World-volume effective actions of exotic five-branes

We construct world-volume effective actions of exotic 5 2 2 $$ {5}_2^2 $$ -branes in type IIA and IIB string theories. The effective actions are given in fully space-time covariant forms with two Killing vectors associated with background isometries. The effective theories are governed by the six-dimensional N $$ \mathcal{N} $$ = (2, 0) tensor multiplet and N $$ \mathcal{N} $$ = (1, 1) vector multiplet, respectively. Performing the S-duality transformation to the 5 2 2 $$ {5}_2^2 $$ -brane effective action in type IIB string theory, we also work out the world-volume action of the 5 3 2 $$ {5}_3^2 $$ -brane. We discuss some additional issues relevant to the exotic five-branes in type I and heterotic string theories