Complex cobordism ring and conformal field theory over Z
Complex cobordism ring and conformal field theory over Z
复制标题
Z 上的复共边环和共形场论
DOI：
10.1007/bf01445226
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发表时间：
1991
影响因子：
1.4
通讯作者：
K. Ueno
中科院分区：
文献类型：
--
作者：
T. Katsura;Y. Shimizu;K. Ueno
在自由费米子的共形场论中，福克空间起着核心作用，并提供了数学的几个分支之间的联系，如Virasoro代数的表示理论，KP方程理论，代数曲线和形式群的模[BeSc，KNTY]。另一方面，弦理论引起了人们对椭圆形理论的注意，参见。[La].我们最初的动机是在（算术-几何）共形场论[KSU 1，2]的背景下系统地描述椭圆形属，从而对复配边环MU* 和玻色子Fock空间~ r，o之间的联系有了基本的理解。作为应用，我们用KP族给出了一般（乘法序列）的一个新的解释，为了使主要结果公式化，我们引入一些符号。玻色子Fock空间~ T，O是Q上的多项式环，其中t 1，t2，.参见（2.2）.第二章。我们使用符号t=（t1，t2....）简言之，并且kt=（kt 1，kt 2，.）对于k~ Z.有一个自然配对的gr. o本身（3. I），它在KP层次理论中起着重要的作用。
In conformal field theory for free fermions, the Fock space plays a central role and provides a link among several branches of mathematics such as representation theory of the Virasoro algebra, theory of KP equation, moduli of algebraic curves and formal groups [BeSc, KNTY]. On the other hand, string theory drew much attention to the theory of elliptic genera, cf.[La]. Our original motivation having been to give a systematic account of elliptic genera in the context of (arithmetico-geometric) conformal field theory [KSU1, 2], we are led to a basic understanding of the connection between the complex cobordism ring MU* and the boson Fock space~ r, o. As an application, we give a new interpretation of genera (multiplicative sequences) in terms of the KP hierarchy.To formulate the main results, let us introduce some notation. The boson Fock space~ T, O is a polynomial ring over Q in indeterminates tl, t2,..., cf.(2.2). We use the notation t=(tl, t2....) for short and also kt=(ktl, kt2,...) for k~ Z. There is a natural pairing of gr. o with itself (3. I), which plays an important role in the theory of the KP hierarchy.