Scientific Series

Continuous-variable SICPOVMS seem unlikely to exist, for a variety of reasons. But that doesn't rule out the possibility of other 2-designs for the continuous-variable Hilbert space L2(R). In particular, it would be nice if the coherent states -- which form a rather nice 1-design -- could be generalized in some way to get a 2-design comprising *Gaussian* states. So the question is: "Can we build a 2-design out of Gaussian states?". The answer is "No, but in a very surprising way!" Like coherent states, Gaussian states have a natural transitive symmetry group. For coherent states, it's the Heisenberg group. For Gaussian states, it's the affine symplectic group -- the Heisenberg group plus squeezings and rotations. And this group acts irreducibly on the symmetric subspace of L2(R) x L2(R)... which, by Schur's Lemma, implies that the Gaussian states *should* be a 2-design. Yet a very simple explicit calculation shows that they are not! The resolution is fascinating -- it turns out that the "symplectic twirl" involves an integral that does not quite converge, and this provides a loophole out of Schur's Lemma. So, in the end, we: (1) Show that Gaussian 2-designs do not exist, (2) Demonstrate a major stumbling block to *any* symplectic-covariant 2-designs for L2(R), (3) Gain a pretty complete understanding of *one* of the [formerly] mysterious discrepancies between discrete and continuous Hilbert spaces.

String theory should give a well-defined answer to the following question: What is the state of matter in the limit of infinite energy density? We use results obtained from the understanding of black hole entropy to conjecture this equation of state, noting that the maximum entropy state in string theory has vastly more entropy than the states used in traditional approaches to early Universe Cosmology. The evolution of the Universe with this equation of state can be obtained in closed form.

A serious shortcoming of spinfoam loop gravity is the absence of matter. I present a minimal and surprisingly simple coupling of a chiral fermion field in the framework of spinfoam quantum gravity. This result resonates with similar ones in early canonical loop theory: the naive fermion hamiltonian was found to be just the extension of the simple

It is argued that the correct quantization of a scalar field theory in de Sitter spacetime involves a de Sitter invariant state which is not the Bunch-Davies vacuum. A novel but natural de Sitter invariant alternative exists and it is suggested that this and is the prefered state for scalar field theories. The argument is based on the exact solution of an interacting scalar field theory.

Cosmic inflation has given us a remarkably successful cosmological phenomenology. But the original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize. I review the status of "eternal inflation" with an eye on the roles various infinities have (both helpful and unhelpful) in our current understanding. I then discuss attempts to construct an alternative cosmological framework that is truly finite, using ideas about equilibrium and dark energy. I report some recent results that point to observable signatures.

The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of $Tr\phi^n$ (for all $n$) operators. We show that at low energies independently of the dimensionality $D$ the Hamiltonian system in question reduces to the {\it integrable} effective theory. The obtained Hamiltonian system describes large wavelength KdV type (Burger--Hopf) equation with an external potential and is related to the effective theory obtained by Das and Jevicki for the matrix quantum mechanics.

The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory. Although researches in this direction were not successful for long time because of the notorious difficulties in lattice SUSY, however, recent progress made it possible; nonperturbative formulations free from the parameter fine-tuning were proposed, some of them are confirmed to work numerically, and nontrivial evidence for the validity of the gauge/gravity duality has been obtained. In these talks I review the state of the art in this field. I start with reviewing basics of the Monte-Carlo. Then I explain how to put supersymmetric theories on computer and show actual numerical results. 1st talk : basics of Monte-Carlo simulation. 2nd talk : 1d SYM (matrix quantum mechanics). 3rd talk : how to put 2d, 3d and 4d SYM on computer. In the talks I concentrate on basic ideas and omit technical details (e.g. algorithms to accelerate simulations). They will be explained after the talks if people are interested in. References: 1st talk : standard textbooks e.g. Heinz J. Rothe, "Lattice Gauge Theories: An Introduction", Third Edition, World Scientific. 2nd talk : 0706.1647 [hep-lat], 0707.4454 [hep-th], 0811.2081 [hep-th], 0811.3102 [hep-th], 0911.1623 [hep-th], 1012.2913 [hep-th]. 3rd talk : hep-lat/0302017, hep-lat/0311021, 1010.2948 [hep-lat] (2d SYM); hep-th/0211139 (3d SYM); 1004.5513 [hep-lat], 1009.0901 [hep-lat] (4d SYM)

