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 $a$, $c$ charges and the overall coefficient factor ${\mathcal{C}}_T$ of the energy-momentum tensor two-point function, namely $c=\frac{1}{d-1}\ell \frac{\partial a}{\partial \ell }={\mathcal{C}}_T$, where $\ell$ is the AdS 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 Riemann tensor at most linearly.

Latex, 18 pages, comments and references added

References in corpus (12)

• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Black Holes in Higher-Derivative Gravity
• Critical Gravity in Four Dimensions
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Einsteinian cubic gravity
• Aspects of general higher-order gravities
• Holographic Heat Current as Noether Current
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities
• Holographic Studies of The Generic Massless Cubic Gravities
• C-Functions in Lovelock Gravity

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