A10 – TQFT from and for 4d SUSY gauge theories
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.
Get these publications as bibtex-file
"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
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]
"Consistent systems of correlators in non-semisimple conformal field theory"
Fuchs, Jürgen and Schweigert, Christoph
Adv. Math. 307, 598-639 (2017)
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)
eprint: 1412.6968 [math.CT]
"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)
eprint: 1203.4568 [hep-th]
"Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms"
Fuchs, Jurgen and Schweigert, Christoph and Stigner, Carl
J.Algebra 363, 29-72 (2012)
eprint: 1106.0210 [math.QA]
"Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I"
Adv.Theor.Math.Phys. 15, 471-564 (2011)
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)
eprint: 0909.1105 [hep-th]
"Nonrational conformal field theory"
eprint: 0803.0919 [hep-th]