{"paper":{"title":"Exact $\\nabla^4 R^4$ couplings and helicity supertraces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Boris Pioline, Guillaume Bossard","submitted_at":"2016-10-21T07:46:57Z","abstract_excerpt":"In type II string theory compactified on a $d$-dimensional torus $T^d$ down to $D=10-d$ dimensions, the $R^4$ and $\\nabla^4 R^4$ four-graviton couplings are known exactly, for all values of the moduli, in terms of certain Eisenstein series of the U-duality group $E_{d}(\\mathbb{Z})$. In the limit where one circle in the torus becomes large, these couplings are expected to reduce to their counterpart in dimension $D+1$, plus threshold effects and exponentially suppressed corrections corresponding to BPS black holes in dimension $D+1$ whose worldline winds around the circle. By combining the weak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06693","kind":"arxiv","version":1},"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"}