Sixth international school on field theory and gravitation

Aqui alguns dos assuntos a tratar na escola.


Petr Horava
Progress in Quantum Gravity with Anisotropic Scaling

I will give an overview of the basic concepts in quantum gravity with Lifshitz-type anisotropic scaling, as well as some recent developments in this rapidly developing field. Among the topics discussed are the relationship to the lattice formulation of quantum gravity via causal dynamical triangulations, and the possibility of extending the gauge symmetries of the theory to "nonrelativistic general covariance" which eliminates the scalar graviton polarization and makes the theory at long distances closely reminiscent of general relativity.

John Donoghue
Effective Field Theory and General Relativity

Effective Field Theory is a technique for extracting the predictions from a theory, using only the appropriate interactions and degrees of freedom that occur at low energy. This makes it ideal for quantum General Relativity where we know that GR is the appropriate low energy theory. I will discuss the techniques, applications and limitations of the Effective Field Theory approach.

Steve Carlip
1. Spontaneous Dimensional Reduction?

Several lines of evidence hint that quantum gravity at distances slightly larger than the Planck scale may become effectively two-dimensional. I will summarize the evidence for this "spontaneous dimensional reduction," and suggest a further argument based on the effect of vacuum fluctuations on light cones. If this description proves to be correct, it suggests an interesting relationship between small-scale quantum spacetime and the behavior of cosmologies near a spacelike singularity.



Effective Conformal Descriptions of Black Hole Entropy

It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though,is the universality of these thermodynamic properties: their very simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I discuss the proposal that this universality arises from an approximate conformal symmetry, which permits an effective ``conformal dual'' description that is largely independent of the microscopic details.

Andrei Mironov
Supersymmetric gauge theories: integrability and dualities

N=2 supersymmetric gauge theories at low energies are associated with integrable systems. This correspondence can be lifted up to the gauge theories in the graviphoton background, the corresponding integrable systems being quantized, and can be encoded in terms of conformal blocks of 2d conformal field theories. It can be also further extended to various dimenions. In particular, its extension to Chern-Simons theory has much to do with knot theory. A review of all these correspondences will be presented.



Gianluca Calcagni
Field theory on fractal spacetime

We discuss how to construct field theories on spacetime geometries with fractal properties. Based on fractional calculus, we introduce continuous spacetimes whose dimension changes with the scale, and that display discrete symmetries in the ultraviolet and ordinary Poincare' symmetries in the infrared. These theories are generally argued to be power-counting renormalizable under certain assumptions.