We evaluate string one-loop contributions to the Kahler metric of D-brane moduli (positions and Wilson lines), in toroidal orientifolds with branes at angles. Contributions due to bulk states in the loop are known, so we focus on the contributions due to states localized at intersections of orientifold images. We show that these quantum corrections vanish. This does not follow from the usual nonrenormalization theorems of supersymmetric field theory.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

Stigner, Carl

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

Schweigert, Christoph

Hamburg University, Germany.

Partition functions, mapping class groups and Drinfeld doubles2013In: Symmetries and Groups in Contemporary Physics: Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics / [ed] Chengming Bai (Nankai University, China), Jean-Pierre Gazeau (Paris Diderot University, France), Mo-Lin Ge (Nankai University, China), Singapore: World Scientific, 2013, p. 405-410Conference paper (Refereed)

Abstract [en]

Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete expressions obtained for the case of Drinfeld doubles of finite groups. The results for doubles are independent of the characteristic of the underlying field, and the general results do not require any assumptions of semisimplicity.

We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool is the theory of permutation equivariant modular functors developed by Barmeier et al. in math.CT/0812.0986 and math.QA/1004.1825.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

Schweigert, Christoph

Hamburg University.

Coends in conformal field theory2017In: Lie Algebras, Vertex Operator Algebras, and Related Topics / [ed] Katrina Barron, Elizabeth Jurisich, Antun Milas, Kailash Misra, American Mathematical Society (AMS), 2017, p. 65-81Chapter in book (Refereed)

Abstract [en]

The idea of "summing over all intermediate states" that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal vertex algebras, one deals with coends in functor categories. Working with these coends involves quite a few subtleties which, even though they have in principle already been understood twenty years ago, have not been sufficiently appreciated by the conformal field theory community.

Based on the modular functor associated with a -- not necessarily semisimple -- finite non-degenerate ribbon category D, we present a definition of a consistent system of bulk field correlators for a conformal field theory which comprises invariance under mapping class group actions and compatibility with the sewing of surfaces. We show that when restricting to surfaces of genus zero such systems are in bijection with commutative symmetric Frobenius algebras in D, while for surfaces of any genus they are in bijection with modular Frobenius algebras in D. This provides additional insight into structures familiar from rational conformal field theories and extends them to rigid logarithmic conformal field theories.

Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensionaltopological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantumcomputing. We explain an obstruction to the existence of surface defects thattakes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allowsone to exhibit Brauer-Picard groups as symmetry groups of three-dimensionaltopological field theories.

7.

Fuchs, Jürgen

et al.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.

Dijkgraaf-Witten theories are extended three-dimensional topological field theories of Turaev-Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in quantum field theories are of interest in various applications and provide structural insight. We perform a geometric study of boundary conditions and surface defects in Dijkgraaf-Witten theories. A crucial tool is the linearization of categories of relative bundles. We present the categories of generalized Wilson lines produced by such a linearization procedure. We establish that they agree with the Wilson line categories that are predicted by the general formalism for boundary conditions and surface defects in three-dimensional topological field theories that has been developed in arXive:1203.4568.