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dbr:Gopakumar–Vafa_invariant
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ゴパクマー・ヴァッファ不変量 Gopakumar–Vafa invariant
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In theoretical physics, Rajesh Gopakumar and Cumrun Vafa introduced in a series of papers new topological invariants, called Gopakumar–Vafa invariants, that represent the number of BPS states on a Calabi–Yau 3-fold. They lead to the following generating function for the Gromov–Witten invariants on a Calabi–Yau 3-fold M: , where 理論物理学では、 (Rajesh Gopakumar) とカムラン・ヴァッファ (Cumrun Vafa) は、3次元カラビ・ヤウ多様体のBPS状態(BPS state)の数を表す、新しい位相不変量、ゴパクマー・ヴァッファ不変量 (ゴパクマー・ヴァッファふへんりょう、Gopakumar-Vafa invariant) を、一連の論文で導入した。（、 を参照。また、、 も参照。）彼らは、3-次元カラビ・ヤウ多様体 M のグロモフ・ウィッテン不変量の母函数となる次の公式を導いた。 ここに、 はグロモフ・ウィッテン不変量を、 は種数 g を持つ (pseudoholomorphic curve) の数を、 はBPS状態の数を表す。
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dbr:Annals_of_Mathematics dbr:Calabi–Yau_manifold dbr:Cumrun_Vafa dbr:BPS_state dbr:Pseudoholomorphic_curve dbr:Gromov–Witten_invariant dbr:Rajesh_Gopakumar dbc:Quantum_field_theory dbc:Algebraic_geometry dbc:String_theory dbr:Theoretical_physics dbr:Topological_quantum_field_theory dbr:Genus_(mathematics)
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In theoretical physics, Rajesh Gopakumar and Cumrun Vafa introduced in a series of papers new topological invariants, called Gopakumar–Vafa invariants, that represent the number of BPS states on a Calabi–Yau 3-fold. They lead to the following generating function for the Gromov–Witten invariants on a Calabi–Yau 3-fold M: , where * is the class of pseudoholomorphic curves with genus g, * is the topological string coupling, * with the Kähler parameter of the curve class , * are the Gromov–Witten invariants of curve class at genus , * are the number of BPS states (the Gopakumar–Vafa invariants) of curve class at genus . 理論物理学では、 (Rajesh Gopakumar) とカムラン・ヴァッファ (Cumrun Vafa) は、3次元カラビ・ヤウ多様体のBPS状態(BPS state)の数を表す、新しい位相不変量、ゴパクマー・ヴァッファ不変量 (ゴパクマー・ヴァッファふへんりょう、Gopakumar-Vafa invariant) を、一連の論文で導入した。（、 を参照。また、、 も参照。）彼らは、3-次元カラビ・ヤウ多様体 M のグロモフ・ウィッテン不変量の母函数となる次の公式を導いた。 ここに、 はグロモフ・ウィッテン不変量を、 は種数 g を持つ (pseudoholomorphic curve) の数を、 はBPS状態の数を表す。
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