Precision holography for non-conformal branes

TL;DR

<3-5 sentence high-level summary>Kanitscheider, Skenderis, and Taylor develop a comprehensive precision holography framework for non-conformal branes preserving 16 supersymmetries. They formulate holographic renormalization in the dual frame where near-horizon geometries are conformal to $AdS_{p+2}\times S^{8-p}$ with a linear dilaton, deriving general asymptotics, counterterms, and non-linear one-point and two-point functions, all compatible with M-theory uplifts. A radial Hamiltonian formulation highlights the underlying generalized conformal structure, yielding Ward identities and anomaly structures, notably for the D4-brane. The work applies the formalism to compute condensates in Witten’s YM$_4$ model and non-extremal D1-branes, illustrating the physical content of generalized conformal holography and its connections to the M2/M5 system. This precision holography clarifies how mass, stress-energy, and operator vevs are encoded in non-AdS asymptotics and supports broader holographic explorations of non-conformal gauge theories.

Abstract

We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p \leq 4, including the case of fundamental string solutions, is conformal to AdS_{p+2} x S^{8-p} with a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropriate Dirichlet boundary conditions, find the corresponding counterterms and compute the holographic 1-point functions, all in complete generality and at the full non-linear level. The result for the stress energy tensor properly defines the notion of mass for backgrounds with such asymptotics. The analysis is done both in the original formulation of the method and also using a radial Hamiltonian analysis. The latter formulation exhibits most clearly the existence of an underlying generalized conformal structure. In the cases of Dp-branes, the corresponding dual boundary theory, the maximally supersymmetric Yang-Mills theory SYM_{p+1}, indeed exhibits the generalized conformal structure found at strong coupling. We compute the holographic 2-point functions of the stress energy tensor and gluon operator and show they satisfy the expected Ward identities and the constraints of generalized conformal structure. The holographic results are also manifestly compatible with the M-theory uplift, with the asymptotic solutions, counterterms, one and two point functions etc of the IIA F1 and D4 appropriately descending from those of M2 and M5 branes, respectively. We present a few applications including the computation of condensates in Witten's model of holographic YM_4 theory.