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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.

A10 – TQFT from and for 4d SUSY gauge theories

Project Leaders

Christoph Schweigert (e-mail | group homepage)

Jörg Teschner (e-mail | group homepage)


AGT-correspondences give profound relations between certain families of N=2 supersymmetric gauge theories in four dimensions and conformal field theories in two dimensions. Subsequent investigations of the AGT-correspondences revealed a new type of topological field theory associated to these theories that captures completely the dependence of important physical quantities on the gauge coupling constants, including perturbative and non-perturbative corrections.

The topological field theories associated to N=2 gauge theories are the central objects of study in this project. We propose to develop a precise mathematical framework for them in which loop and surface operators will play a particularly important role. We also plan to generalize these structures to a wider class gauge theories and to investigate relations with topological string theory.


Raphaël Belliard

Tobias Ohrmann

Elli Pomoni

Former members

Aswin Balasubramanian

Maxime Gabella

Jan Hesse


Get these publications as bibtex-file

"Trinion Conformal Blocks from Topological strings"
Coman, Ioana and Pomoni, Elli and Teschner, Joerg
eprint: 1906.06351 [hep-th]

"Masses, Sheets and Rigid SCFTs"
Balasubramanian, Aswin and Distler, Jacques
eprint: 1810.10652 [hep-th]

"Modularization of small quantum groups"
Gainutdinov, Azat M. and Lentner, Simon and Ohrmann, Tobias
eprint: 1809.02116 [math.QA]

"The logarithmic Cardy case: Boundary states and annuli"
Fuchs, Jürgen and Gannon, Terry and Schaumann, Gregor and Schweigert, Christoph
Nucl. Phys. B930, 287-327 (2018)
doi: 10.1016/j.nuclphysb.2018.03.005
eprint: 1712.01922 [math.QA]

"Orbifold Construction for Topological Field Theories"
Schweigert, C. and Woike, L.
J. Pure Appl. Algebra (2018)
doi: 10.1016/j.jpaa.2018.05.020
eprint: 1705.05171 [math.QA]

"Supersymmetric field theories and geometric Langlands: The other side of the coin"
Balasubramanian, Aswin and Teschner, Jörg
String Math 2016 Paris, France, June 27-July 2, 2016, Proc. Symp. Pure Math. (2018)
eprint: 1702.06499 [hep-th]

"Toda conformal blocks, quantum groups, and flat connections"
Coman, Ioana and Pomoni, Elli and Teschner, Jörg
eprint: 1712.10225 [hep-th]

"A guide to two-dimensional conformal field theory"
Teschner, Joerg
eprint: 1708.00680 [hep-th]

"Classical conformal blocks and isomonodromic deformations"
Teschner, Joerg
eprint: 1707.07968 [hep-th]

"Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence"
Teschner, Joerg
eprint: 1707.07873 [math-ph]

"Hochschild Cohomology and the Modular Group"
Lentner, S. and Mierach, S. N. and Schweigert, C. and Sommerhaeuser, Y.
ArXiv e-prints (2017)
eprint: 1707.04032 [math.RA]

"A GNS construction of three-dimensional abelian Dijkgraaf–Witten theories"
Müller, Lukas and Schweigert, Christoph
Rev. Math. Phys. 30, 1850005 (2017)
doi: 10.1142/S0129055X18500058
eprint: 1703.05018 [math.QA]

"Quantum groups and Nichols algebras acting on conformal field theories"
Lentner, Simon D.
eprint: 1702.06431 [math.QA]

"Factorizable R-Matrices for Small Quantum Groups"
Lentner, Simon and Ohrmann, Tobias
SIGMA 13, 076 (2017)
doi: 10.3842/SIGMA.2017.076
eprint: 1612.07960 [math.QA]

"Frobenius algebras and homotopy fixed points of group actions on bicategories"
Hesse, Jan and Schweigert, Christoph and Valentino, Alessandro
Theor. Appl. Categ. 32, 652-681 (2017)
eprint: 1607.05148 [math.QA] [ link ]

"Consistent systems of correlators in non-semisimple conformal field theory"
Fuchs, Jürgen and Schweigert, Christoph
Adv. Math. 307, 598-639 (2017)
doi: 10.1016/j.aim.2016.11.020
eprint: 1604.01143 [math.QA]

"Quantisation of super Teichmüller theory"
Aghaei, Nezhla and Pawelkiewicz, Michal and Teschner, Joerg
Commun. Math. Phys. 353, 597-631 (2017)
doi: 10.1007/s00220-017-2883-0
eprint: 1512.02617 [hep-th]

"A trace for bimodule categories"
Fuchs, Jürgen and Schaumann, Gregor and Schweigert, Christoph
Appl. Categ. Struct. 25, 227-268 (2017)
doi: 10.1007/s10485-016-9425-3
eprint: 1412.6968 [math.CT]

"Line operators in theories of class S, quantized moduli space of flat connections, and Toda field theory"
Coman, Ioana and Gabella, Maxime and Teschner, Joerg
JHEP 10, 143 (2015)
doi: 10.1007/JHEP10(2015)143
eprint: 1505.05898 [hep-th]

"Bicategories for boundary conditions and for surface defects in 3-d TFT"
Fuchs, Jürgen 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]

"Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms"
Fuchs, Jürgen and Schweigert, Christoph and Stigner, Carl
J.Algebra 363, 29-72 (2012)
doi: 10.1016/j.jalgebra.2012.04.008
eprint: 1106.0210 [math.QA]

"Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I"
Teschner, J.
Adv.Theor.Math.Phys. 15, 471-564 (2011)
doi: 10.4310/ATMP.2011.v15.n2.a6
eprint: 1005.2846 [hep-th]

"Gauge Theory Loop Operators and Liouville Theory"
Drukker, Nadav and Gomis, Jaume and Okuda, Takuya and Teschner, Joerg
JHEP 1002, 057 (2010)
doi: 10.1007/JHEP02(2010)057
eprint: 0909.1105 [hep-th]

"Nonrational Conformal Field Theory"
Teschner, Jörg
New Trends in Mathematical Physics, Springer Netherlands (2009)
doi: 10.1007/978-90-481-2810-5_46
eprint: 0803.0919 [hep-th]


PhD thesis: "Non-semisimple modular tensor categories from small quantum groups"
Tobias Ohrmann
Universität Hamburg (2018)
[ link ]

PhD thesis: "Group Actions on Bicategories and Topological Quantum Field Theories"
Jan Hesse
Universität Hamburg (2017)
[ link ]

Impressum  | last modified 27 Aug 2019