TwoDimensional Nonabelian BF Theory in Lorenz Gauge as a Solvable Logarithmic TCFT
Abstract
We study twodimensional nonabelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (GromovWitten invariants). We found that the theory is exactly solvable in the sense that all correlators are given by finitedimensional convergent integrals. Surprisingly, this theory turns out to be logarithmic in the sense that there are correlators given by polylogarithms and powers of logarithms. Furthermore, we found fields with "logarithmic conformal dimension" (elements of a Jordan cell for L_{0}). We also found certain vertex operators with anomalous dimensions that depend on the nonabelian coupling constant. The shift of dimension of composite fields may be understood as arising from the dependence of subtracted singular terms on local coordinates. This generalizes the wellknown explanation of anomalous dimensions of vertex operators in the free scalar field theory.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 December 2019
 DOI:
 10.1007/s00220019036387
 arXiv:
 arXiv:1902.02738
 Bibcode:
 2019CMaPh.376..993L
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Ver. 2: Section 6.3 ("A remark on logarithmic phenomena") expanded. An expository tweak: switched to the indexfree notations throughout the text