Green Functions of N=1 SYM and Radial/Energy-Scale Relation

Details Green Functions of N=1 SYM and Radial/Energy-Scale Relation Green Functions of N=1 SYM and Radial/Energy-Scale Relation

2002-10-04

arxiv.org/abs/hep-th/0210041v2

Phys.Rev. D67 (2003) 105012

Physics

High Energy Physics

High Energy Physics - Theory

revtex4 file, 9 pages, no figs

Scientific paper

10.1103/PhysRevD.67.105012

We study counter-terms of one- and two-point Green functions of some special operators in ${\cal N}=1$ SYM from their SUGRA duals from the consideration of AdS/CFT or gauge/gravity correspondence. We consider both the Maldacena-Nunez solution and the Klebanov-Strassler-Tseytlin solution that are proposed to be SUGRA duals of ${\cal N}=1$ SYM. We obtain radial/energy-scale relation for each solution by comparing SUGRA calculations with the field theory results. Using these relations we evaluate the $\beta$-function of ${\cal N}=1$ SYM. We find that the leading order term can be accurately obtained for both solutions and the higher order terms exhibit some ambiguities. We discuss the origin of these ambiguities and conclude that more studies are needed to check whether these SUGRA solutions are exactly dual to ${\cal N}=1$ SYM.

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