I think you need to ask your frame manufacturer if the dropout can handle the torque with only anti-rotation washers or if you need a torque arm. Below I derive the formula for the torque (verified, matches the values from Rohloff manual). The values for the Shimano Alfine 11 are (with 42 and 16 teeth sprockets):
Expressed as a fraction of pedal torque.
To fit an anti-rotation washer you could, as mentioned by others and myself, put a wedge in the open space. Make sure you put the wedge on the side that gets less torque. To fix the wedge it could be glued to the frame or to the dropout or to a separate washer. A good glue connection should be ok because if done right there is little force on the connection and most on the wedge internally.
How to get the amount of torque that is applied to the dropout:
Power is torque times angular velocity. Power at the pedals is thus
Power is conserved (minus some drivetrain losses which are ignored).
and thus the input torque to the hub is
and to the ground
The quotient of the angular velocities can be calculated from the
ratio of teeth counts of the sprockets. It's the inverse of the relation of the teeth counts (the more teeth in relation to the other, the slower the sprocket turns in relation to the other). There is a table for IGHratio(gear).
Now we use that
by construction and get the result
=τpedal((#teeth hub)/(#teeth pedal)(1/IGHratio(gear)-1)
# Rohloff Speedhub
#r = [0, 0.279, 0.316, 0.360, 0.409, 0.464, 0.528, 0.600, 0.682, 0.774, 0.881, 1.000, 1.135, 1.292, 1.467]
# Shimano Alfine 11
r = [0, 0.527, 0.681, 0.770, 0.878, 0.995, 1.134, 1.292, 1.462, 1.667, 1.888, 2.153]
for i in range(1,len(r)):
print(str(i) + ".\t" + str(d(i)))
And for the curious: The reason the torques are much smaller than with the Rohloff is because the gear ratios are more centered: They are between divided by 2 and multiplied by 2 for the Shimano one and between divided by 4 and times 3/2 for the Rohloff. A smaller part of the reason is that the gear range of the Rohloff one is larger overall.