  Orbital angular momentum (OAM) light possesses in addition to its usual
helicity ($s=\pm \hbar$, depending on its circular polarization) an orbital
angular momentum $l$. This means that in principle one can transfer more than a
single quantum of $\hbar$ during an optical transition from light to a quantum
system. However, quantum objects are usually so small (typically in the nm
range) that they only locally probe the dipolar character of the local electric
field. In order to sense the complete macroscopic electric field, we utilize
Rydberg excitons in the semiconductor cuprite ($\text{Cu}_2\text{O}$), which
are single quantum objects of up to $\mu m$ size. Their interaction with
focused OAM light, allows for matching the focal spot size and the wavefunction
diameter. Here, the common dipole selection rules ($\Delta j=\pm 1$) should be
broken, and transitions of higher $\Delta j$ with higher order OAM states
should become more probable. Based on group theory, we analyze in detail the
optical selection rules governing this process. Then we are able to predict
what kind of new exciton transitions (quantum number $n$ and $l_{\text{exc}}$)
one would expect in absorption spectroscopy on $\text{Cu}_2\text{O}$ using
different kinds of OAM light.
