Precision holography for non-conformal branes

TL;DR

This paper develops a comprehensive holographic renormalization framework for non-conformal branes with 16 supersymmetries, enabling precise calculations of correlation functions and mass definitions in these backgrounds.

Contribution

It introduces the most general asymptotic solutions, counterterms, and holographic renormalization procedures for non-conformal branes, extending the understanding of their dual field theories.

Findings

Derived the general asymptotic solutions and counterterms for non-conformal branes.

Computed holographic 1-point and 2-point functions satisfying Ward identities.

Confirmed the compatibility of holographic results with M-theory uplifts and applications.

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.