Lifshitz holographic renormalization from anti-de Sitter

Lifshitz space-times with critical exponent z = 2 can be obtained by dimensional reduction of Schrodinger space-times with critical exponent z = 0. The latter space-times are asymptotically anti-de Sitter (AdS) solutions of AdS gravity coupled to an axion-dilaton system (or even just a massless scalar field). This basic observation is used to perform holographic renormalization for four-dimensional asymptotically locally Lifshitz space-times by dimensional reduction of the corresponding problem of holographic renormalization for five-dimensional asymptotically AdS space-times coupled to an axion-dilaton system. In this setup the four-dimensional structure of the Lifshitz-Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be summarized.