کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665425 | 1633814 | 2015 | 62 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Chiral differential operators: Formal loop group actions and associated modules
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Chiral differential operators (CDOs) are closely related to string geometry and the quantum theory of 2-dimensional Ï-models. This paper investigates two topics about CDOs on smooth manifolds. In the first half, we study how a Lie group action on a smooth manifold can be lifted to a “formal loop group action” on an algebra of CDOs; this turns out to be a condition on the equivariant first Pontrjagin class. The case of a principal bundle receives particular attention and gives rise to a type of vertex algebras of great interest. In the second half, we introduce a construction of modules over CDOs using the said “formal loop group actions” and semi-infinite cohomology. Intuitively, these modules should have a geometric meaning in terms of “formal loop spaces”. The first example we study leads to a new conceptual construction of an arbitrary algebra of CDOs. The other example, called the spinor module, may be useful for a geometric theory of the Witten genus.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 323-384
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 323-384
نویسندگان
Pokman Cheung,