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T双対不変な弦の有効理論―計量亜代数に基づく構成と真空解―

三浦 滉平 東北大学

2022.03.25

概要

弦理論の背景時空はT双対性と呼ばれる特徴を持ち,そのT双対性を用いて弦理論の背景場の幾何学的な性質が調べられている.一方で,弦理論の有効理論として知られる超重力理論はT双対性に対して共変ではない.そこで,超重力理論をT双対性に対して共変な形に拡張したのが,二重場理論(DFT)である.

しかし,従来の標準的な二重場理論は,Buscher則によって与えられる最も単純なT双対性に対してのみ共変であり,より一般的なT双対性である非アーベル的T双対性やPoisson-LieT双対性に対しては共変ではなかった.そこで近年,これらのより一般的なT双対性に対しても共変な二重場理論としてWZW二重場理論(DFTWZW)が提案された.しかし,このWZW二重場理論は特殊な背景時空上でしか構成がされておらず,非アーベル的T双対性やPoisson-LieT双対性を示すような場合には二重場理論を構成することができていない.

そこで本論文では一般の背景場に拡張した場合であっても二重場理論を構成可能であることを明らかにし,その構成した新たな二重場理論が実際に従来の標準的な二重場理論やWZW二重場理論を含む拡張になっていることを示した.また,この新たな二重場理論を用いて非アーベル的T双対性やPoisson-LieT双対性を導出可能であることを示し,これまで明らかになっていなかったユニモジュラーではない代数構造を持つ場合のPoisson-LieT双対性を導出することに成功した.

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