the addition of vorticity in compact extra dimensions.

We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions. For nonlocality detection, we show that, when viewed as a vector in R^n, the set of boxes admitting an infinite TI classical extension forms a polytope, i.e., a convex set defined by a finite number of linear inequalities. Using DMRG, we prove that some of these inequalities can be violated by distant parties conducting identical measurements on an infinite TI quantum state. Both our entanglement witnesses and our Bell inequalities can be used to certify entanglement and nonlocality in large spin chains (namely, finite, and not TI chains) via neutron scattering.

Our attempts at generalizing our results to TI systems in 2D and 3D lead us to the virtually unexplored problem of characterizing the marginal distributions of infinite TI systems in higher dimensions. In this regard, we show that, for random variables which can only take a small number of possible values (namely, bits and trits), the set of nearest (and next-to-nearest) neighbor distributions admitting a 2D TI infinite extension forms a polytope. This allows us to compute exactly the ground state energy per site of any classical nearest-neighbor Ising-type TI Hamiltonian in the infinite square or triangular lattice. Remarkably, some of these results also hold in 3D.

In contrast, when the cardinality of the set of possible values grows (but remaining finite), we show that the marginal nearest-neighbor distributions of 2D TI systems are not described by a polytope or even a semi-algebraic set. Moreover, the problem of computing the exact ground state energy per site of arbitrary 2D TI Hamiltonians is undecidable.