Prof. Hermann Nicolai

Am Mühlenberg 1

14476 Potsdam-Golm

Prof. Hermann Nicolai

Prof. Hermann Nicolai
Prof. Hermann Nicolai
Location Potsdam

Quantum Gravity and Unified Theories

Phone: +49 331 567-7216
Fax: +49 331 567-7297
Room: 1.16

Main Focus

My work is concerned with various aspects of quantum gravity and unified theories, especially supergravity, superstring and supermembrane theories. More specifically, I am presently interested in the following topics:

Dimensionally reduced gravity and supergravity: (i) Infinite dimensional symmetries generalizing the Geroch group, especially the ones based on exceptional Lie groups which arise in the dimensional reduction of maximal supergravity. (ii) Exact quantization of such models as "midi-superspace" models of quantum gravity in the framework of the theory of integrable systems, e.g. by means of the so-called isomonodromic ansatz. Identification of observables (non-local conserved charges) and implementation of the Geroch group at the quantum level. (iii) Search for a realization of hyperbolic Kac Moody algebras, and especially E10, in gravity and supergravity (and possibly M Theory) by generalizing and extending the BKL-type description of the chaotic oscillations of the metric near a spacelike singularity. In this context, I have recently become interested in string (or M Theory) cosmology, as I believe that the chaos which occurs in all "supertheories" may invalidate many of the approximations made in standard (e.g. inflationary) cosmology.

String and superstring theory: (i) Mathematical aspects, in particular the relation between indefinite Kac Moody algebras and Borcherds algebras; affine vertex operator constructions (at arbitrary level); explicit construction and investigation of root spaces of hyperbolic Kac Moody algebras (such as E10). (ii) Higher-dimensional supersymmetric extended objects; supermembranes and supersymmetric matrix models; construction of vertex operators for the supermembrane; analysis of BPS multiplets; understanding the role of d=11 supergravity in string theory.

Maximal gauged supergravities in three dimensions:
our recent construction of maximal (N=16) gauged supergravities in three dimensions has revealed a surprising wealth of structures, which we are currently trying to explore: these theories accommodate all the exceptional groups (in various real forms), with certain supergroups (again including exceptional ones) as background isometries. These theories are not only of interest in their own right, but should play an important role in the so-called AdS/CFT correspondence, and might also become relevant for understanding certain issues in three-dimensional differential geometry.

Canonical gravity:
One of my long term interests is to find a generalization of Ashtekars variables for higher-dimensional gravity and supergravity by fusion of gravitational and non-gravitational degrees of freedom. I would also like to understand better some of the conceptual issues of quantum gravity in the framework of supergravity and string theory.

A key issue
in my opinion is the apparent incompatibility of a deSitter-type universe and all the (maximally supersymmetric) "supertheories" currently on the market (which strongly prefer Anti-deSitter) and under study as candidates for a unified theory.

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