nLab full field algebra

Idea

Where a vertex operator algebra encodes one chiral half of a 2d CFT, a full field algebra combines two vertex operator algebras to produce a genuine 2d CFT defined on the complex plane (i.e. on genus 0, notice that to define it on all genera one needs still more information, see at FRS-theorem).

Related concepts

• chiral algebra

References

• Yi-Zhi Huang, Liang Kong, Full field algebras, Commun. Math. Phys. 272 (2007) 345-396 [arXiv:0511328, doi:10.1007/s00220-007-0224-4]

• Liang Kong, Full field algebras, operads and tensor categories, Adv. Math.213:271-340, 2007 [arXiv:0603065, doi:10.1016/j.aim.2006.12.007]

Survey and review includes

• Liang Kong, Conformal field theory and a new geometry, in Hisham Sati, Urs Schreiber (eds.), Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics 83, AMS (2011) [arXiv:1107.3649, ISBN:978-0-8218-5195-1]