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arXiv · 1307.0773

S-duality as Fourier transform for arbitrary $\epsilon_1,\epsilon_2$

N. Nemkov
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Abstract

The AGT relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that for the four-point conformal block the modular transform up to the non-perturbative contributions can be written in form of the ordinary Fourier transform when $\beta\equiv-\epsilon_1/\epsilon_2=1$. Here we extend this conjecture to general values of $\epsilon_1,\epsilon_2$. Namely, we argue that for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters $\epsilon_1,\epsilon_2$. The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant $g^2\equiv-\epsilon_1\epsilon_2$ and hypermultiplet masses.

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N. Nemkov. 2013-07-02. S-duality as Fourier transform for arbitrary $\epsilon_1,\epsilon_2$. https://doi.org/10.1088/1751-8113/47/10/105401

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