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arXiv 0801.1160hep-thmath.DG
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具有通量的拓扑A-型模型

Topological A-Type Models with Flux

Vid Stojevic

摘要:

我们研究变形的A-模型中存在的通量,我们的意思是秩三张量反对称的上/下指标,使用AKSZ建设。一般来说,这些都是拓扑膜模型,我们表明,通量有关的柯朗括号概括扭曲由一个封闭的3-从$H$的变形,在这个意义上说,满足AKSZ主方程意味着一个几乎广义复杂的结构相对于变形柯朗括号的可积性条件。此外,主方程对推广$dH=0$的通量施加条件。膜模型可以定义在一个大类的$U(m)$ -和$U(m) \times U(m)$ -结构流形,包括几何形状的启发$(1,1)$超对称$σ$ -模型与额外的超对称性,由于几乎复杂的(但不一定是复杂的)结构在目标空间。此外,我们表明,该模型可以定义在三个特定的半平坦流形有关的岩泽流形。当只开启$H$ -通量时,就有可能得到一个拓扑弦模型,我们对开启了闭3-形式的卡-丘情形也是这样做的。A-模型的最简单变形是由于非平凡$b$ -场的$(2,0)+ (0,2)$分量。该模型一般不再评估全纯映射,并定义了新的拓扑不变量。由于$H$ -通量导致的变形可能更彻底,完全阻止辅助场被积分出来。

英文摘要:

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from $H$, in the sense that satisfying the AKSZ master equation implies the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize $dH=0$. The membrane model can be defined on a large class of $U(m)$- and $U(m) \times U(m)$-structure manifolds, including geometries inspired by $(1,1)$ supersymmetric $σ$-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. Furthermore, we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only $H$-flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau with a closed 3-form turned on. The simplest deformation from the A-model is due to the $(2,0)+ (0,2)$ component of a non-trivial $b$-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to $H$-flux can be more radical, completely preventing auxiliary fields from being integrated out.

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