| Summary: | Abstract We construct static vacuum localized black holes and non-uniform black strings in ten spacetime dimensions, where one of the dimension is compactified on a circle. We study the phase diagram of black objects with these boundary conditions, especially near the critical point where localized black holes and non-uniform black strings merge. Remarkably, we find that the merger happens at a cusp in the phase diagram. We verify that the critical geometry is controlled by a Ricci-flat double-cone as previously predicted. However, unlike the lower dimensional cases, we find that physical quantities approach to their critical values according to a power law plus a logarithmic correction. We extract the critical exponents and find very good agreement with the predictions from the double-cone geometry. According to holography, localized black holes and black strings are dual to thermal states of (1 + 1)-dimensional SU(N) maximal Super-Yang Mills theory compactified on a circle; we recover and extend the details of the (recently found) 1st order phase transition in this system from the gravity side.
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