Symmetry breaking phase transitions in the Aharony-Bergman-Jafferis- Maldacena theory with a finite U(1) chemical potential

We consider the U(1) charged sector of ABJM theory at finite temperature, which corresponds to the Reissner-Nordstrom AdS black hole in the dual type IIA supergravity description. Including back-reaction to the bulk geometry, we show that phase transitions occur to a broken phase where SU(4) R-symmetry of the field theory is broken spontaneously by the condensation of dimension one or two operators. We construct the composite operators out of fields in ABJM theory and describe the phase transition with the dual gravity solutions. We show numerically and analytically that the relevant critical exponents for the dimension one operator agree precisely with those of mean field theory in the strongly coupled regime of the large N planar limit.