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arXiv · 1405.3965

Generalized dilatation operator method for non-relativistic holography

Wissam Chemissany·Ioannis Papadimitriou
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Abstract

We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent $z$ and any value of the hyperscaling violation parameter $θ$ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.

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Wissam Chemissany, Ioannis Papadimitriou. 2014-08-16. Generalized dilatation operator method for non-relativistic holography. https://doi.org/10.1016/j.physletb.2014.08.057

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