Scientific Series

The massless fields of closed string theory on toroidal backgrounds naturally depend on coordinates dual to momentum and coordinates dual to winding. Their dynamical theory, which contains gravitation, must include diffeomorphism and dual diffeomorphism invariance. We begin a serious attempt to construct this generalized form of field theory.

The black body nature of the first acoustic peak of the cosmic microwave background (CMB) was tested using foreground reduced WMAP 5-year data, by producing subtraction maps between pairs of cosmological bands, viz. the Q, V, and W bands, for masked sky areas that avoid the Galactic disk. The resulting maps revealed a non black body signal that has three main properties. (a) It fluctuates on the degree scale preferentially in one half of the sky, producing an extra {\it random} noise there of amplitude $\approx$ 3.5 $\mu$K, which is $\gtrsim$ 10 $\sigma$ above the pixel noise even after beam size differences between bands are taken into account. (b) The signal exhibits large scale asymmetry in the form of a dipole ($\approx$ 3 $\mu$K) in the Q-V and Q-W maps; and (c) a quadrupole ($\approx$ 1.5 $\mu$K) in the Q-V, Q-W, and V-W maps. While (b) is due most probably to cross-band calibration residuals of the CMB COBE dipole, the amplitude of (c) is well beyond systematics of the kind, and in any case no {\it a priori} quadrupole in the CMB exists to leave behind such a residual. The axes of symmetry of (a), (b), and (c) are tilted towards the same general direction of the ecliptic plane. This strongly suggests that foreground emission contaminates the CMB signatures at the 4 -- 5 % level even on the angular scale of the first acoustic peak.

This talk will present an overview of work done in the past decade on quantum state and process tomography, describing the basic notions at an introductory level, and arguing for a pragmatic approach for data reconstruction. The latest results include recent numerical comparison of different reconstruction techniques, aimed at answering the question: "is 'the best' the enemy of 'good enough'?"

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the first application of his concept of phase space, and the prototype of the conical intersections and fermionic sign changes that now pervade physics and chemistry. But the fine structure of the bright cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena arise when chirality and absorption are incorporated in addition to biaxiality.

Since Einstein first applied his equations of General Relativity to Cosmology, Dark Energy has had a major role in physicists’ efforts to explain the observations of our Universe. Many red herrings have been followed over the past 90 years, where Dark Energy has gone in and out of fashion. However, starting in the 1990s, a broadly supported and sustained view has emerged that the Universe is dominated by Dark Energy – a form of matter with negative pressure. I will give a brief overview of the history of Dark Energy, describe the range of observations that have lead to the adoption of Dark Energy in the standard model of Cosmology, and look to future observations that will refine our understanding of Dark Energy.

We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon,as seen by an infalling observer. For D-brane probes, we construct a map from physics seen by an infalling observer to physics seen by an asymptotic observer that can be generalized to other AdS black holes.

As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies. We carry out a hybrid quantization which combines loop and Fock techniques. We discuss the main results of this hybrid quantization, which include the resolution of the cosmological singularity, the construction of the Hilbert space of physical states, and the recovery of a conventional quantization for the inhomogeneities. In addition, an analysis of the model at the effective level confirms the robustness of the Big Bounce scenario, with preservation -or partial amplification- of the amplitudes of the inhomogeneous modes through the bounce in a statistical average.

Cosmologists are struggling to understand why the expansion rate of our universe is now accelerating. There are two sets of explanations for this remarkable observation: dark energy fills space or general relativity fails on cosmological scales. If dark energy is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $dlnG/dlna = \Omega^\gamma$, where $\Omega$ is the matter density independent of scale in a dark matter plus dark energy model. By combining measurements of the amplitude of redshift space, $\beta = (1/b) dlnG/dlna$ with measurements of galaxy bias, $b$, from cross-correlations with CMB lensing, redshift surveys will be able to determine the logarithmic growth rate as a function of scale and redshift. I will discuss the role of upcoming surveys in improving our ability to understand the origin of cosmic acceleration.

A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission. Joint work with Robert Koenig.

Key notions from statistical physics, such as "phase transitions" and "critical phenomena", are providing important insights in fields ranging from computer science to probability theory to epidemiology. Underlying many of the advances is the study of phase transitions on models of networks. Starting from the classic ideas of Erdos and Renyi, recent attempts to control and manipulate the nature of the phase transition in network connectivity will be discussed. Next, the influence of self-organization on phase transitions will be presented, as well as connections between the jamming transition in models of granular materials and constraint satisfaction problems in computer science. Finally, turning to network growth, I will show that local optimization can play a fundamental role leading to the mechanism of Preferential Attachment, which previously had been assumed as a basic axiom and, furthermore, resolves a long standing controversy between Herb Simon and Benoit Mandelbrot.

Gauge theories with deformed products of fields in the lagrangian constitute an interesting generalization of the gauge/string duality. We review a systematic procedure to find the string duals of such theories, called the TsT transformation, and illustrate its properties by means of a few examples.

In my talk I will provide an overview of the applications of Wilson's modern renormalization group (RG) to problems in quantum gravity. I will first discuss the development of the RG for continuum gravity within the framework of Feynman's covariant path integral approach. Then I will discuss a number of issues that arise when implementing the path integral approach with an explicit lattice UV regulator, and later how non-perturbative RG flows and universal non-trivial scaling dimensions can in principle be extracted from these calculations. Towards the end I will discuss recent attempts at formulating RG flows for gravitational couplings within the framework of a set of manifestly covariant, but non-local, effective field equations suitable for quantum cosmology.