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

2013

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

Nemkov, N.

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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 $\epsilon_1,\epsilon_2$.

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