# Orthogonal gauge theory on branes and orientifolds

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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 $O(2n)$ ?

This post imported from StackExchange Physics at 2017-07-05 16:17 (UTC), posted by SE-user user40085
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?
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.
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