Abstract
We calculate graviton $n$-point functions in an anti-de Sitter black brane background for effective gravity theories whose linearized equations of motion have at most two time derivatives. We compare the $n$-point functions in Einstein gravity to those in theories whose leading correction is quadratic in the Riemann tensor. The comparison is made for any number of gravitons and for all physical graviton modes in a kinematic region for which the leading correction can significantly modify the Einstein result. We find that the $n$-point functions of Einstein gravity depend on at most a single angle, whereas those of the corrected theories may depend on two angles. For the four-point functions, Einstein gravity exhibits linear dependence on the Mandelstam variable $s$ versus a quadratic dependence on $s$ for the corrected theory.
Highlights
1.1 Motivation and ObjectivesThe gauge–gravity duality [1, 2, 3, 4] can be used to relate properties of a strongly coupled fluid to those of a weakly coupled theory of anti-de Sitter (AdS) gravity [5]
A vast literature is devoted to using graviton and other two-point functions as a means for calculating the two-point correlations of various operators in the gauge theory; see, [6, 7]
It is only necessary to include the contribution from the Riemann-tensor-squared term of LGB since it already contains all physical information about the scattering of four tensor modes [24]
Summary
The gauge–gravity duality [1, 2, 3, 4] can be used to relate properties of a strongly coupled fluid to those of a weakly coupled theory of anti-de Sitter (AdS) gravity [5] (and references therein). The present treatment broadens the scope to graviton n-point functions for arbitrary n This is meant as preparation for using the corresponding multi-point correlation functions of the gauge-theory stress tensor as a probe of the gravitational dual of the quark–gluon plasma. This plasma is produced in heavy-ion collisions and, so, of direct observational relevance [11]. The latter further constrains the form of the interaction terms and limits them to a small finite number for each spacetime dimensionality This implies that the effective theory of perturbations is of the “Lovelock class” of gravitational models, as defined in detail below. For the 4-point functions, the distinction is expressed through a quadratic dependence on the Mandelstam variable s for the Gauss–Bonnet theory versus a linear dependence on s for Einstein’s
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