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AdS/CFT four-point functions: how to succeed at $$z$$-integrals without really trying. (English) Zbl 0958.81143
Summary: A new method is discussed which vastly simplifies one of the two integrals over $$\text{AdS}_{d+1}$$ required to compute exchange graphs for four-point functions of scalars in the AdS/CFT correspondence. The explicit form of the bulk-to-bulk propagator is not required. Previous results for scalar, gauge boson and graviton exchange are reproduced, and new results are given for massive vectors. It is found that precisely for the cases that occur in the $$\text{AdS}_5\times S^5$$ compactification of type IIB supergravity, the exchange diagrams reduce to a finite sum of graphs with quartic scalar vertices. The analogous integrals in $$n$$-point scalar diagrams for $$n>4$$ are also evaluated.

MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E30 String and superstring theories in gravitational theory
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