Abstract
We construct analytic solutions of Einstein gravity coupled to a dilaton field with a potential given by a sum of two exponentials, by rewriting the equations of motion in terms of an integrable Toda chain. These solutions can be interpreted as domain walls interpolating between different asymptotics, and as such they can have interesting applications in holography. In some cases, we can construct a solution which interpolates between an AdS fixed point in the UV limit and a hyperscaling violating boundary in the IR region. We also find analytic black brane solutions at finite temperature. We discuss the properties of the solutions and the interpretation in terms of RG flow.
Highlights
The notion of the renormalization group has dominated our thinking about quantum field theories and statistical systems since its elaboration by K
In the spirit of “bottom-up” holography, we remark that there are some relatively simple models of gravity coupled to a scalar field, that allow for interesting examples of RG flows that can be found analytically
For the middle solution, when the dilaton increases from −∞ to ∞, the scale factor decreases from large positive values to large negative values
Summary
The notion of the renormalization group has dominated our thinking about quantum field theories and statistical systems since its elaboration by K. In the spirit of “bottom-up” holography, we remark that there are some relatively simple models of gravity coupled to a scalar field, that allow for interesting examples of RG flows that can be found analytically This is due to the fact that the Einstein equations, with the Ansatz that corresponds to domain-walls solutions, reduce to dynamical equations that are completely integrable (they can be reduced to the equations of a Toda chain). For the middle solution, when the dilaton increases from −∞ to ∞, the scale factor decreases from large positive values to large negative values This behaviour corresponds to the running coupling in an asymptotically UV free theory, so it is of interest from the point of view of possible applications in QCD.
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