论文标题
T偶尔和异国情调的De Rham复合物
T-duality and the exotic chiral de Rham complex
论文作者
论文摘要
让$ z $成为基本歧管$ m $上的主要圆形捆绑包，配备了一个积分封闭的$ 3 $ -form $ h $，称为The Flux。令$ \ wideHat {z} $为$ m $的t二圆捆绑包，带有flux $ \ widehat {h} $。 Han和Mathai最近构建了$ \ Mathbb {Z} _2 $ - 偏差的空间$ \ MATHCAL {a}^{\ bar {k}}}（\ wideHat {z}）$。它具有额外的$ \ mathbb {z} $ - 对零的分级进行分级，使得与不变的扭曲差异形式的空间$ω^{\ bar {k}}（\ wideHat {z}，\ wideHat {z}，\ wideHat {h} {h} {h}）扭曲的微分$ d _ {\ wideHat {h}} = d + \ wideHat {h} $。 t偶型同构$ω^{\ bar {k}}（z，h）^{\ Mathbb {t}} \ rightArrowω^{\ overline {k+1}}}}（\ wideHat {z} Bouwknegt，Evslin和Mathai延伸到同构$ω^{\ bar {k}}}（z，h）\ rightArrow \ Mathcal \ Mathcal {a}^{\ edimalline {k+1}}}（\ wideHat {z}）$。在本文中，我们介绍了异国情调的手性de rham复合物$ \ Mathcal {a}^{\ text {ch}，\ widehat {h}，\ bar {k}}}（\ wideHat {z} $，其中包含$ \ \ nathcal {a}^a}^a} \ bar} {零子复合。我们给出同构$ω^{\ text {ch}，h，h，\ bar {k}}（z）\ rightarrow \ rightarrow \ mathcal {a}^{\ text {ch}，\ wideHat {hat {h} $ω^{\ text {ch}，h，\ bar {k}}}（z）$表示$ z $的扭曲手性rham复合物，它授课上述T-二维图。
Let $Z$ be a principal circle bundle over a base manifold $M$ equipped with an integral closed $3$-form $H$ called the flux. Let $\widehat{Z}$ be the T-dual circle bundle over $M$ with flux $\widehat{H}$. Han and Mathai recently constructed the $\mathbb{Z}_2$-graded space of exotic differential forms $\mathcal{A}^{\bar{k}}(\widehat{Z})$. It has an additional $\mathbb{Z}$-grading such that the degree zero component coincides with the space of invariant twisted differential forms $Ω^{\bar{k}}(\widehat{Z}, \widehat{H})^{\widehat{\mathbb{T}}}$, and it admits a differential that extends the twisted differential $d_{\widehat{H}} = d + \widehat{H}$. The T-duality isomorphism $Ω^{\bar{k}}(Z,H)^{\mathbb{T}} \rightarrow Ω^{\overline{k+1}}(\widehat{Z}, \widehat{H})^{\widehat{\mathbb{T}}}$ of Bouwknegt, Evslin and Mathai extends to an isomorphism $Ω^{\bar{k}}(Z,H) \rightarrow \mathcal{A}^{\overline{k+1}}(\widehat{Z})$. In this paper, we introduce the exotic chiral de Rham complex $\mathcal{A}^{\text{ch},\widehat{H},\bar{k}}(\widehat{Z})$ which contains $\mathcal{A}^{\bar{k}}(\widehat{Z})$ as the weight zero subcomplex. We give an isomorphism $Ω^{\text{ch},H,\bar{k}}(Z) \rightarrow \mathcal{A}^{\text{ch},\widehat{H},\overline{k+1}}(\widehat{Z})$ where $Ω^{\text{ch},H,\bar{k}}(Z)$ denotes the twisted chiral de Rham complex of $Z$, which chiralizes the above T-duality map.
