# Orthogonal gauge theory on branes and orientifolds

Consider a stack of $n$ $D3$ branes in type IIB string theory. The gauge theory on the world-volume has gauge group $U(n)$.

Consider now a stack of $n$ $D3$ branes on top of an orientifold plane $O3^{-}$. According to, e.g. Table 1 in this paper, the gauge theory on the world-volume has gauge group $SO(2n)$. How do we know it is $SO(2n)$ and not $O(2n)$ ?

• Why would you think it could be $\mathrm{O}(2n)$? Can you name any other example with a disconnected gauge group? How would such a theory differ in practice from one where we just look at the identity connected component? – ACuriousMind Jul 3 '17 at 12:01
• For an example with $O(n)$ groups, you can look at the brane construction summarized in Table 1 of 1408.6835. More generally, in the ADHM construction for moduli space of instantons it is the full orthogonal group which always appears, as far as I know. – Antoine Jul 3 '17 at 16:05