Novel color superconducting phases of $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

Abstract

We revisit the large-N c phase diagram of N = 4 super Yang-Mills theory at finite R-charge density and strong coupling, by means of the AdS/CFT correspondence. We conjecture new phases that result from a black hole shedding some of its charge through the nucleation of probe color D3-branes that remain at a finite distance from the black hole when the dual field theory lives on a sphere. In the corresponding ground states the color group is partially Higgsed, so these phases can be identified as having a type of color superconductivity. The new phases would appear at intermediate values of the R-charge chemical potential and we expect them to be metastable but long-lived in the large-N c limit.

Brane nucleation instabilities in non-AdS/non-CFT

“…There seems to be no obvious instabilities in the classical gravity solution, but "color" branes, with a worldvolume parallel to the horizon, feel an effective potential that allows them to escape from the horizon to infinity at low enough temperature. Interestingly, a similar mechanism has been shown to exist even in N = 4 super Yang-Mills at finite R-charge chemical potential [67].…”

“…The overall sign of this depends on the parameters of the background, in addition to the angular momentum of the probe J ψ . 5 As was argued in [67], the magnitude of the angular momentum is given by the average angular momentum of the branes that source the background (other values are statistically suppressed). Since our backgrounds all have zero angular momentum (zero R-charge), we will set J ψ = 0.…”

“…The advantage to setting Q R = 0 is two-fold: it simplifies the equations of motion somewhat, and in Sec. 4 it will allow us to use arguments from [67] to set the probe brane angular momenta to zero. Since we also fix µ B , we are working in a mixed ensemble of fixed R-charge and baryon chemical potential.…”

“…We recall that our gravitational backgrounds are sourced by a stack of N c "color" branes as well as a density of wrapped, "baryonic" branes. Following [67,73], we will compute an effective potential for a probe brane of each type, as well as that of a D5-brane, as a function of the radial coordinate. If this potential has a global minimum outside the horizon, we interpret this as a sign of an instability -the branes want to condense outside of the black brane.…”

“…As the temperature is lowered, the disordered phase can become unstable towards the breaking of symmetries, either internal [15], spacetime [16,17], or both [18][19][20]. There is a whole zoo of ordered phases that include superfluids [15,[18][19][20][21][22], anisotropic states [23][24][25][26][27][28][29][30][31][32][33][34][35][36], striped phases , and even color superconducting phases [62][63][64][65][66][67].…”