{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/3761"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/3761","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"Affine fusion tadpoles","abstract":"Fusion dimensions are integer-valued quantities equal to the dimensions of the spaces of conformal blocks, which describe the interactions of a conformal field theory (CFT). Our focus was on the Wess-Zumino-Witten models, a particularly interesting type of CFT, whose primary fields correspond to representations of affine Lie groups. Arguably, affine fusion tadpoles are the simplest g>0 fusion dimension, having only a single incoming field and g=1. We study the symmetries of the SU(N) tadpole and Verlinde formula with the intention of finding a non-negative-integer decomposition. Such a decomposition might be indicative of a combinatorial atom for fusion. From produced tables we found that tadpole values appeared to be polynomial in the level k. Several conjectures were made and we sketch a method obtaining general forms of SU(N) tadpoles via dominant weight sums.","abstract_html":"Fusion dimensions are integer-valued quantities equal to the dimensions of the spaces of conformal blocks, which describe the interactions of a conformal field theory (CFT). Our focus was on the Wess-Zumino-Witten models, a particularly interesting type of CFT, whose primary fields correspond to representations of affine Lie groups. Arguably, affine fusion tadpoles are the simplest g>0 fusion dimension, having only a single incoming field and g=1. We study the symmetries of the SU(N) tadpole and Verlinde formula with the intention of finding a non-negative-integer decomposition. Such a decomposition might be indicative of a combinatorial atom for fusion. From produced tables we found that tadpole values appeared to be polynomial in the level k. Several conjectures were made and we sketch a method obtaining general forms of SU(N) tadpoles via dominant weight sums.","abstract_has_math":false,"creators":["Urichuk, Andrew","University of Lethbridge. Faculty of Arts and Science"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-27T20:02:32Z","subjects":["physics","Verlinde formula","conformal blocks","combinatorial","combinatorics","tadpole","affine","conformal field theory (CFT)","fusion product","Wess-Zumino-Witten (WZW) models","group","partial sums","Weyl","Galois","tensor product"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/3761"],"render_values":[{"text":"hdl:10133/3761","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["physics","Verlinde formula","conformal blocks","combinatorial","combinatorics","tadpole","affine","conformal field theory (CFT)","fusion product","Wess-Zumino-Witten (WZW) models","group","partial sums","Weyl","Galois","tensor product"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/3761"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Fusion dimensions are integer-valued quantities equal to the dimensions of the spaces of conformal blocks, which describe the interactions of a conformal field theory (CFT). Our focus was on the Wess-Zumino-Witten models, a particularly interesting type of CFT, whose primary fields correspond to representations of affine Lie groups. Arguably, affine fusion tadpoles are the simplest g>0 fusion dimension, having only a single incoming field and g=1. We study the symmetries of the SU(N) tadpole and Verlinde formula with the intention of finding a non-negative-integer decomposition. Such a decomposition might be indicative of a combinatorial atom for fusion. From produced tables we found that tadpole values appeared to be polynomial in the level k. Several conjectures were made and we sketch a method obtaining general forms of SU(N) tadpoles via dominant weight sums."]},{"key":"dc:title","label":"Title","values":["Affine fusion tadpoles"]}]}],"canonical_facts":{"dc:date.issued":["2015"],"dc:description.other":["Fusion dimensions are integer-valued quantities equal to the dimensions of the spaces of conformal blocks, which describe the interactions of a conformal field theory (CFT). Our focus was on the Wess-Zumino-Witten models, a particularly interesting type of CFT, whose primary fields correspond to representations of affine Lie groups. Arguably, affine fusion tadpoles are the simplest g>0 fusion dimension, having only a single incoming field and g=1. We study the symmetries of the SU(N) tadpole and Verlinde formula with the intention of finding a non-negative-integer decomposition. Such a decomposition might be indicative of a combinatorial atom for fusion. From produced tables we found that tadpole values appeared to be polynomial in the level k. Several conjectures were made and we sketch a method obtaining general forms of SU(N) tadpoles via dominant weight sums."],"dc:identifier":["hdl:10133/3761"],"dc:subject":["physics","Verlinde formula","conformal blocks","combinatorial","combinatorics","tadpole","affine","conformal field theory (CFT)","fusion product","Wess-Zumino-Witten (WZW) models","group","partial sums","Weyl","Galois","tensor product"],"dc:title":["Affine fusion tadpoles"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:32Z"}