| Abstract: |
The modular differential equations that allow us to find rational 2d CFTs have additional solutions that do not correspond to CFT, called "quasi-characters". In the two-character case these have been classified and shown to form a linear basis for all possible admissible characters. The solutions are found to have curious properties, including that the "degeneracies" alternate in sign only up to dimension c/12, and have a fixed sign beyond that. I will review the construction and use of quasi-characters and describe recent work to prove these curious properties. This also leads to a way to estimate degeneracies in the intermediate region where the dimensions are of order c, which could have applications to normal characters as well.
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