Holographic (a,c) charges and their universal relation in d=6 from massless higher-order gravities

Abstract

Recent studies of holographic properties of massless higher-order gravities, whose linear spectrum contains only the (massless) graviton, yielded some universal relations in d=4 dimensions between the holographic a and c charges and the overall coefficient factor CT of the energy-momentum tensor two-point function, namely, c=1d-1=CT, where is the anti-de Sitter radius. The second equality was shown to be valid in all dimensions. In this paper, we establish the first equality in d=6 by examining these quantities from D=7 higher-order gravities. Consequently, the overall coefficient of the two-point function of the energy-momentum tensor is proportional to this c charge, generalizing the well-known d=4 result. We identify the relevant c charge as the coefficient of a specific combination of the three type-B anomalies. Modulo total derivatives, this combination involves the Riemann tensor at most linearly.