What kind of bonds can form between benzene and transition metals in π-complexes?
In theory benzene and a transition metal could form &sigma;, &pi;, &delta;, and even &phi; bonds as the symmetry allows this. 

Here are the orbitals of benzene, calculated at the PBE0/def2-TZVPP level of theory in the D6h  point group with Gamess.



The (valence) orbitals of chromium on the same level of theory in the same point group are as follows:



The linear combination of these orbitals would yield orbitals that have the above mentioned bond symmetries. We will ignore for now that they will most likely not occupied in a complex like bis(benzene)chromium.


benzene a2u + Cr s &rarr; &sigma;
benzene a2u + Cr dz² &rarr; &sigma;
benzene e1g + Cr dxz &rarr; &pi;
benzene e1g + Cr dyz &rarr; &pi;
benzene e2u + Cr dxy &rarr; &delta;
benzene e2u + Cr dx²-y² &rarr; &delta;


If we look at f-orbitals (that is of course not very feasible for chromium), we could construct another bond type: 


benzene a1g + Cr fx(x2−3y2) &rarr; &phi;


The necessary orbital looks like this:



Of course which of these bonds will form or not depends on the metal in question, the occupation of the orbitals and more. After all, there are also p orbitals which can overlap to form &sigma; and &pi; bonds.



Colour code: Occupied orbitals are shown in blue and orange, while virtual orbitals are shown in yellow and red. Phases have been assigned randomly. The total density of the molecule uses a violet contour.