“Gopakumar–Vafa invariant”的意思、由来-开放百科全书

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Gopakumar–Vafa invariant

释义

As a partition function in topological quantum field theory
Notes
References

In theoretical physics, Rajesh Gopakumar and Cumrun Vafa introduced in a series of papers^[1]^[2]^[3]^[4] 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 .

As a partition function in topological quantum field theory

Gopakumar–Vafa invariants can be viewed as a partition function in topological quantum field theory. They are proposed to be the partition function in Gopakumar–Vafa form:

Notes

1. ^{{harvnb|Gopakumar|Vafa|1998a}}
2. ^{{harvnb|Gopakumar|Vafa|1998b}}
3. ^{{harvnb|Gopakumar|Vafa|1998c}}
4. ^{{harvnb|Gopakumar|Vafa|1998d}}

References

{{Citation |last1=Gopakumar |first1=Rajesh |last2=Vafa |first2=Cumrun |date=1998a |title=M-Theory and Topological strings-I |arxiv=hep-th/9809187|bibcode=1998hep.th....9187G }}
{{Citation |last1=Gopakumar |first1=Rajesh |last2=Vafa |first2=Cumrun |date=1998b |title=M-Theory and Topological strings-II |arxiv=hep-th/9812127|bibcode=1998hep.th...12127G }}
{{Citation |last1=Gopakumar |first1=Rajesh |last2=Vafa |first2=Cumrun |date=1998c |title=On the Gauge Theory/Geometry Correspondence |arxiv=hep-th/9811131|bibcode=1998hep.th...11131G }}
{{Citation |last1=Gopakumar |first1=Rajesh |last2=Vafa |first2=Cumrun |date=1998d |title=Topological Gravity as Large N Topological Gauge Theory |arxiv=hep-th/9802016|bibcode=1998hep.th....2016G }}
{{citation

| last1 = Ionel | first1 = Eleny-Nicoleta | author1-link = Eleny Ionel
| last2 = Parker | first2 = Thomas H.
| doi = 10.4007/annals.2018.187.1.1
| issue = 1
| journal = Annals of Mathematics
| mr = 3739228
| pages = 1–64
| series = Second Series
| title = The Gopakumar–Vafa formula for symplectic manifolds
| volume = 187
| year = 2018}}{{DEFAULTSORT:Gopakumar-Vafa invariant}}{{quantum-stub}}

3 : Quantum field theory|Algebraic geometry|String theory

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