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I will describe the emergence of geometric (Berry) phases in supersymmetric systems. In theories with degenerate states, non-Abelian geometric phases can arise. I show how supersymmetry helps to ensure the existence of this phenomenon by invoking the examples of systems with (2,2) and (4,4) supersymmetry. In the former, I show how instantons contribute crucially to the form of the non-Abelian phase. The latter system applies to D0-D4 brane dynamics in string theory, leading to a surprising re-interpretation of the Berry phase in terms of gravitational precession of a probe brane. Towards the end will comment on some work in progress on the geometric phase in (8,8) SUSY systems.

In this talk, I will talk about recent developments in studying strongly coupled gauge theory using the gauge/gravity duality in string theory. In particular, the inclusion of fundamental degrees of freedom and finite chemical potential is reviewed. As an example, I will discuss the results from analyzing the gravitational dual of a none-supersymmetric gauge theory at low temperature and finite baryon chemical potential.

After a brief motivation for studying 3d gravity, a review of Strominger argument will be given, showing that 3d quantum gravity with negative cosmological constant is a conformal field theory. Classical phase space tools will be introduced to develop semi-classical analyses of gravity with zero cosmological constant, and, with negative cosmological constant and closed timelike curves.

There has been much interest, in the past few years, in the kappa-Poincare\'/kappa-Minkowski framework as a possible scenario for a deformation of Poincare\' symmetries at Planck scale. I will show how it is possible to give a physical characterization of the concept of quantum symmetries described by a nontrivial Hopf algebra. In particular, I will discuss the generalization of the Noether analysis for a scalar field in kappa-Minkowski space-time and derive conserved charges associated with each generator of the kappa-Poincare\' Hopf-algebra. Then I will report on a recent proposal for the quantization of a scalar field enjoying kappa-Poincare\' symmetries, which consists in a construction of the Fock-space of the theory consistent with the structure of deformed symmetries. Finally I will comment on possible applications of deformed symmetries scenarios in cosmology.

Alternative gauge choices for worldsheet supersymmetry can elucidate dynamical phenomena obscured in the usual superconformal guage. In the particular example of the tachyonic E_8 heterotic string, we use a judicious gauge choice to show that the process of closed-string tachyon condensation can be understood in terms of a worldsheet super-Higgs effect. The worldsheet gravitino assimilates the goldstino and becomes a dynamical propagating field. Conformal, but not superconformal, invariance is maintained throughout.

While Calabi-Yau compactifications of string theory are mathematically elegant, they typically result in many massless scalars in the low-energy, four-dimensional theory. Thus, it is interesting to consider non-Kahler compactifications in the hopes of deriving more phenomenologically interesting models. These models have received little attention in the heterotic theory owing to their mathematical complexity, however in recent work we have found a potential way to derive interesting features of such compactifications using gauged linear sigma models.

The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantumly and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. Conceptually different from already existing models, we have developed a novel theoretical approach to understand this transition from the quantum to a macrorealistic world. It neither needs to refer to the environment of a system (decoherence) nor to change the quantum laws itself (collapse models) but puts the stress on the limits of observability of quantum phenomena due to our measurement apparatuses. First, we demonstrated that for unrestricted measurement accuracy a system’s time evolution cannot be described classically, not even if it is arbitrarily large and macroscopic. Under realistic conditions in every-day life, however, we are only able to perform coarse-grained measurements and do not resolve individual quantum levels of the macroscopic system. As we could show, it is this mere restriction to fuzzy measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum laws: the system’s time evolution governed by the Schrödinger equation and the state projection induced by measurements. This resolves the apparent impossibility of how classical realism and deterministic laws can emerge out of fundamentally random quantum events. We find the sufficient condition for these classical evolutions for isolated systems under coarse-grained measurements. Then we demonstrate that nevertheless there exist ”non-classical” Hamiltonians which are in conflict with macroscopic realism. Thus, though at every instant of time the quantum state appears as a classical mixture, its time evolution cannot be understood classically. We argue why such Hamiltonians are unlikely to be realized in nature.

A conceptual framework is proposed for understanding the relationship between observables and operators in mechanics. We claim that the transformations generated by the objective properties of a physical system must be strictly interpreted as gauge transformations. It will be shown that this postulate cannot be consistently implemented in the framework of classical mechanics. We argue that the uncertainty principle is a consequence of the mutual intertwining between objective properties and gauge-dependant properties. Hence, in classical mechanics gauge-dependant properties are wrongly considered objective. It follows that the quantum description of objective physical states is not incomplete, but rather that the classical notion is overdetermined.

Relational particle mechanics are theories of relative angles and relative (ratios of) separations only. These bear a number of resemblances to the geometrodynamical formulation of general relativity and as such are useful analogues for at least some approaches to the notorious problem of time in quantum gravity. I have recently provided a fairly complete study of the configuration spaces of these theories in spatial dimension 1 and 2, am subsequently studying the redused forms of these theories at the quantum level, and this shall provide a number of useful examples for the conceptual discussion of various problem of time strategies

In this talk we propose a Reduced Phase Space Quantization approach to Loop Quantum Gravity. The idea is to combine the relational formalism introduced by Rovelli in the extended form developed by Dittrich and the Brown-Kuchar-Mechanism. The relational formalism can be used to construct gauge invariant observables for constrained systems such as General Relativity, while the Brown-Kuchar-Mechanism is a particular application of the relational formalism in which pressureless dust is taken as the clock of the system. By combining these two we obtain a framework in which the constraints of General Relativity deparametrize such that the algebra of observables has a very simple structure and furthermore we obtain a so called physical Hamiltonian generating the evolution of those observables. The quantization of the reduced phase space and the physical Hamiltonian can be obtained by using standard LQG techniques and gives a direct access to the physical Hilbert space, which is much harder to achieve in the standard Dirac quantization. Additionally we will analyze the quantization in the Algebraic Quantum Gravity context and discuss the differences that occur. Finally we will present recent results where this framework has been applied to cosmological perturbation theory.