2013/01/28 by Koushik Balasubramanian, Balasubramanian, Koushik · 1 citation
Engineering · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1301.6653
openalex publication_date 2013/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we propose gravity duals for 3+1 dimensional Lorentz invariant theories exhibiting discrete scale invariance. We construct non-singular solutions of a six dimensional gravitational theory that are warped products of AdS5 and a circle. The presence of non-trivial warp factor explicitly breaks the symmetries of AdS5 to discrete scale invariance and also breaks translation symmetry along the circle. The matter content of the 6D gravitational theory does not violate the null energy condition. In addition, we show that the linearized fluctuations around these 6D backgrounds are stable i.e., the fluctuations do not violate the Breitenlohner-Freedman stability criterion. The dual theories display periodic RG trajectories, but these RG flows do not violate the a-theorem. In particular, the dual field theory is not a soft deformation (deformation by marginal or relevant operators) of a 3+1 dimensional conformal field theory and hence the a-theorem and similar monotonicity constraints on RG flows do not apply to these examples. The holographic c-theorem also does not apply to these solutions. Finally, we present solutions of type II supergravity that exhibit discrete scale invariance to demonstrate that such solutions can be embedded in string theory.