Melanie Becker, Professor of Physics

String theory is one of the most beautiful and exciting areas of modern theoretical physics whose ultimate goal is to reconcile quantum mechanics with Einstein's theory of general relativity.

Only through the marriage of these two theories will it ever be possible to understand fundamental questions such as the origin of our universe. This is a challenging problem, especially because for many years string theory was only able to describe perturbative physics. The situation changed in the mid 1990s when M-theory was discovered and non-perturbative effects in the string coupling constant were beginning to be understood. In 1995 M.Becker co-discovered that non-perturbative effects in string theory come from extended objects, called p-branes, that wrap supersymmetric cycles of the internal geometry [1]. This allowed the precise description and calculation of non-perturbative effects in the string coupling constant and showed that string theory is not merely a "theory of strings", but that higher dimensional extended objects (branes) play a crucial role. In 1997 M.Becker and her collaborators showed that M(atrix)-Theory can be used as a fundamental theory that describes M-theory in terms of point-like objects called D0-branes [3, 4].

Ever since its discovery, string theory has aimed to calculate the values of the coupling constants of the standard model of elementary particles. For many years no progress could be made because once string theory is compactified on a Calabi-Yau manifold, a large number of massless (and thus unphysical) scalars appears. This is the famous "moduli space problem", which emerges because the shape and size of the internal Calabi-Yau manifold is not determined by the string. In 1996 M.Becker made a fundamental discovery in collaboration with K.Becker, which subsequently lead to the solution of the moduli space problem [2]. We realized that Calabi-Yau manifolds are only a simplification of a more general class of internal geometries, called flux compactifications, in which additional tensor fields (which naturally emerge in string theory) are not set to zero by hand. Such flux compactifications lead to a potential for the moduli fields, and thus serve as the main candidates for realistic string theory compactifications nowadays. The heterotic string has traditionally been the theory of choice for constructing string theory models that are interesting for particle phenomenology. Even though this perspective has changed after the discovery of string dualities and other approaches have become available (intersecting brane models, F-theory GUTs, branes at singularities), it turns out that the "torsional geometries" or equivalently "heterotic flux compactifications" provide an extremely rich territory not only for particle phenomenology but also for algebraic geometry [5, 6]. Torsional geometries are an active area of current research for Becker. Other topics of current research involve: three-dimensional gravity and Kerr/CFT, holography and its applications to condensed matter and flux compactifications in general.

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References

1. K. Becker, M. Becker and A. Strominger, “Five-Branes, Membranes And Nonperturbative String Theory,” Nucl. Phys. B 456, 130 (1995) [arXiv:hep-th/9507158].

2. K. Becker and M. Becker, “M-Theory on Eight-Manifolds,” Nucl. Phys. B 477, 155 (1996) [arXiv:hep- th/9605053].'

3. K. Becker and M. Becker, “A two-loop test of M(atrix) theory,” Nucl. Phys. B 506, 48 (1997) [arXiv:hep- th/9705091].

4. K. Becker, M. Becker, J. Polchinski and A. A. Tseytlin, “Higher order graviton scattering in M(atrix) theory,” Phys. Rev. D 56, 3174 (1997) [arXiv:hep-th/9706072].

5. K. Becker, M. Becker, K. Dasgupta and P. S. Green, “Compactifications of heterotic theory on non-Kaehler complex manifolds. I,” JHEP 0304, 007 (2003) [arXiv:hep-th/0301161].

6. K. Becker, M. Becker, J. X. Fu, L. S. Tseng and S. T. Yau, “Anomaly cancellation and smooth non-Kaehler solutions in heterotic string theory,” Nucl. Phys. B 751, 108 (2006) [arXiv:hep-th/0604137].