Surface operators in gauge theory are analogous to Wilson and ’t Hooft
line operators except that they are supported on a two-dimensional surface
rather than a one-dimensional curve. In a previous paper, we constructed
a certain class of half-BPS surface operators in N = 4 super
Yang–Mills theory, and determined how they transform under S-duality.
Those surface operators depend on a relatively large number of freely
adjustable parameters. In the present paper, we consider the opposite
case of half-BPS surface operators that are “rigid” in the sense that they
do not depend on any parameters at all. We present some simple constructions
of rigid half-BPS surface operators and attempt to determine
how they transform under duality. This attempt is only partially successful,
suggesting that our constructions are not the whole story. The
partial match suggests interesting connections with quantization. We
discuss some possible refinements and some string theory constructions
which might lead to a more complete picture.