{"paper":{"title":"Complex eigenvalue instantons and the Fredholm determinant expansion in the Gross-Witten-Wadia model","arxiv_id":"2308.06320","primary_cat":"hep-th","submitted_at":"2023-08-11T18:00:02+00:00","version_compiled":"v3"},"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 v3","sentences":[{"i":0,"p":0.98,"id":"s0","own":true,"role":"contribution","text":"We study the leading nonperturbative corrections to the strong-coupling (ungapped) phase of the Gross-Witten-Wadia (GWW) integral over unitary matrices, to one-loop order.","hedge":{"p":0.8,"label":"asserted"},"own_p":0.92,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":1,"p":0.95,"id":"s1","own":true,"role":"method","text":"We compute these corrections directly in terms of eigenvalue tunneling in a holomorphic presentation of the integral over eigenvalues.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.95,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"The leading nonperturbative contribution to the partition function comes from a pair of complex eigenvalue instantons.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.53,"quantitative":false,"quantitative_p":0.44,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.64,"id":"s3","own":false,"role":"interpretation","text":"We show that these are in fact \"ghost instantons\", which are extrema of the one-eigenvalue effective potential on the \"unphysical sheet\" of the spectral curve and have been discussed in detail recently by Mari\\~no, Schiappa, and Schwick.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.47,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.33,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.64}},{"i":4,"p":0.67,"id":"s4","own":false,"role":"contribution","text":"Further, we discuss the relationship of these instantons to the Fredholm determinant expansion of the unitary matrix integral, which has recently become an object of interest in the computations of BPS indices of supersymmetric gauge theories and black holes.","hedge":{"p":0.53,"label":"asserted"},"own_p":0.31,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.3,"limitation":0.0,"future_work":0.0,"contribution":0.67,"interpretation":0.03}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"result","text":"We find that, after taking the 't Hooft limit, the first correction given by the Fredholm determinant expansion of the GWW integral agrees precisely with the leading nonperturbative correction, to one-loop order.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.64,"quantitative":true,"quantitative_p":0.92,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.97,"text":"We find that, after taking the 't Hooft limit, the first correction given by the Fredholm determinant expansion of the GWW integral agrees precisely with the leading nonperturbative correction, to one-loop order.","location":"abstract s5","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per 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