Holographic Renormalzation has been a crucial element of holography (AdS/CFT correspondance) that enables us to compute physical quantities in weakly coupled gravity and to map them in strongly coupled quantum field theory. While this subject has been extensively studied more than 15 years, it brings new physical significances and surprises as the holography expands its realms. We have a chance to add something new to that trends recently by generalizing the holographic renormalization in the context of Einstein‐Maxwell‐Dilaton (EMD) theories.
Holographic renormalization has two parts that are intimately related. One is imposing consistent boundary conditions to ensure the equations of motion of the gravity theories. Another is computing physical quantities (normally infinite) and rendering them to be finite by subtracting divergent pieces. Then the resulting physical quantities can be identified with those of the quantum field theory living on the boundary of the gravity theory.
EMD theories have gravity, Maxwell, and Dilaton fields as their basic ingredients. Dilaton is a type of scalar field that arises naturally in string theory. Until now, the boundary conditions have been imposed separately for the scalar fields and the Maxwell fields, which is very natural. We observe that the dilation has an unusual coupling with the Maxwell field that describes the Electrodynamics. This unusual coupling can be exploited to find a new possibility in imposing consistent boundary conditions that mix the boundary condition between the Maxwell and scalar fields. In particular, the expectation value of the field theory scalar operator can be a function of the expectation value of the current operator (dual Maxwell field).
This investigation clarifies two interesting physical properties among other possible phenomena. One is the splitting of a conserved charge between the Maxwell field and the scalar field, Dilaton. This is related to non‐Fermi liquid properties. Another is finite boundary terms that happens in the presence of the scalar fields. There is a very interesting direct consequences. Physical quantities are not fully fixed due to the finite boundary terms. That manifests in the massless scalar or the scalar with mass saturating the so-called Breitenlohner-Freedman bound. Our examples indicate that thermodynamic properties can be completely fixed, while the expectation values of the dual field theories remain unfixed. It is further required to have input from the field theory side to fix them. There is a parallel stories in field theories. Finite radiative corrections are not completely fixed until experimental inputs are provides. This has been investigated by Roman Jackiw.
For more details, see the paper at arXiv and at the journal home page.