Recursion relations in CFT and N=2 SYM theory

Details Recursion relations in CFT and N=2 SYM theory Recursion relations in CFT and N=2 SYM theory

2009-09-18

arxiv.org/abs/0909.3412v2

JHEP 0912:038,2009

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, v2: a note and a reference added, typos corrected

Scientific paper

10.1088/1126-6708/2009/12/038

Based on prototypical example of Al.Zamolodchikov's recursion relations for the four point conformal block and using recently proposed Alday-Gaiotto-Tachikawa (AGT) conjecture, recursion relations are derived for the generalized prepotential of ${\cal N}=2$ SYM with $f=0,1,2,3,4$ (anti) fundamental or an adjoint hypermultiplets. In all cases the large expectation value limit is derived explicitly. A precise relationship between generic 1-point conformal block on torus and specific 4-point conformal block on sphere is established. In view of AGT conjecture this translates into a relation between partition functions with an adjoint and 4 fundamental hypermultiplets.

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