The holographic dictionary is well developed for asymptotically AdS_d solutions obtained from consistent truncations of ten- or eleven-dimensional supergravity. However, many physically relevant solutions, such as bubbling geometries dual to very heavy operators, lie outside any known consistent truncation, making it difficult to compute holographic correlation functions. In this talk I will discuss an observable that is known exactly in field theory but not accesible with holographic methods, since its dual geometry does not lie within any consistent truncation. I will show how to compute a conformal anomaly of 1/2-BPS surface operators in N=4 super Yang–Mills directly from the ten-dimensional type IIB supergravity action by adding a suitable nine-dimensional counterterm. This example illustrates the need for a higher-dimensional approach to holographic renormalization applicable to general asymptotically AdS_p x M_q geometries.
