Holographic c-theorems in arbitrary dimensions

Abstract

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte

Scale invariance, conformality, and generalized free fields

“…[20]), and it appears that new ideas are needed in that case also. In holographic theories in both even and odd dimensions, there is a unified understanding of c-theorems defined using entanglement entropy [21][22][23][24][25][26]. These are only partially understood from the purely field theory perspective, and further work along these lines may shed light on the relation between scale and conformal invariance as well.…”

Twist operators in higher dimensions

“…comes from the geometric approach to the replica trick, where one first analytically continues the background geometry to non-integer n [61] -see also the discussion in [62]. 24 It is interesting that eq.…”

An effective theory for holographic RG flows

“…A fairly complete analysis is possible for 2d QFTs, but in general dimensions more involved computations are required. In a 'slow-flow' limit where one can neglect mixing with AdS gravity, the leading low-energy τ action can still be determined in general d. We assume that the bulk dynamics satisfy the null energy condition (NEC), which implies holographic [16] c or a theorems [17,18], in two or higher dimensions, respectively.…”

“…We have provided a holographic derivation of the Wess-Zumino action for τ , reproducing the anomaly matching coefficient. Note that the monotonicity of the c-function along the RG flow follows from the null energy condition (NEC) of the bulk action [16]. Indeed, to satisfying the NEC, we must demand H(r) to be a monotonic decreasing function along the radial direction, H(r) < 0, so that…”