Gerbes of chiral differential operators. II

By V. Gorbounov, F. Malikov, V. Schechtman. 2000

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The aim of this paper is a study of certain class of chiral (vertex) algebras which we call chiral algebras of differential operators. I.0. To explain this notion, let us take up a ”naive” approach to vertex algebras. Let us fix (in this Introduction) a ground field k of characteristic 0. Recall (cf. [K]) that a Z≥0-graded vertex algebra is a Z≥0-graded k-vector space V = ⊕i≥0 Vi equipped with a distinguished vacuum vector 1 ∈ V0 and a family of bilinear operations (n) : V ⊗k V −→ V, x⊗ y 7→ x(n)y, (n ∈ Z), the operation (n) having the degree −n − 1, that is, Vi(n)Vj ⊂ Vi+j−n−1 where by definition Vi = 0 for i < 0. These operations must satisfy a family of quadratic Borcherds identities. Throughout this paper we shall deal only with Z≥0graded vertex algebras, so we shall omit the words ”Z≥0-graded” when speaking about them. Note that in particular the operation (−1) has degree 0. It is neither commutative nor associative in general.

Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics

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In Mathematical Physics

  1. G. Moore
  2. E. Witten
  3. A. Kapustin
  4. Yukinobu Toda
  5. T. Bridgeland
  6. P. Aspinwall
  7. Michael R Douglas
  8. G. Segal

In Numerical Analysis

  1. E. Witten

In Statistical and Nonlinear Physics

  1. E. Witten
  2. G. Moore
  3. A. Kapustin
  4. Michael R Douglas
  5. P. Aspinwall
  6. Balázs Szendrői
  7. G. Segal
  8. T. Bridgeland

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