The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory. Although researches in this direction were not successful for long time because of the notorious difficulties in lattice SUSY, however, recent progress made it possible; nonperturbative formulations free from the parameter fine-tuning were proposed, some of them are confirmed to work numerically, and nontrivial evidence for the validity of the gauge/gravity duality has been obtained. In these talks I review the state of the art in this field. I start with reviewing basics of the Monte-Carlo. Then I explain how to put supersymmetric theories on computer and show actual numerical results. 1st talk : basics of Monte-Carlo simulation. 2nd talk : 1d SYM (matrix quantum mechanics). 3rd talk : how to put 2d, 3d and 4d SYM on computer. In the talks I concentrate on basic ideas and omit technical details (e.g. algorithms to accelerate simulations). They will be explained after the talks if people are interested in. References: 1st talk : standard textbooks e.g. Heinz J. Rothe, "Lattice Gauge Theories: An Introduction", Third Edition, World Scientific. 2nd talk : 0706.1647 [hep-lat], 0707.4454 [hep-th], 0811.2081 [hep-th], 0811.3102 [hep-th], 0911.1623 [hep-th], 1012.2913 [hep-th]. 3rd talk : hep-lat/0302017, hep-lat/0311021, 1010.2948 [hep-lat] (2d SYM); hep-th/0211139 (3d SYM); 1004.5513 [hep-lat], 1009.0901 [hep-lat] (4d SYM)

Though the observed CMB is at very low energy, it encodes ultra high-energy physics in spatial variations of the photon temperature and polarization fluctuations. This effect is believed to be dominated by the initial quantum state of the Universe. I will describe the first theoretical tools by which to construct such a state from fundamental physics. There are three specific observational effects this initial state will produce: a ringing signal in the power spectrum of quantum field fluctuations, an enfolded type of non-Gaussian fluctuations, and a calculable primordial gravitational wave background. We may soon be able to compare these predictions against experiment, allowing one to rule out classes of quantum gravity models. Now is the critical time to undertake such investigations, with a number of ongoing and planned experiments such as WMAP, Planck, and CMBPol poised to collect a wealth of precision data.

The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory. Although researches in this direction were not successful for long time because of the notorious difficulties in lattice SUSY, however, recent progress made it possible; nonperturbative formulations free from the parameter fine-tuning were proposed, some of them are confirmed to work numerically, and nontrivial evidence for the validity of the gauge/gravity duality has been obtained. In these talks I review the state of the art in this field. I start with reviewing basics of the Monte-Carlo. Then I explain how to put supersymmetric theories on computer and show actual numerical results. 1st talk : basics of Monte-Carlo simulation. 2nd talk : 1d SYM (matrix quantum mechanics). 3rd talk : how to put 2d, 3d and 4d SYM on computer. In the talks I concentrate on basic ideas and omit technical details (e.g. algorithms to accelerate simulations). They will be explained after the talks if people are interested in. References: 1st talk : standard textbooks e.g. Heinz J. Rothe, "Lattice Gauge Theories: An Introduction", Third Edition, World Scientific. 2nd talk : 0706.1647 [hep-lat], 0707.4454 [hep-th], 0811.2081 [hep-th], 0811.3102 [hep-th], 0911.1623 [hep-th], 1012.2913 [hep-th]. 3rd talk : hep-lat/0302017, hep-lat/0311021, 1010.2948 [hep-lat] (2d SYM); hep-th/0211139 (3d SYM); 1004.5513 [hep-lat], 1009.0901 [hep-lat] (4d SYM)

Recently, several neutrino physics has witnessed an accumulation of anomalous results. In the first part of this talk, we will discuss the tension that the MINOS experiments has seen between oscillations of neutrinos and anti-neutrinos. We will show that, phenomenologically, this tension can be explained if neutrinos are hypothesized to have new interactions mediated by higher-dimensional operators, but we will also show that problems arise when one attempts to embed these operators into renormalizable models. In the second part of the talk, we will address several results hinting at the existence of sterile neutrinos. We will present results from a global fit to worldwide neutrino oscillation data, and will show that one sterile neutrino is not enough to reconcile all data sets, and that 5-neutrino models, while being in much better agreement with the data, still have some tension.