The heterotic string, the tangent bundle and derived categories
The heterotic string, the tangent bundle and derived categories
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杂优势弦、切丛和派生范畴
DOI：
10.4310/atmp.1998.v2.n5.a4
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发表时间：
1998
影响因子：
1.5
通讯作者：
R. Donagi
中科院分区：
文献类型：
--
作者：
P. Aspinwall;R. Donagi
我们考虑了K3曲面上的E8 xE 8杂化弦的紧化，其中“自旋连接嵌入规范群”，以及Calabi-Yau三重X上IIA型弦（或F-理论）的对偶图像。事实证明，同样的X也作为24个点状瞬子上的杂种紧化的对偶而出现。X必然是奇性的，我们看到这个奇性允许X上的Ramond-Ramond模分裂成不同的分量，一个分量包含（杂合的对偶）切丛，而另一个分量包含点状瞬子。作为一个实际应用，我们得到的结果，紧化的K3的切丛与ADE奇性的杂合弦获得非微扰增强规范对称性，只是在相同的方式作为IIA型弦奇异K3表面。在一个更哲学的层次上，我们讨论如何自然地说，杂合弦是紧化使用的对象在派生范畴的相干层。这是必要的，以适当地扩展概念的T-对偶的杂化弦上的K3曲面。
We consider the compactification of the E8xE8 heterotic string on a K3 surface with "the spin connection embedded in the gauge group" and the dual picture in the type IIA string (or F-theory) on a Calabi-Yau threefold X. It turns out that the same X arises also as dual to a heterotic compactification on 24 point-like instantons. X is necessarily singular, and we see that this singularity allows the Ramond-Ramond moduli on X to split into distinct components, one containing the (dual of the heterotic) tangent bundle, while another component contains the point-like instantons. As a practical application we derive the result that a heterotic string compactified on the tangent bundle of a K3 with ADE singularities acquires nonperturbatively enhanced gauge symmetry in just the same fashion as a type IIA string on a singular K3 surface. On a more philosophical level we discuss how it appears to be natural to say that the heterotic string is compactified using an object in the derived category of coherent sheaves. This is necessary to properly extend the notion of T-duality to the heterotic string on a K3 surface.