Cohomology of elementary states in twistor conformal field theory

✍ Scribed by Robin Horan; Stephen Huggett

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 803 KB
• Volume: 14
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00127969

✦ Synopsis

In Twistor Conformal Field Theory the Riemann surfaces and holomorphic functions of two-dimensional conformal field theory are replaced by flat" twistor spaces (arising from conformally-flat four-manifolds) and elements of the holomorphic first cohomology. The analogue of a Laurent Series is the expansion of a cohomology element in "elementary states" and we calculate the dimension of the space of these states for twistor spaces of compact hyperbolic manifolds. Our method follows the strategy used in the classical problem of calculating the number of meromorphic functions with prescribed poles on a Riemann surface. We express the problem globally (in terms of the cohomology of a blown-up twistor space), calculate the holomorphic Euler characteristic of this blown-up space, and then use some vanishing theorems to isolate the first cohomology term.