Modular properties of characters of the W3 algebra

Nicholas Iles; Gerard M T Watts

doi:10.1007/JHEP01(2016)089

Modular properties of characters of the W₃ algebra

Nicholas Iles, Gerard M T Watts

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Abstract

Abstract: In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W₃ algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of W₀ ⁿ 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 W₀ 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.

Original language	English
Article number	89
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of High Energy Physics
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1007/JHEP01(2016)089
Publication status	Published - 18 Jan 2016

Keywords

AdS-CFT Correspondence
Conformal and W Symmetry

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art%3A10.1007%2FJHEP01%282016%29089Final published version, 520 KBLicence: CC BY

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AB - Abstract: In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of W0 n 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 W0 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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KW - Conformal and W Symmetry

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JF - Journal of High Energy Physics

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Modular properties of characters of the W₃ algebra

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Keywords

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