Loop Equations for Gromov-Witten Invariant of P¹
We show that non-stationary Gromov-Witten invariants of P¹ can be extracted from open periods of the Eynard-Orantin topological recursion correlators ωg,ₙ whose Laurent series expansion at ∞ compute the stationary invariants. To do so, we overcome the technical difficulties to global loop equations...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Sprache: | English |
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Інститут математики НАН України
2019
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| Zitieren: | Loop Equations for Gromov-Witten Invariant of P¹ / G. Borot, P. Norbury // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. |
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Borot, G. Norbury, P. 2025-12-04T13:05:43Z 2019 Loop Equations for Gromov-Witten Invariant of P¹ / G. Borot, P. Norbury // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 32G15; 14D23; 53D45 arXiv: 1905.01890 https://nasplib.isofts.kiev.ua/handle/123456789/210234 https://doi.org/10.3842/SIGMA.2019.061 We show that non-stationary Gromov-Witten invariants of P¹ can be extracted from open periods of the Eynard-Orantin topological recursion correlators ωg,ₙ whose Laurent series expansion at ∞ compute the stationary invariants. To do so, we overcome the technical difficulties to global loop equations for the spectral x(z)=z+1/z and y(z)=lnz from the local loop equations satisfied by the ωg,ₙ, and check these global loop equations are equivalent to the Virasoro constraints that are known to govern the full Gromov-Witten theory of P¹. This work was initiated during a visit of G.B. to the University of Melbourne, supported by P. Zinn-Justin, whom he thanks for hospitality. G.B. also thanks Hiroshi Iritani for discussions on mirror symmetry, and acknowledges the support of the Max-Planck-Gesellschaft. Part of this work was carried out during a visit of P.N. to Ludwig-Maximilians-Universität which he thanks its hospitality. P.N. is supported by the Australian Research Council grants DP170102028 and DP180103891. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Loop Equations for Gromov-Witten Invariant of P¹ Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Loop Equations for Gromov-Witten Invariant of P¹ |
| spellingShingle |
Loop Equations for Gromov-Witten Invariant of P¹ Borot, G. Norbury, P. |
| title_short |
Loop Equations for Gromov-Witten Invariant of P¹ |
| title_full |
Loop Equations for Gromov-Witten Invariant of P¹ |
| title_fullStr |
Loop Equations for Gromov-Witten Invariant of P¹ |
| title_full_unstemmed |
Loop Equations for Gromov-Witten Invariant of P¹ |
| title_sort |
loop equations for gromov-witten invariant of p¹ |
| author |
Borot, G. Norbury, P. |
| author_facet |
Borot, G. Norbury, P. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We show that non-stationary Gromov-Witten invariants of P¹ can be extracted from open periods of the Eynard-Orantin topological recursion correlators ωg,ₙ whose Laurent series expansion at ∞ compute the stationary invariants. To do so, we overcome the technical difficulties to global loop equations for the spectral x(z)=z+1/z and y(z)=lnz from the local loop equations satisfied by the ωg,ₙ, and check these global loop equations are equivalent to the Virasoro constraints that are known to govern the full Gromov-Witten theory of P¹.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210234 |
| citation_txt |
Loop Equations for Gromov-Witten Invariant of P¹ / G. Borot, P. Norbury // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 17 назв. — англ. |
| work_keys_str_mv |
AT borotg loopequationsforgromovwitteninvariantofp1 AT norburyp loopequationsforgromovwitteninvariantofp1 |
| first_indexed |
2025-12-07T21:24:50Z |
| last_indexed |
2025-12-07T21:24:50Z |
| _version_ |
1850886262380036096 |