Causality constraints on corrections to the graviton three-point coupling

Abstract

We consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We argue that these are constrained by causality. We devise a thought experiment involving a high energy scattering process which leads to causality violation if the graviton three-point vertex contains the additional structures. This violation cannot be fixed by adding conventional particles with spins J ≤ 2. But, it can be fixed by adding an infinite tower of extra massive particles with higher spins, J > 2. In AdS theories this implies a constraint on the conformal anomaly coefficients a−c c 1 ∆ 2 gap in terms of ∆ gap , the dimension of the lightest single trace operator with spin J > 2. For inflation, or de Sitter-like solutions, it indicates the existence of massive higher spin particles if the gravity wave non-gaussianity deviates significantly from the one computed in the Einstein theory.

One-loop effective actions and higher spins. Part II

“…Other topics, such as the discussion of the ambiguities inherent in the choice of the conserved currents in the initial matter model, will be included in a subsequent article. This is a good point to mention that our research is indebted to several preexisting works, in particular with [17][18][19] as far as the inspiration is concerned, with [20][21][22][23][24][25][26][27][28][29] as far as the methods are concerned and with [4,5,[30][31][32][33][34][35][36][37][38][39][40][41] for HS theories. Other papers of ours, related to the present one are, beside [1,42,43].…”

Analytic bootstrap at large spin

“…Recently it has been pointed out that in the context of the AdS/CFT correspondence, there is a connection between the CFT anomalous dimensions and the bulk Shapiro time delay [27][28][29][30]. In [30] it was argued that to preserve causality, the Shapiro time delay should be positive and hence the anomalous dimensions of double trace operators negative.…”

“…In [30] it was argued that to preserve causality, the Shapiro time delay should be positive and hence the anomalous dimensions of double trace operators negative. Thus it is of interest to see what happens to γ(n, ) for n > 0.…”

A microscopic description of absorption in high-energy string-brane collisions

“…The differential operator reflects the presence of higher derivative corrections to the gravitational couplings in the bosonic string [7,10]. As far as the imaginary part is concerned the derivatives generate terms suppressed by additional powers of log(α s) and we will neglect them for consistency with the approximations made in deriving eq.…”

“…10 When we have a stack of N Dp-branes, the open state carries 9 The components of the momenta are given in the following order: (t, vol, perp), where t is the time direction, vol the p-dimensional branes volume, perp the (25−p)-dimensional space transverse to the branes. 10 In terms of the string coupling constant gs and the Regge slope α this constant is given by g 2 p+1 = 2πgs(2π √ α ) p−3 . The Chan-Paton factors are normalized as Tr(λ i λ j ) = δ ij .…”