academic work
research & background

String theory is a branch of mathematical physics based upon the idea of one-dimensional fundamental objects, which are called strings. This approach of using extended objects takes care of many problems encountered in the point particle based description of nature via quantum field theories, e.g. the well-established Standard Model of Particle Physics. While mathematical self-consistency specifies certain parts of the theory almost uniquely, the dimensional compactification, which is necessary to make contact with our four-dimensional world, yields an entire landscape of possible vacua with no obvious method to point out the right one. Another issue is the fact that our current theoretical understanding of string theory itself is somewhat limited, as we only have an perturbative (i.e. “approximative”) understanding whereas the non-perturbative “full” theory still remains unknown…

Recent Research:

My research work in mathematical physics is currently focused on understanding the geometric properties of the Large Volume Scenario and Swiss Cheese-type Calabi-Yau manifolds. A plan for the future is to spend a significant amount of (cloud) computing time on related string landscape scans. Lately I’ve also become interested in modern constructions of Calabi-Yau 3-folds, which are currently investigated.

Before that I was working on F-theory GUT model building (a branch of non-perturbative string theory), following the developments in this area since its “minirevolution” in early 2008. During the better part of 2010 and continuing in 2011 I worked somewhat off the phenomenological main stream on related mathematical methods, namely the computation of cohomology group dimensions in toric settings, see the cohomCalg project.

Contributions:

F-theory is a hypothesized theory, that so far can only be described indirectly via dualities. From a conservative perspective, F-theory is just a geometrization of a symmetry within perturbative type IIB string theory. On the other hand, it can be realized as a particular limit of the non-perturbative M-theory. A third description relates F-theory to the heterotic string. All of those indirect definitions are equally valid and highlight the intricate structure of interconnects and links between the various branches of string theory. Overall, F-theory offers an elegant perspective that unifies many non-perturbative aspects like instantons, 7-branes, geometry backreactions etc. The price, however, to work within the F-theory framework comes in the form of various technical and mathematical challenges—which makes this subject all the more interesting to me…

After some early failed attempts to get a better understanding of the strong-coupling regime of IIB orientifolds based on (p,q) 7-branes and ABC-brane collections, it turned out that F-theory is indeed the right framework to discuss non-perturbative aspects of type IIB string theory. The work revealed a number of more or less surprising restrictions on the gauge group one can obtain in global F-theory models obtained from simple IIB uplifts. In a more involved investigation of the model building properties, the usage of the spectral cover description of the gauge flux allowed us to provide further details on the phenomenological issues in global F-theory GUT model building. In particular, we were able to find a rather simple global model having three chiral matter generations as an explicit example. In our next project we considered instantons, more precisely the uplift of D3-brane instantons in IIB-orientifolds with their supposed uplift counterparts, the M5-brane instantons.

Parallel to this project, we also investigated a new algorithm for computing the cohomology of line bundles on toric varieties, a task which appeared more and more often in our work on instantons. Considerable time was spend on a suitable implementation and subsequent questions arising from this project. During the work on direct applications of this algorithm in theoretical physics a generalization of the algorithm to equivariant geometries was conjectured. to be continued…

I’ve written an elementary introduction into the subject of string theory and F-theory in case you want to know more.

Academic timeline:

Chronicles enroute to a PhD:

My PhD time at the Max-Planck-Institute of Physics in Munich, Germany lasted from June 2008 till February 2011. During this time I had the chance to participate in many conferences, workshops and schools throughout Europe and visited Vienna, Würzburg, Hamburg, Warsaw, Paris, Geneva and the infamous Castle Ringberg at Tegernsee in southern Bavaria. A particular highlight was the magnificient 4-week stay at the KITP in Santa Barbara, California as a participant of the “Strings at the LHC and in the Early Universe” program in spring 2010. At the end of 2010 I finished my dissertation which summarized most of the work published in my first three publications.

Undergraduate time in Bielefeld:

In July 2007, I finished my diploma in theoretical physics (in German called “Diplomarbeit”, internationally comparable with a M.Sc.) entitled “Semi-Realistic Orbifold Compactification of Heterotic Strings” at the University of Bielefeld. For the thesis I investigated the different classical methods of space-time compactification, particularly Calabi-Yau and orbifold compactifications of the E8xE8-heterotic string, which yield semi-realistic effective 4-dimensional theories that are quite comparable with the Standard Model. Rather large portions of the text focused on the mathematical background of spinors and bundles, which are relevant to fully understand the requirement of minimal supersymmetry in the resulting effective theories.

While reading into the subject of string theory I developed a great interest in the technical details of the Calabi-Yau compactification process, where one needs far more advanced mathematical tools to access the relevant topological and geometrical information of those particular spaces. However, this required a thorough understanding of spinor geometry, which ultimately resulted in the thesis as presented above.

In June 2007 I went to the large international Strings 2007 conference held in Madrid, Spain. Here I met my later PhD advisor R. Blumenhagen for the first time. Therefore I like to remember this conference as one of the main cornerstones along my academic road.

During the last days of April 2008 I completed my second diploma in pure mathematics. In the thesis—called “Dimensional Reduction of Spin(7)-Instantons”—I considered certain generalizations of classical 4d gauge instantons to higher dimensions, using certain 8-dimensional base spaces with the reduced holonomy group Spin(7). The available general methods are then applied in two particular examples. There are a number of fine points that I would have liked to improve, but the deadline to the beginning of my PhD work at the MPI in Munich was rather restrictive.

Lecture Notes:

During my time of study, I did typeset a number of lecture notes in LaTeX for exam preparations. However, I did not correct the mistakes found in the printouts, such that the documents itself most likely contain quite a number of errors. Nevertheless, as some of those notes are still drifting around in "unofficial" versions in the Bielefeld university, I will offer them for download regardless of any errors.

Furthermore, there is a huge collection of lecture notes available on the website of Ulrich Theis, which can be found here. More lecture notes are available in the arXiv.org ePrint-Archives and on the pages of numerous professors—just search for certain names.