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Alvarez-Gaume, Luis; Kehagias, Alex; Kounnas, Costas; Lüst, Dieter; Riotto, Antonio (2016): Aspects of quadratic gravity. In: Fortschritte der Physik - Progress of Physics, Vol. 64, No. 2-3: pp. 176-189
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Abstract

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure R-2 theory is indeed ghost free. Then we point out that for flat backgrounds the pure R-2 theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-theory. We demonstrate that string theory on non-compact manifolds, like a line bundle over , may indeed lead to gravity dynamics determined by a higher curvature action. The authors discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, the physical propagating modes in some specific backgrounds are analyzed in detail. After confirming that the pure R-2 theory is indeed ghost free it is pointed out that for flat backgrounds the pure R-2 theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence there is a subtle interplay between the UV and IR properties of higher order gravity. The corresponding Newton's law for general quadratic curvature theories is calculated and it is discussed how quadratic actions may be obtained from a fundamental theory like string- or M-theory. It is demonstrated that string theory on non-compact CY3 manifolds, like a line bundle over CP2, may indeed lead to gravity dynamics determined by a higher curvature action.