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**Precision holography for non-conformal branes.**
*(English)*
Zbl 1245.81187

Summary: 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 \(AdS_{p+2} \times S^{8 - p}\) 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 D\(p\)-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.