Abstract
Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-trivially deformed strongly coupled quantum field theories at large-Nc. The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The distributions are phenomenological in the sense that they do not correspond to the smearing of known probe D-brane embeddings. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the c-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the c-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.
Highlights
Introduction and summaryEnergy conditions considered in the context of general relativity are crucial ingredients in several general theorems, such as Penrose’s singularity theorem and no-go theorems for closed timelike curves or wormholes [1]
Some of our solutions violate the null energy condition (NEC) in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the c-functions proposed in the literature are monotonic
It should be noted that the distributions we use do not correspond to the smearing of known probe D-branes, so it is possible that the solutions we find are not part of string theory
Summary
Energy conditions considered in the context of general relativity are crucial ingredients in several general theorems, such as Penrose’s singularity theorem and no-go theorems for closed timelike curves or wormholes [1]. There is an interesting relation between the properties of the RG flow in field theory and the NEC in the gravity dual Under certain conditions, such as underlying Lorentz invariance and unitarity, it is possible to find quantities that measure the number of degrees of freedom and are monotonically decreasing along the RG flow as one goes from higher to lower energy scales [3,4,5,6]. These families include distributions corresponding to the backreaction of branes with the profile corresponding to probe flavor branes and (infinitely) many others Most of those solutions might not correspond to any limit of a configuration of sources existing in string theory, it is still interesting to study them as we expect them to enjoy the perks associated to supersymmetry, in particular they should be stable within the classical supergravity approximation. Let us review how each of these are determined using the gravity dual description
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