c-functions in higher-derivative flows across dimensions
Evan Deddo (Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, 48109, USA); James Liu (Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, 48109, USA); Leopoldo Pando Zayas (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA, Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, 48109, USA, The Abdus Salam International Centre for Theoretical Physics, Trieste, 34014, Italy); Robert Saskowski (Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, 48109, USA)
In the context of gravitational theories describing renormalization group flows across dimensions via AdS/CFT, we study the role of higher-derivative corrections to Einstein gravity. We use the Null Energy Condition to derive monotonicity properties of candidate holographic central charges formed by combinations of metric functions. We also implement an entropic approach to the characterization of the four-derivative flows using the Jacobson-Myers functional and demonstrate, under reasonable conditions, monotonicity of certain terms in the entanglement entropy via the appropriate generalization of the Ryu-Takayanagi prescription. In particular, we show that any flow from a higher dimensional theory to a holographic CFT2 satisfies a type of monotonicity. We also uncover direct relations between NEC-motivated and entropic central charges.
