Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence - INSPIRE

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Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence

Linda I. Uruchurtu
(
- Cambridge U., DAMTP
)

Nov, 2008

31 pages

Published in:

JHEP 03 (2009) 133

e-Print:

0811.2320 [hep-th]

DOI:

10.1088/1126-6708/2009/03/133

Report number:

DAMTP-2008-106

View in:

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Abstract: (arXiv)

The four-point correlation function of two 1/2 BPS primaries of conformal weight

\Delta=2

and two 1/2-BPS primaries of conformal weight

\Delta=n

is calculated in the large 't Hooft, large

N

limit. These operators are dual to Kaluza-Klein supergravity fields

s_k

with masses

m^2=-4

and

m^2=n(n-4)

. Given that the existing formalism for evaluating sums of products of SO(6) tensors that determine the effective couplings is only suitable for primaries with small conformal dimensions, we make us of an alternative formalism based on harmonic polynomials introduced by Dolan and Osborn. We then show that the supergravity lagrangian relevant to the computation is of sigma-model type (i.e., the four-derivative couplings vanish) and that the final result for the connected amplitude splits into a free and an interacting part, as expected on general grounds.

AdS/CFT correspondence
soliton: BPS
Kaluza-Klein model
n-point function: 4
supergravity
sigma model: nonlinear
duality

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