1307.0773 (N. Nemkov)

S-duality as Fourier transform for arbitrary $\e_1,\e_2$    [PDF]

N. Nemkov

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 $\be\equiv-\e_1/\e_2=1$. Here we extend this conjecture to general values of $\e_1,\e_2$. 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 $\e_1,\e_2$. The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant $g^2\equiv-\e_1\e_2$ and hypermultiplet masses.

View original: http://arxiv.org/abs/1307.0773