Mirror Symmetry for Topological Sigma Models With Generalized Kähler Geometry

Abstract

We consider topological sigma models with generalized Kähler target spaces. The mirror map is constructed explicitly for a special class of target spaces and the topological A and B model are shown to be mirror pairs in the sense that the observables, the instantons and the anomalies are mapped to each other. We also apply the construction to open topological models and show that A branes are mapped to B branes. Furthermore, we demonstrate a relation between the field strength on the brane and a two-vector on the mirror manifold.

SU(3) × SU(3) compactification and mirror duals of magnetic fluxes

“…First one notes that when B is non-trivial, Φ ± are actually not quite sections of S ± . Instead one must consider the extension E 15) defined as follows. If on the overlap of two patches U α ∩ U β the B-field is patched by…”

“…From (6.9) we see that the matrices p A I and q AI 15 Note that combinations of scalars (ξ I ,ξ I ) which is dual to the massive tensors given by (6.8) precisely drops out of the expression for P 3 as is required for consistency. Alternatively one can formulate the supergravity in a redundant form where both scalar degrees of freedom together with antisymmetric tensors are kept [62].…”

Heterotic–type IIA duality with fluxes

“…Similarly, using (A.9) again the second term in the second line of (3.25) yields the invariant tensor on the corresponding SO(2, n v − 1) space 5) where V ol(P 1 ) denotes the volume of the P 1 base of the K3-fibered Calabi-Yau manifold. In the computation of (4.4) and (4.5) we have not determined the exact numerical factors as this would require establishing a precise map between the fields on both sides.…”

The biHermitian topological sigma model

“…[12][13][14][15][16][17][18][19][20][21][22][23][24][25]. All these were somehow unsatisfactory either because they remained confined to the analysis of geometrical aspects of the sigma models or because they yielded field theories, which though interesting in their own, were not directly suitable for quantization, showed no apparent kinship with Witten's A and B models and were of limited relevance for string theory.…”