Research

My primary research interest is the theory of fundamental interactions, and to contribute to the development of a quantum theory of fundamental interactions including gravity. Specifically, I'm developing and following an approach known as „Matrix Theory“, focusing on the IKKT or IIB matrix model. This can be viewed as a constructive approach to string theory, which avoids the "landscape" problem and its inherent lack of predictivity.The model is extremely simple, and leads naturally to a quantum structure of space-time. A central aspect of this programe is to establish a suitable notion of quantum geometry, which is fairly well developed by now.

The basic idea of this approach is that 3+1-dimensional space-time arises as a (brane-like) solution or "vacuum condensate" in the matrix model, and physics arises from fluctuations on this brane. For Yang-Mills gauge theories, this works in a very nice and convincing way; the main challenge has been to recover gravity. The 10-dimensional (super)gravity usually studied in string theory is not the answer here: it merely leads to a weak short-range interaction on the brane. Rather, gravity is described through a dynamical frame, which arises from the underlying noncommutative structure of the space-time brane.

A big step towards understanding gravity in this framework is taken in a recent paper, which demonstrates that the Einstein-Hilbert action arises indeed as quantum effect at one loop, in the presence of finite or "fuzzy" extra dimensions. Hence the classical matrix model defines a "pre-gravity theory" which is well suited for quantization, and "real" gravity similar to Einstein's general relativity arises as quantum effective action, which is well-defined within this framework.
In plain words: you should not quantize gravity (it doesnt work). Rather, gravity is already a quantum effect of the underlying matrix theory!
(This realizes Sakharov's idea without the cosmological constant problem. Also, there is no need for an unpredictive "landscape" of string compactifications)

Of course it remains to be seen if all this can provide a comprehensive and realistic physical theory. Some further steps in this direction are as follows:

• There is a remarkable class of „covariant quantum spaces", whose fluctuation modes lead to the spin 2 fluctuations required for gravity, as well as a tower of higher-spin modes; see this review article for details. 
• Simple cosmological space-time solutions featuring a Big Bounce were found, and the fluctuation modes were shown to be ghost-free.
• Recent progress allows to access also the non-linear regime.

The goal in the next years is to develop this theory further.

  Research Project "Quantum Spacetime and Gravity in Matrix Models at one Loop"   supported by the FWF,  P 364679

        Members of this research group:  Tung Tran (postdoc), Alessandro Manta (PhD student),  Eva-Maria Kolba (Master's student), HS

  (completed) Research Project "Matrix Models, Quantum Spaces, and Gravity"  supported by the FWF,  P 32086

(completed) Research Project "Squashed Extra Dimensions in Gauge Theory and Matrix Models"  supported by FWF,   P 28590

(completed) Project "Branes, Gauge Theory and Gravity in Matrix Models"  supported by the FWF,  P24713,     related press release

(completed) project "Matrix Models, Quantum Spaces, and Gravity"  supported by FWF,  P21610