Conference

Extension of the minimal supersymmetric standard model (MSSM) that include a U(1)\' gauge symmetry are motivated by top-down constructions and offer an elegant solution to the MSSM mu problem. In this talk I will describe some of the opportunities that such models offer, such as a new mechanism for mediation of supersymmetry breaking, as well as some of the challenges in constructing viable supersymmetric U(1)\' models.

I will discuss a simple two-dimensional theory, whose unparticle sector is a modification of the Schwinger model, that gives new insights into the qualitative features of unparticle physics. I will analyze the transition between the short-distance perturbative physics and large-distance unparticle behavior. Then I will show how to compute processes that involve unparticle self-interactions, for which nontrivial higher n-point functions of the conformal theory are essential.

The AdS/CFT correspondence has recently been extended to field theories satisfying the non-relativistic generalization of conformal symmetry, the Schroedinger symmetry. These holographic descriptions offer the potential to do calculations in the strong coupling regime of experimentally-realized condensed matter systems, such as fermions at unitarity. In this talk, we will outline the holographic formulation of such NRCFTs at zero temperature. We will then discuss the embedding of the appropriate geometry into IIB supergravity, and the finite temperature generalization that results. We will conclude with a brief discussion of the holographic description of non-relativistic conformal hydrodynamics and current research projects.

I will review the present status of the black hole entropy computation in Loop Quantum Gravity within the isolated horizon framework. Starting from the recently discovered discretization effect, I will give an overview of the subsequent developments that have been obtained motivated by it. Through this further analysis of the problem I will present some new related results and the promising new open windows that they give rise to.

While analogue models for gravity have so far provided some insights on the kinematical aspects of general relativity, the emergence of gravitational dynamics is still unclear. In this talk I will present two models which aim at filling this gap. In the first one a BEC model is considered, to uncover the gravitational dynamics hidden in these systems. In particular, the emergence of a modified Newtonian dynamics and of the cosmological constant will be discussed. A second model will be used to show how Nordstrom theory of gravity emerges from a system defined in Minkowski spacetime, showing how background independent theories of gravity could emerge from background dependent models.

The question whether SICs exist can be viewed as a question about the structure of the convex set of quantum measurements, or turned into one about quantum states, asserting that they must have a high degree of symmetry. I\'ll address Chris Fuchs\' contrast of a \'probability first\' view of the issue with a \'generalized probabilistic theories\' view of it. I\'ll review some of what\'s known about the structure of convex state and measurement spaces with symmetries of a similar flavor, including the quantum one, and speculate on connections to recent SIC triple product results. And I\'ll present some old calculations, which will look familiar to old hands but may be worth contemplating yet again, reducing the Heisenberg-symmetric-SIC existence problem to the existence of solutions to a set of simultaneous polynomials in unit-modulus complex variables.

Abstract: Complete sets of mutually unbiased bases are clearly \'cousins\' of SICs. One difference is that there is a \'theory\' for MUBs, in the sense that they are straightforward to construct in some cases, and probably impossible to construct in others. Moreover complete sets of MUBs do appear naturally in the algebraic geometry of projective space (in particular they come from elliptic curves with certain symmetries). I will describe some unsuccessful attempts I have made to go from MUBs to SICs.

I present three realizations about the SIC problem which excited me several years ago but which did not - unsurprisingly - lead anywhere. 1. In odd dimensions d, the metaplectic representation of SL(2,Z_d) decomposes into two irreducible components, acting on the odd and even parity subspaces respectively. It follows that if a fiducial vector | Psi> possesses some Clifford-symmetry, the same is already true for both its even and its odd parity components |Psi_e>, |Psi_o>. What is more, these components have potentially a larger symmetry group than their sum. Indeed, this effect can be verified when looking at the known numerical solutions in d=5 and d=7. A finding of remarkably little consequence! 2. In composite dimensions d=p_1^r_1 ... p_k^r_k, all elements of the Clifford group factor with respect to some tensor decomposition C^d=C^(p_1^r_1) x ... x C^(p_k^r_k) of the underlying Hilbert space. This structure may potentially be used to simplify the constraints on fiducial vectors. My optimism is vindicated by the following, ground-breaking result: In even dimensions 2d not divisible by four, the Hilbert space is of the form C^2 x C^d. So it makes sense to ask for the Schmidt-coefficients of a fiducial vector with respect to that tensor product structure. They can be computed to be 1/2(1 +/- sqrt{3/(d+1)}), removing one (!) parameter from the problem and establishing that, asymptotically, fiducial vectors are maximally entangled. 3. Becoming slightly more esoteric, I could move on to talk about discrete Wigner functions and show in what sense finding elements of a set of MUBs corresponds to imposing that a certain matrix be positive, while a similar argument for fiducial vectors requires a related matrix to be unitary. Now, positivity has \'local\' consequences: it implies constraints on small sub-matrices. Unitarity, on the other hand, seems to be more \'global\' in that all algebraic consequences of unitarity involve \'many\' matrix elements at the same time. This point of view suggests that SICs are harder to find than MUBs (in case anybody wondered). If we solve the problem by Wednesday, I\'ll talk about quantum expanders.