Superfluidity in the AdS/CFT Correspondence

A chemical potential may be introduced into the AdS/CFT correspondence by setting the D3 branes of the construction spinning. In the field theory the fermionic modes are expected to condense as Cooper pairs, although at zero temperature the chemical potential destabilizes the scalar sector of the N=4 theory obscuring this phenomena. We show, in the case where a chemical potential is introduced for a small number of the gauge colours, that there is a metastable vacuum for the scalar fields where fermionic Cooper pairing is apparently manifest. In this vacuum the D3 branes expand non-commutatively (to balance the centrifugal force) into a D5 brane, in a mechanism analogous to Harmark and Savvidy's (M)atrix theory construction of a spinning D2 brane. We show that the D5 brane acts as a source for the RR 3-form whose UV scaling and symmetries are those of a fermion bilinear. The D5 brane rotates within the S^5 and so decays by the emission of RR fields which we interpret as the metastable vacuum decaying via higher dimension operators.