Maria Emilia Guimaraes

"DEFORMATION OF COMPLEX STRUCTURES IN TOPOLOGICAL FIELD THEORY"

We study a Lie algebra of formal vector eldsWn with it application to the perturbative deformed
holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries
in the B-model. We show that equivalent classes of deformations are describing by a Hochschild
cohomology theory of DG-algebra A = (A;Q), Q = @ + @deform, which is dend to be the
cohomology of (􀀀1)nQ+dHoch. Here @ is the initial non-deformed BRST operator while @deform
is the deformed part whose algebra is a Lie algebra of linear vector elds gln. We discuss the
identication of the harmonic structure (HT(X);H
(X)) of ane space X and the group
Extn
X(O4;O4) (the HKR isomorphism), and bulk-boundary deformation pairing.