Chiral algebras

Contents......Page 1
Introduction......Page 3
1.1. Pseudo-tensor categories......Page 13
1.2. Complements......Page 20
1.3. Compound tensor categories......Page 26
1.4. Rudiments of compound geometry......Page 34
2.1. D-modules: Recollections and notation......Page 55
2.2. The compound tensor structure......Page 69
2.3. D_X-schemes......Page 81
2.4. The spaces of horizontal sections......Page 91
2.5. Lie* algebras and algebroids......Page 97
2.6. Coisson algebras......Page 115
2.7. The Tate extension......Page 119
2.8. Tate structures and characteristic classes......Page 131
2.9. The Harish-Chandra setting and the setting of c-stacks......Page 145
3.1. Chiral operations......Page 159
3.2. Relation to "classical" operations......Page 165
3.3. Chiral algebras and modules......Page 166
3.4. Factorization......Page 174
3.5. Operator product expansions......Page 196
3.6. From chiral algebras to associative algebras......Page 202
3.7. From Lie* algebras to chiral algebras......Page 214
3.8. BRST, alias semi-infinite, homology......Page 229
3.9. Chiral differential operators......Page 240
3.10. Lattice chiral algebras and chiral monoids......Page 259
4.1. The cookware......Page 277
4.2. The construction and first properties......Page 298
4.3. The BV structure and products......Page 315
4.4. Correlators and coinvariants......Page 327
4.5. Rigidity and flat projective connections......Page 232
4.6. The case of commutative D_X algebras......Page 343
4.7. Chiral homology of the de Rham-Chevalley algebras......Page 349
4.8. Chiral homology of chiral envelopes......Page 355
4.9. Chiral homology of lattice chiral algebras......Page 359
Bibliography......Page 365
Index and Notation......Page 371