# Horowitz-Myers conjecture Horowitz and Myers conjectured that the lowest-energy [[0231 Bulk solutions for CFTs on non-trivial geometries|bulk solution]] dual to CFTs on a $T^p\times R$ is the [[0567 AdS soliton|AdS soliton]]:$d s^{2}=\frac{r^{2}}{l^{2}}\left[\left(1-\frac{r_{0}^{p+1}}{r^{p+1}}\right) d \tau^{2}+\left(d x^{i}\right)^{2}-d t^{2}\right]+\left(1-\frac{r_{0}^{p+1}}{r^{p+1}}\right)^{-1} \frac{l^{2}}{r^{2}} d r^{2},$where $i=1,...,p-1$. It is interesting that this solution has lower energy than the Poincare AdS metric (with periodic identifications in the $i$-directions, which would be the first thing to guess for the ground state given that it has the most symmetry. ## Refs - original work: [[1998#Horowitz, Myers]] - proof: [[2024#Brendle, Hung]] ## Implications - no state-operator map for states on a torus: [[2018#Belin, de Boer, Kruthoff]]