  We investigate theoretically the transport properties of a closed
Aharonov-Bohm interferometer containing two quantum dots in the strong coupling
regime. We find two distinct physical scenarios depending on the strength of
the interdot Coulomb interaction. When the interdot Coulomb interaction is
negligible only spin fluctuations are important and each dot develops a Kondo
resonance at the Fermi level independently of the applied magnetic flux. The
transport is characterized by the interference of these two independent Kondo
resonances. On the contrary, for large interdot interaction, only one electron
can be accommodated onto the double dot system. In this situation, not only the
spin can fluctuate but also the orbital degree of freedom (the pseudo-spin). As
a result, we find different ground states depending on the value of the applied
flux. When $\phi=\pi$ (mod $2\pi$) ($\phi=2\pi\Phi/\Phi_0$, where $\Phi$ is
applied flux, and $\Phi_0=h/e$ the flux quantum) the electronic transport can
take place via simultaneous correlations in the spin and pseudo-spin sectors,
leading to the highly symmetric SU(4) Kondo state. Nevertheless, we find
situations with $\phi>0$ (mod $2\pi$) where the pseudo-spin quantum number is
not conserved during tunneling events, giving rise to the common SU(2) Kondo
state with an enhanced Kondo temperature. We investigate the crossover between
both ground states and discuss possible experimental signatures of this physics
as a function of the applied magnetic flux.
