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The SFB 676 has been funded by the DFG from 2006 to 2018. The project was completed with a special colloquium in June 2018. A book with the scientific results of the SFB 676 has been published in September 2018.

J. Haller and M. Grefe (eds.), “Particles, Strings and the Early Universe: The Structure of Matter and Space-Time,” Hamburg (2018), DOI: 10.3204/PUBDB-2018-00782.

Many research directions developed within the SFB 676 will be continued within the Cluster of Excellence "Quantum Universe" starting 1 January 2019.

A4 – Mathematical Foundations of String Theory

Project Leaders

Christoph Schweigert (e-mail | group homepage)


In an algebraic approach to conformal field theory, topological world sheet defects have been shown to encode information on symmetries and dualities, both of Kramers-Wannier type and T-dualities. In this project, bibranes have been identified as the corresponding geometric structure on target spaces - including those with a topologically non-trivial B-field.

We propose to extend the study of space-time and world sheet aspects of defects and to apply it to string compactifications on T-folds which arise as mirrors and T-duals of flux compactifications.


Birgit Richter

Former members

Andrea Almasy

Till Barmeier

Alexander Barvels

Thomas Nikolaus

Gor Sarkissian

Urs Schreiber

Danny Stevenson

Rafal Suszek

Efrossini Tsouchnika

Alessandro Valentino

Konrad Waldorf

Christoph Wockel


Get these publications as bibtex-file

"Bicategories for boundary conditions and for surface defects in 3-d TFT"
Fuchs, Jurgen and Schweigert, Christoph and Valentino, Alessandro
Commun.Math.Phys. 321, 543-575 (2013)
doi: 10.1007/s00220-013-1723-0
eprint: 1203.4568 [hep-th]

"Four Equivalent Versions of Non-Abelian Gerbes"
Nikolaus, Thomas and Waldorf, Konrad
Pacific Journal of Math. 264, 355-420 (2013)
doi: http://dx.doi.org/10.2140/pjm.2013.264.355
eprint: 1103.4815 [math.DG]

"Lifting problems and transgression for non-abelian gerbes"
Thomas Nikolaus and Konrad Waldorf
Advances in Mathematics 242, 50 - 79 (2013)
doi: http://dx.doi.org/10.1016/j.aim.2013.03.022
[ link ]

"Bicategories in Field Theories - An Invitation"
Nikolaus, Thomas and Schweigert, Christoph
Strings, Gauge Fields, and the Geometry Behind-- The Legacy of Maximilian Kreuzer (2011)
doi: 10.1142/9789814412551_0004
eprint: 1111.6896

"A Smooth Model for the String Group"
Nikolaus, Thomas and Sachse, Christoph and Wockel, Christoph
Int. Math. Res. Notices 16, 3678-3721 (2011)
doi: http://dx.doi.org/10.1093/imrn/rns154
eprint: 1104.4288 [math.AT]

"Equivariance In Higher Geometry"
Nikolaus, Thomas and Schweigert, Christoph
Adv.Math. 226, 3367-3408 (2011)
doi: http://dx.doi.org/10.1016/j.aim.2010.10.016
eprint: 1004.4558 [math.AT]

"Bundle Gerbes for Orientifold Sigma Models"
Gawedzki, Krzysztof and Suszek, Rafal R. and Waldorf, Konrad
Adv.Theor.Math.Phys. 15, 621-688 (2011)
eprint: 0809.5125 [math-ph]

"Geometry of infinite dimensional Grassmannians and the Mickelsson-Rajeev cocycle"
Stevenson, D.
Journal of Geometry and Physics 60, 664-677 (2010)
doi: 10.1016/j.geomphys.2009.12.010
eprint: 0802.3608 [math.DG]

"On the Rosenberg-Zelinsky sequence in abelian monoidal categories"
Barmeier, T. and Fuchs, J. and Runkel, I. and Schweigert, C.
J. reine angew. Math. 642, 1-36 (2010)
eprint: 0801.0157 [math.CT]

"Gerbes and Lie Groups"
Schweigert, C. and Waldorf, K.
Developments and Trends in Infinite-Dimensional Lie Theory, Progress in Mathematics, Birkhäuser (2010)
eprint: 0710.5467 [math.DG]

"Defects and Permutation branes in the Liouville field theory"
Sarkissian, Gor
Nucl. Phys. B821, 607-625 (2009)
doi: 10.1016/j.nuclphysb.2009.06.012
eprint: 0903.4422 [hep-th]

"Bundle Gerbes and Surface Holonomy"
Fuchs, J. and Nikolaus, T. and Schweigert, C. and Waldorf, K.
Proceedings of the 5th European Congress of Mathematicians (2009)
[ link ]
eprint: 0901.2085 [math.DG]

"Some remarks on defects and T-duality"
Sarkissian, Gor and Schweigert, Christoph
Nucl. Phys. B819, 478-490 (2009)
doi: 10.1016/j.nuclphysb.2009.04.016
eprint: 0810.3159 [hep-th]

