Mathematical structures of cohomological field theories

Morphisms of Cohomological Field Theories

We introduce a notion of morphism of CohFT’s, on the basis of the analogy with A∞ morphisms, and discuss the relationship with morphisms of F -manifolds introduced by Manin and Hertling [5]. The structure maps of a morphism of CohFT’s have as input a cohomology class on the moduli space of scaled affine lines (complexified multiplihedron) studied in Ma’u-Woodward [9]. The main result is a compu...

Cohomological Field Theories with Kähler Structure

Historically the cohomological field theory first has been introduced as a twisted version of global space-time supersymmetric quantum field theory, specifically the N = 2 supersymmetric Yang-Mills theory in four dimensional space-time [1]. The global space-time supersymmetry, by definition, requires the existence of a spinor which is constant everywhere on the space-time manifold M . A spinor ...

Structures in Mathematical Theories

New mathematical structures in renormalizable quantum field theories

Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the role they can play in future developments. PACS classification: 11.10Gh 11.15Bt 11.10Jj

Noncommutative Cohomological Field Theories and Topological Aspects of Matrix models

We study topological aspects of matrix models and noncommutative cohomological field theories (N.C.CohFT). N.C.CohFT have symmetry under the arbitrary infinitesimal noncommutative parameter θ deformation. This fact implies that N.C.CohFT possess a less sensitive topological property than K-theory, but the classification of manifolds by N.C.CohFT has a possibility to give a new view point of glo...