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
- Geometric T-duality: Buscher rules in general topology
Ann. Henri Poincaré, to appear
arxiv:2207.11799 - Smooth Functorial Field Theories from B-Fields and D-Branes
together with Severin Bunk
J. Homotopy Relat. Struct. 16.1 (2021): 75-153
arxiv:1911.09990 - Transgression of D-branes
together with Severin Bunk
Adv. Theor. Math. Phys., Vol. 25, No. 5 (2021), pp. 1095-1198.
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 Krzysztof Gawedzki, Rafal R. Suszek
Adv. Theor. Math. Phys. 15 (3), 621-688 (2011)
arxiv:0809.5125 - Bi-branes: Target Space Geometry for World Sheet topological Defects
together with Christoph Schweigert, Jürgen Fuchs
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
Presentation Video - Geometric T-Duality: Buscher rules in general topology
Program "Higher Structures and Field Theory", Erwin-Schrödinger-Institut für Mathematische Physik, August 2022
Video