The ideal slot theory is usually presented in terms of dipole theory, on the basis of the "Booker extension" of "Babinet's principle". The earliest reference in my notes is by Booker from 1946, "Slot aerials and their relations to complementary wire aerials."
Slots and (strip) dipoles are complementary by interchanging the electric and magnetic fields. To use the results for round dipoles for strip dipoles, use twice the diameter for the width of the strip. For horizontal polarization, the dipole will be horizontal while the slot will be vertical. For half-wavelength the impedance of the dipole is (72 +j42.5) Ohm, while the equivalent slot is (363 -j211) Ohm (i.e. the dipole is inductive longer than the resonant length, whereas the slot is capacitive). Wire dipoles have low impedance at odd half-wavelengths, while slots have low impedance at even half-wavelengths. It is possible to combine them for bandwidth improvement.
Moving the feedpoint off-center is a technique sometimes used for enhancing bandwidth. As usual, the theoretical results are based on simplifying assumptions, such as infinitely thin dipoles, sheets of infinite extent, perfect conductors, etc.
An interesting development is the use of a parasitic wire with a slot:
T. Morioka, S. Araki, K. Hirasawa
Slot antenna with parasitic element for dual band operation
Electronics Letters, vol. 33, no. 25, 4 Dec 1997, pp. 2093-2094.
Hopefully there are better web pages on the subject, but here is one: