2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228764In this paper we consider black p-branes on square torus. We find an indication of a cascade of Gregory-Laflamme transitions between black p-brane and (p-1)-brane. Through AdS/CFT correspondence, these transitions are related to the breakdown of the U(1) symmetry in super Yang-Mills on torus. We argue a relationship between the cascade and recent Monte-Carlo data.15 pages, 3 figures, LaTeX, v2: comments and references added, v3: minor changes and a reference addedHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext