There is an interesting paper in arxiv by Bouchard et al., titled topological open strings on orbifold. As I believe that the readership of the this blog is varied, I need to describe briefly what is topological string.
Topological Strings
Topological string has operators which is the algebra of operators in string theory. The algebra preserves certain SUSY and this can be obtained by certain “topological” twist of the worldsheet in String Theory. These operators are associated with certain spin. This is analogous to topological field theory and hence the topological string theory (TS) do not have any degrees of freedom. There are basically two topological string theory( A-model and B-model). Also, there are only certain kinds of admissible spacetime admits the criteria for topological string theory. Strings on ordinary background are not the topological strings. A procedure known as topological twist is required. These theories have two U(1) symmetries. The R-symmetry (two U(1) symmetries) may lead to two A model and B models. This will make the theory BRST exact. Topological theory are related to Chern Simons theory and Gromov Witten invariants. Also there exist relations to mirror symmetry.
Topological String Theory on Calabi Yaus
The good thing about the topological string sector is that one can exactly calculate the amplitude and one can study the moduli spaces. Topological string amplitudes are modular object with special transformation properties under the modular group. At large radius limits topological string amplitudes are generating functions of Gromov Witten invariants. When going to orbifold points of the moduli space the amplitudes become generating functions for orbifold Gromov–Witten invariants. In this paper they try to relate the Gromov Witten invariants to orbifold to Gromov witten invariants. They extend the result by Aganagic, Bouchard and Klemm of closed strings to open strings.
