For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
for higher abelian targets
for symplectic Lie n-algebroid targets
FQFT and cohomology
Types of quantum field thories
What is called the A-model topological string is the 2-dimensional topological conformal field theory corresponding to the Calabi–Yau category called the Fukaya category of a symplectic manifold . This is is effectively the Gromov–Witten theory of .
The A-model arose in formal physics from considerations of superstring-propagation on Calabi-Yau spaces: it may be motivated by considering the vertex operator algebra of the 2dSCFT given by the supersymmetric sigma-model with target space and then deforming it such that one of the super-Virasoro generators squares to . The resulting “topologically twisted” algebra may then be read as being the BRST complex of a TCFT.
See the references on Lagrangian formulation.
On coisotropic branes in symplectic target manifolds that arise by complexification of phase spaces, the boundary path integral of the A-model computes the quantization of that phase space. For details see
The A-model was first conceived in
An early review is in
The motivation from the point of view of string theory is reviewed for instance in
A summary of these two reviews is in
around page 19 in
section 5.3 of
formalizing at least aspects of the observations in