"AQFT from n-functorial QFT"
Schreiber, Urs
Commun. Math. Phys. 291, 357-401 (2009)
doi: 10.1007/s00220-009-0840-2
eprint: 0806.1079 [math.CT]

"The Classifying Space of a Topological 2-Group"
Baez, John.~C. and Stevenson, Danny
The Abel Symposium 2007, Springer (2009)
[ link ]
eprint: 0801.3843 [math.AT]

"L-infinity-Algebra Connections and Applications to String- and Chern-Simons n-Transport"
Sati, H. and Schreiber, U. and Stasheff, J.
Quantum Field Theory (2009)
[ link ]
doi: 10.1007/978-3-7643-8736-5_17
eprint: 0801.3480

"Parallel Transport and Functors"
Schreiber, U. and Waldorf, K.
Journal of Homotopy and Related Structures 4, 187-244 (2009)
eprint: 0705.0452 [math.DG]

"Bi-branes: Target space geometry for world sheet topological defects"
Fuchs, Jurgen and Schweigert, Christoph and Waldorf, Konrad
J. Geom. Phys. 58, 576-598 (2008)
doi: 10.1016/j.geomphys.2007.12.009
eprint: hep-th/0703145

"WZW orientifolds and finite group cohomology"
Gawedzki, Krzysztof and Suszek, Rafal R. and Waldorf, Konrad
Commun. Math. Phys. 284, 1-49 (2008)
doi: 10.1007/s00220-008-0525-2
eprint: hep-th/0701071

"Uniqueness of open/closed rational CFT with given algebra of open states"
Fjelstad, Jens and Fuchs, Jurgen and Runkel, Ingo and Schweigert, Christoph
Adv. Theor. Math. Phys. 12, 1283-1375 (2008)
eprint: hep-th/0612306

"Module categories for permutation modular invariants"
Barmeier, T. and Fuchs, J. and Runkel, I. and Schweigert, C.
International Mathematics Research Notes 2010, 3067-3100 (2008)
doi: 10.1093/imrn/rnp235
eprint: 0812.0986 [math.CT]

"Connections on non-abelian Gerbes and their Holonomy"
Schreiber, U. and Waldorf, K.
ArXiv e-prints (2008)
eprint: 0808.1923 [math.DG]

"The basic bundle gerbe on unitary groups"
Murray, M. and Stevenson, D.
Journal of Geometry and Physics 58, 1571-1590 (2008)
doi: 10.1016/j.geomphys.2008.07.006
eprint: 0804.3464 [math.DG]

"Smooth Functors vs. Differential Forms"
Schreiber, U. and Waldorf, K.
eprint: 0802.0663 [math.DG]

"Kramers-Wannier dualities for WZW theories and minimal models"
Schweigert, Christoph and Tsouchnika, Efrossini
J. Geom. Phys. 10, 773-789 (2008)
doi: 10.1142/S0219199708002983
eprint: 0710.0783 [hep-th]

"The inner automorphism 3-group of a strict 2-group"
Roberts, D. and Schreiber, U.
J. Geom. Phys. 58, 576-598 (2008)
eprint: 0708.1741 [math.CT]

"Unoriented WZW models and holonomy of bundle gerbes"
Schreiber, Urs and Schweigert, Christoph and Waldorf, Konrad
Commun. Math. Phys. 274, 31-64 (2007)
doi: 10.1007/s00220-007-0271-x
eprint: hep-th/0512283

"More Morphisms between Bundle Gerbes"
Waldorf, K.
Theory and Applications of Categories 18, 240-273 (2007)
eprint: arXiv:math/0702652

"Topological defects for the free boson CFT"
Fuchs, Jurgen and Gaberdiel, Matthias R. and Runkel, Ingo and Schweigert, Christoph
J. Phys. A40, 11403 (2007)
doi: 10.1088/1751-8113/40/37/016
eprint: 0705.3129 [hep-th]


PhD thesis: "Higher categorical structures in geometry : general theory and applications to quantum field theory"
Nikolaus, Th.
Universität Hamburg (2011)
[ link ]

Diploma thesis: "Defects in the GL1|1 Wess-Zumino-Witten Model"
Tormählen, M.
Universität Hamburg (2011)
[ link ]

PhD thesis: "Permutation equivariant ribbon categories from modular functors"
Barmeier, T.
Universität Hamburg (2010)
[ link ]

Master thesis: "Equivariant gerbes and descent"
Nikolaus, T.
Universität Hamburg (2009)
[ link ]

PhD thesis: "Quantum Groups and Field Theory"
Tsouchnika, Efrossini
Universität Hamburg (2008)
[ link ]

PhD thesis: "Algebraic structure for bundle gerbes and the Wess-Zumino term in conformal field theory"
Waldorf, K.
Universität Hamburg (2007)
[ link ]

Impressum  | last modified 27 Jul 2018