{"paper":{"title":"Geometries of Quantum Field Theories","arxiv_id":"2609.28210","primary_cat":"hep-th","submitted_at":"2026-09-23T14:46:51+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.99,"id":"s0","own":false,"role":"background","text":"This is an English translation of a book originally published in Japanese by Saiensu-sha in 2015.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.09,"main_claim_p":0.01,"quantitative":true,"quantitative_p":0.76,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.99,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":1,"p":0.52,"id":"s1","own":false,"role":"background","text":"The book is an introduction to the 3d-3d correspondence, the relation between 3d $\\mathcal{N}=2$ supersymmetric gauge theories and the geometry of 3-manifolds, which arises from the compactification of the 6d $\\mathcal{N}=(2,0)$ theory.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.52,"limitation":0.0,"future_work":0.0,"contribution":0.48,"interpretation":0.0}},{"i":2,"p":0.93,"id":"s2","own":true,"role":"method","text":"The presentation is bottom-up rather than top-down: instead of starting from the 6d theory, we begin by asking what a quantum field theory is, and let the geometry emerge on its own.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.5,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.33,"role_probabilities":{"gap":0.0,"method":0.93,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":3,"p":0.93,"id":"s3","own":false,"role":"contribution","text":"Along the way we discuss renormalization and low-energy effective theories, gauging as an operation which glues field theories together, the resulting $Sp(2n, \\mathbb{Z})$-action on 3d theories, 3d $\\mathcal{N}=2$ supersymmetric theories and their dualities, the squashed three-sphere partition function and supersymmetric localization, duality domain walls of 4d $\\mathcal{N}=2$ theories, quantum Teichmuller theory, complex Chern-Simons theory and the quantization of the moduli space of flat $SL(2, \\mathbb{C})$-connections on 3-manifolds, with quantum dilogarithm functions as a recurring thread.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.21,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.34,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.93,"interpretation":0.0}},{"i":4,"p":0.58,"id":"s4","own":false,"role":"contribution","text":"The emphasis throughout is on geometric and algebraic structures which are invisible in a single field theory, and appear only in the theory space of quantum field theories.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.31,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.01,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.58,"interpretation":0.36}},{"i":5,"p":0.68,"id":"s5","own":false,"role":"contribution","text":"Appendices summarize supersymmetry in various dimensions, classical and quantum dilogarithm functions, and cluster algebras.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.35,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.23,"result":0.0,"background":0.08,"limitation":0.0,"future_work":0.0,"contribution":0.68,"interpretation":0.0}},{"i":6,"p":0.7,"id":"s6","own":false,"role":"contribution","text":"Exercises with difficulty ratings are included in each 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