# A10 – TQFT from and for 4d SUSY gauge theories

### Project Leaders

Christoph Schweigert (e-mail | group homepage)

Jörg Teschner (e-mail | group homepage)

### Abstract

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.

### Researchers

### Former members

Aswin Balasubramanian

Maxime Gabella

Jan Hesse

### Publications

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]

### Theses

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 ]