PhD defence by Jens A. Gesser – Niels Bohr Institute - University of Copenhagen

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Niels Bohr Institute > Calendar > 2008 > PhD defence by Jens A...

PhD defence by Jens A. Gesser

Title of talk:  The Nature of ZZ-branes

Title of Ph.D. Thesis:  Non-compact Geometries in 2D Euclidean Quantum Gravity

Academic advisor:  Prof. Jan Ambjørn

The development of a Quantum theory of Gravity generalizing Einsteins theory of Gravity has long been a goal of theoretical Physics.  In order to obtain some insight in Quantum Gravity, which may help us develop a Quantum theory of Gravity in 3 + 1 dimensions , one studies Euclidean Quantum Gravity in two dimensions, in which case Quantum Gravity simplifies considerably due to the topological nature of the Einstein-Hilbert action. In the process of gauge-fixing  Liouville theory appears as the appropriate field theory governing the geometrical degrees of freedom of the world-sheet. Classical  Liouville theory admits a basic solution, which describes the geometry of a non-compact constant negative curvature surface, the Lobachevskiy plane or pseudosphere.  In hep-th/0101152 Zamolodchikov and Zamolodchikov quantize the Lobachevskiy plane. Quite surprisingly, they  find a two-parameter family of solutions to quantum Liouville theory and to each of these solutions they associate a boundary condition, referred to as a ZZ boundary condition, imposed  at infinity of the Lobachevskiy plane.  Only the basic  (1,1) solution  is consistent with standard loop perturbation theory and this solution is interpreted as the “natural” quantization of the Lobachevskiy plane.  The nature of the remaining solutions and the corresponding boundary conditions at infinity is not resolved by Zamolodchikov and Zamolodchikov. They write: “The most intriguing point is the nature of the “excited ” vacua…A meaning of these quantum excitations of the (physically infinite faraway) absolute remains to be comprehended.”  In this talk we will show, that we may interpret the so-called principal ZZ boundary conditions spanning the set of ZZ boundary conditions in the (p,q) minimal model coupled to 2D Euclidean Quantum Gravity as effective boundary conditions obtained by integrating out the matter degrees of freedom. In this sense there only exists one ZZ boundary condition in Liouville theory when coupled to the (p,q) minimal model, the basic (1,1) ZZ boundary condition. All the other principal ZZ boundary conditions may be viewed as effective boundary conditions encoding the different matter boundary conditions.