Runkel, Ingo; Szegedy, LorantIST Austria
Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.
Communications in Mathematical Physics
The authors thank Yuki Arano, Nils Carqueville, Alexei Davydov, Reiner Lauterbach, Pau Enrique Moliner, Chris Heunen, André Henriques, Ehud Meir, Catherine Meusburger, Gregor Schaumann, Richard Szabo and Stefan Wagner for helpful discussions and comments. We also thank the referees for their detailed comments which significantly improved the exposition of this paper. LS is supported by the DFG Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. Open access funding provided by Institute of Science and Technology (IST Austria).
Runkel I, Szegedy L. Area-dependent quantum field theory. Communications in Mathematical Physics. 2021;381(1):83–117. doi:10.1007/s00220-020-03902-1
Runkel, I., & Szegedy, L. (2021). Area-dependent quantum field theory. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03902-1
Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-020-03902-1.
I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” Communications in Mathematical Physics, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021.
Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications in Mathematical Physics. 381(1), 83–117.
Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” Communications in Mathematical Physics, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117, doi:10.1007/s00220-020-03902-1.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
2021_CommMathPhys_Runkel.pdf 790.53 KB