Scientific Series

We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state. One implication of this is that the entanglement in these states is very robust (persistent), while an application is in establishing an arbitrary amount of entanglement between well-separated parties (for subsequent use as a communication resource) by local measurements on an appropriate graph. Based on quant-ph/0602139.

Some of the speculations on new physics, beyond what is in the standard model are reviewed. Particular attention is paid to ideas that try to address the hierarchy puzzle, i.e., why is the weak scale so much smaller than the Planck scale. These new theories will be tested at the large hadron collider in the near future.

We discuss D-brane instantons in four-dimensional string compactifications with special emphasis on Eucliden D2-branes in Type IIA orientifolds with spacetime filling D6-branes. These can induce superpotential couplings among the open string fields which are forbidden at the perturbative level since they violate some of the global U(1) symmetries generically present in string theory. Phenomenologcially important couplings of this type include Majorana mass terms for right-handed neutrinos or mu-terms in the Higss sector of the MSSM. If realized in concrete constructions, the exponential suppression of such non-perturbative terms may 'naturally' generate the observed hierarchies characteristic of these couplings. After discussing the general philosophy, we derive the prescription for the CFT computation of such non-perturbative superpotential couplings and exemplify the computation of Majorana mass terms in toroidal intersecting brane worlds. If time permits, we also comment on D2-instanton effetcs potentially destabilising the vacuum or modifying the D-term supersymmetry conditions.

We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in a football compactification, without having to deal with the complications of a delta–like, codimension two brane. Moreover, it allows us to identify the origin of the problems that emerge when one takes the limit of a codimension-two brane.

After reviewing recent developments in the study of the AdS/CFT correspondence between the IR gauge theory living on a stack of D3-branes placed at a Calabi-Yau singularity and type IIB string theory on the near horizon geometry, we focus on the problem of counting chiral BPS operators in this class of CFTs and we match them with the dual string states in the general case of toric CY. Partition functions can be explicitly written in all sectors with fixed baryonic charge using localization over fixed points of the toric actions. These partition functions are related to the volume functions of the Sasaki-Einstein manifold and of its divisors.

We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. We discuss the question, how the theory of information processing looks like in the framework of the generalised quantum theory. In particular we propose a scheme of extended dense coding, in which one transmits two qubits by sending one extended bit, provided it was initially entangled with the extended bit of the receiver.

Neural circuits exhibit complex patterns of spontaneous activity. I will discuss how neural network models can reproduce this activity and how it interacts with responses evoked by sensory stimuli. This work involves analytic, mean-field and computer analyses of large systems of nonlinear differential equations with random parameters.

The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.

Experimentalists at the Relativistic Heavy Ion Collider create exploding droplets of quark-gluon plasma, the stuff which filled the universe for the first microseconds after the big bang. I'll give one theorist's perspective on what we are learning about the properties of quark-gluon plasma from these experiments, including the conclusion that it is closer to an ideal liquid than to an ideal gas and the observation that it "quenches" high energy quarks ("jets") trying to plow through it. The static properties of quark-gluon plasma can be calculated from first principles, but we have no rigorous calculations of what QCD predicts for the viscosity and jet quenching ability of the evidently very strongly interacting quark-gluon plasma that RHIC has discovered. In desperation, theorists are resorting to calculating the properties of quark-gluon plasma in theories other than QCD, wherein difficult dynamical questions like how does a strongly interacting plasma quench jets can be answered by doing easy string theory calculations. I will discuss two examples where such calculations have been compared quantitatively to inferences drawn from existing RHIC data, and close with one prediction for data to come.

Light-cone superstring field theory (LCSFT) and matrix string theory (MST) are closely related. Both theories at the tree level are the Green-Schwarz superstring theory in the light-cone gauge. At the interaction level, the twist fields and the spin fields in MST correspond to the string interaction vertices in LCSFT. Since the CFT fields in MST are characterized by their OPEs, we would like to realize the OPEs by the interaction vertices in LCSFT to see the correspondence. In this talk I will begin with reviews of both theories and proceed to the correspondence between them.

Current measurements from WMAP and other cosmological probes are consistent with a simple inflationary model. Such models predict a background of gravitational waves which may soon be observable in the polarized component of the Cosmic Microwave Background. However, WMAP has observed significant levels of polarized radiation from our galaxy, due to both synchrotron radiation and thermal dust emission. A better understanding of this radiation will be vital if we are to correctly remove it and confidently detect an inflationary signal. As well as discussing the observational case for inflation, I will review the physical origins of the polarized galactic emission, present a simple model for the galactic magnetic field, and discuss current and future directions for improving upon our galactic models.