Sigma models are two-dimensional classical conformal field theories in which the fields are maps from a Riemann surface to a fixed Riemannian manifold, the target space. These field theories typically suffer from an anomaly that can be cancelled by a so-called topological term. This term is exactly the holonomy of a gerbe-connection over the targetspace.

My work in this area deals with defining the topological term in situations where additional structures are either added or omitted. For example, omitting the orientation of the surface requires a so-called Jandl structure on the Gerbe.

An important special case are Lie groups as target spaces, and the corresponding sigma models are called Wess-Zumino-Witten models. Here, one aspect of my work is to give a Lie-theoretical classification of the relevant additional structures.

Below are some articles and manuscripts of talks about this topic.

## Articles associated with this topic

*Smooth Functorial Field Theories from B-Fields and D-Branes*

together with Severin Bunk

J. Homotopy Relat. Struct., to appear

arxiv:1911.09990*Transgression of D-branes*

arxiv:1808.04894*The gauging of two-dimensional bosonic sigma models on world-sheets with defects*

together with Rafal R. Suszek, Krzysztof Gawedzki

Rev. Math. Phys 25 (2013) 1350010

arxiv:1202.5808*Global Gauge Anomalies in two-dimensional Bosonic Sigma Models*

together with Rafal R. Suszek, Krzysztof Gawedzki

Commun. Math. Phys. 302 (2), 513-580 (2011)

arxiv:1003.4154*Bundle Gerbes and Surface Holonomy*

together with Christoph Schweigert, Thomas Nikolaus, Jürgen Fuchs

Proceedings of the 5th European Congress of Mathematics, edited by A. Ran, H. te Riele and J. Wiegerinck, EMS Publishing House, 2008, 167-197

arxiv:0901.2085*Bundle Gerbes for Orientifold Sigma Models*

together with Rafal R. Suszek, Krzysztof Gawedzki

Adv. Theor. Math. Phys. 15 (3), 621-688 (2011)

arxiv:0809.5125*Bi-branes: Target Space Geometry for World Sheet topological Defects*

together with Jürgen Fuchs, Christoph Schweigert

J. Geom. Phys. 58(5), 576-598 (2008)

arxiv:hep-th/0703145 *WZW Orientifolds and finite Group Cohomology*

together with Krzysztof Gawedzki, Rafal R. Suszek

Commun. Math. Phys. 284(1), 1–49 (2007)

arxiv:hep-th/0701071 *Unoriented WZW Models and Holonomy of Bundle Gerbes*

together with Christoph Schweigert, Urs Schreiber

Commun. Math. Phys. 274(1), 31–64 (2007)

arxiv:hep-th/0512283

## Talks associated with this topic

*Introduction to Gerbes in Conformal Field Theory*

Workshop "Gerbes, twisted K-theory and conformal field theory", Mathematisches Forschungsinstitut Oberwolfach, August 2005

Notes*Gerbes in unoriented WZW-Models*

Summer school "Modern Mathematical Physics IV", University of Belgrade, September 2006

Notes*Geometry for 2-Form Gauge Fields*

Conference "Tagung des Sonderforschungsbereichs Particles, Strings and the Early Universe", Deutsches Elektronen-Synchrotron DESY Zeuthen, February 2008

Notes*String Connections and Supersymmetric Sigma Models*

Workshop "Homotopy theory and higher algebraic structures", University of California at Riverside, November 2009

Notes*String structures and supersymmetric sigma models*

Program "Higher structures in string theory and quantum field theory", Erwin-Schrödinger-Institut für Mathematische Physik, December 2015

Notes*An introduction to higher parallel transport*

Seminar "Algebraic and combinatorial perspectives in the mathematical sciences", online, September 2020

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