  Familiar field theories may contain closed subsectors made out of only
fermions, which can be used to explore new and unusual phases of matter in
lower dimensions. We focus on the fermionic su(1,1) sector in N=4 SYM and on
its ground states, which are Fermi surface states/operators. By computing their
spectrum to order $(g_{YM}^2 N)^2$, we argue that fluctuations around this
fermi surface, within the sector and in the limit $k_F\rightarrow\infty$, are
governed by a chiral 1+1 dimensional sector of the "strange metal" coset
$SU(N)_N \otimes SU(N)_N/SU(N)_{2N}$. On the gravity side, the conjectured dual
configuration is an $S=0$ degeneration of a rotating black hole. On general
grounds we expect that the near horizon excitations of
$(S=0,\Omega=1,J\rightarrow\infty)$ degenerations of black holes will be
governed by a chiral sector of a 1+1 CFT.
