MO theory says it's a double bond while VB theory says it's a quadruple bond. It's still controversial.

https://mappingignorance.org/2013/05/22/c2-molecule-doubly-or-quadruply-bonded/

https://en.m.wikipedia.org/wiki/Quadruple_bond

In MO theory, there are 2 pi bonds from the px and py electrons.

The s electrons and the pz electrons (z is the axis along which the carbons are) can be considered to have a sigma bond and an anti-sigma bond, but having both a bond and an anti-bond is the same as having no bond.

So the total bond order is 2.

In VB theory, they have 3 regular bonds plus a weak one.

Wikipedia also says:

"Quadruple bonds between atoms of main-group elements are unknown. Molecular orbital theory shows that there are two sets of paired electrons in the sigma system (one bonding, one antibonding), and two sets of paired electrons in a degenerate π-bonding set of orbitals. This adds up to give a bond order of 2, meaning that there exists a double bond between the two carbon atoms in a dicarbon (C2) molecule. The molecular orbital diagram of diatomic carbon would show that there are two pi bonds and no sigma bonds. However, a recent paper by S. Shaik et al. has suggested that a quadruple bond exists in diatomic carbon,[7] but this is disputed.[8]"