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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

Raphaël Belliard

Tobias Ohrmann

Elli Pomoni


Former members

Aswin Balasubramanian

Maxime Gabella

Jan Hesse


Publications


Get these publications as bibtex-file


"The logarithmic Cardy case: Boundary states and annuli"
Fuchs, Jürgen and Gannon, Terry and Schaumann, Gregor and Schweigert, Christoph
eprint: 1712.01922 [math.QA]

"Orbifold Construction for Topological Field Theories"
Schweigert, C. and Woike, L.
eprint: 1705.05171 [math.QA]

"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]

"Supersymmetric field theories and geometric Langlands: The other side of the coin"
Balasubramanian, Aswin and Teschner, Joerg
String Math 2016 Paris, France, June 27-July 2, 2016 (2017)
eprint: 1702.06499 [hep-th]

"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]

"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]

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

Impressum  | last modified 23 Feb 2018