About: 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

Attributes	Values
rdfs:label	Gopakumar–Vafa invariant (en) ゴパクマー・ヴァッファ不変量 (ja)
rdfs:comment	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。 (ja) 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 (en)
dct:subject	Quantum field theory String theory Algebraic geometry
Wikipage page ID	44541887 (xsd:integer)
Wikipage revision ID	1100573865 (xsd:integer)
Link from a Wikipage to another Wikipage	BPS state Annals of Mathematics Pseudoholomorphic curve Quantum field theory String theory Genus (mathematics) Calabi–Yau manifold Theoretical physics Cumrun Vafa Algebraic geometry Gromov–Witten invariant Rajesh Gopakumar Topological quantum field theory
sameAs	Gopakumar–Vafa invariant Gopakumar–Vafa invariant Gopakumar–Vafa invariant Gopakumar–Vafa invariant
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Quantum-stub dbt:Reflist dbt:Short_description
has abstract	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 . (en) 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。 (ja)
prov:wasDerivedFrom	wikipedia-en:Gopakumar–Vafa_invariant?oldid=1100573865&ns=0
page length (characters) of wiki page	3503 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Gopakumar–Vafa_invariant
is Link from a Wikipage to another Wikipage of	Eleny Ionel Cumrun Vafa Gopakumar-Vafa invariant Gromov–Witten invariant Rajesh Gopakumar
is Wikipage redirect of	Gopakumar-Vafa invariant
is known for of	Cumrun Vafa Rajesh Gopakumar
is known for of	Cumrun Vafa Rajesh Gopakumar
is foaf:primaryTopic of	wikipedia-en:Gopakumar–Vafa_invariant

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