Novel color superconductivity from holography

The nature of dense matter is one of the greatest mysteries in high energy physics. For example, we do not know how QCD matter behaves in neutron star densities as there the matter is strongly coupled. Thus auxiliary methods have to be applied. One of these methods is the AdS/CFT-correspondence. This maps the strongly coupled field theory to weakly coupled gravity theory. The most well known example of this correspondence is the duality between N = 4 Super Yang-Mills and type IIB supergravity in AdS 5 × S 5 . This duality at finite temperature and chemical potential is the one we invoke in our study. It has been hypothesized that the dense matter would be in a color superconducting phase, where pairs of quarks form a condensate. This has natural interpretation in the gravity theory. The AdS 5 × S 5 geometry is sourced by stack of N coincident D3-branes. This N corresponds to the gauge group SU (N ) of N = 4 SYM. Then to study spontaneous breaking of this gauge group, one studies systems where D3-branes have separated from the stack. In this work we present two methods of studying the possibility of separating these branes from the stack. First we present an effective potential for a probe brane, which covers the dynamics of a single D3-brane in the bulk. We do this by using the action principle. Then we construct an effective potential for a shell constructed from multiple branes. We do this by using the Israel junction conditions. Single brane in the bulk corresponds to SU (N ) → SU (N − 1) × U (1) symmetry breaking and a shell of k-branes corresponds to SU (N ) → SU (N − k) × U (1) k symmetry breaking. Similar spontaneous breaking of the gauge group happens in QCD when we transition to a CSC-phase and hence these phases are called color superconducting. We find that for sufficiently high chemical potential the system is susceptible to single brane nucleation. The phase with higher breaking of the gauge group, which corresponds to having shell made out of branes in the bulk, is metastable. This implies that we were able to construct CSC-phases of N = 4 SYM, however, the exact details of the phase diagram structure is left for future research