{"paper":{"title":"S-duality as Fourier transform for arbitrary $\\epsilon_1,\\epsilon_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"N.Nemkov","submitted_at":"2013-07-02T17:41:13Z","abstract_excerpt":"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,\\ep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0773","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}