Higher dimensional holography

TL;DR

This paper develops a higher-dimensional holographic renormalization method by calculating the on-shell action of bubbling solutions in Type IIB supergravity, successfully reproducing the surface operator anomaly in N=4 super Yang-Mills.

Contribution

It introduces a higher-dimensional holographic renormalization approach applicable to complex geometries beyond uplifted AdS solutions, demonstrated through bubbling solutions for surface operators.

Findings

Reproduces the surface operator Euler conformal anomaly holographically.

Highlights the necessity of higher-dimensional holographic renormalization.

Provides a method for intrinsic supergravity solutions not arising from lower-dimensional uplifts.

Abstract

The holographic dictionary is well developed for gravity in asymptotically anti de Sitter $A(AdS_{d+1})$ spacetimes. However, this approach is limited, since many physically relevant configurations, such as bubbling geometries dual to heavy operators, do not arise as an uplift of a lower dimensional $A(AdS_{d+1})$ solution. Instead, they are intrinsic solutions of ten- or eleven-dimensional supergravity. In this work, we address this problem by evaluating the on-shell Type IIB supergravity action, with a suitable boundary counterterm, on the bubbling solutions describing half-BPS surface operators in $\mathcal{N}=4$ super Yang-Mills. This calculation exactly reproduces the surface operator Euler conformal anomaly, an observable known exactly in the field theory but previously inaccessible holographically. This example illustrates the need for a higher-dimensional approach to holographic renormalization applicable to general asymptotically $AdS_{d+1} \times M_q$ geometries.