Norbert Bodendorfer, LMU Munich
Title: Holographic signatures of resolved cosmological singularities
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One of the most important results in string theory is the so called “Maldacena conjecture” or “AdS/CFT correspondence” proposed by Juan Maldacena. This conjecture states that given a space-time with cosmological constant (known as anti De Sitter space-time or AdS) the behavior of gravity in it is equivalent to the behavior of a field theory living on the boundary of the space-time. These field theories are of a special type known as “conformal field theories”. Hence the AdS/CFT name. Conformal field theories are considerably better understood than quantum gravity so to make the latter equivalent to them opens several new possibilities. The discussion of AdS/CFT has mostly taken place in the context of string theory which has general relativity as a classical limit. This opens the question of what kind of imprint the singularities that are known to exist in general relativity leave in the conformal field theory.
On the other hand, loop quantum gravity is known for eliminating the singularities that arise in general relativity. They get replaced by regions of high curvature and fluctuations of it that are not well described by a semiclassical geometry. However, nothing is singular, physical variables may take large –but finite-values. If AdS/CFT were to hold in the context of loop quantum gravity the question arises of what imprint would the elimination of the singularity leave on the conformal field theory. The seminar dealt with this point by considering certain functions known as correlation functions in the conformal field theory that characterize its behavior. In particular how the singularities of general relativity get encoded in these correlation functions and how their elimination in loop quantum gravity changes them. The work is at the moment only a model in five dimensions of a particular space-time known as the Kasner space-time.
Future work will consist in expanding the results to other space-times. Of particular interest would be the extension to black hole spacetimes, which loop quantum gravity also rids of singularities. As is well known, black hole space-times have the problem of the “information paradox” stemming from the fact that black holes evaporate through the radiation that Hawking predicted leaving in their wake only thermal radiation no matter what process led to the formation of the black hole. It is expected that when the evaporation is viewed in terms of the conformal field theory, this loss of information about what formed the black hole will be better understood.
In addition to the specific results, the fact that this work suggests points of contact between loop quantum gravity and string theory makes it uniquely exciting since both fields have developed separately over the years and could potentially benefit from cross pollination of ideas.
