Abstract
In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W 3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of W n0 for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single W 0 inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.
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ArXiv ePrint: 1411.4039
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Iles, N.J., Watts, G.M. Modular properties of characters of the W3 algebra. J. High Energ. Phys. 2016, 89 (2016). https://doi.org/10.1007/JHEP01(2016)089
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DOI: https://doi.org/10.1007/JHEP01(2016)089