The liouville geometry of 2 instantons a
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The liouville geometry of 2 instantons a
arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a i2, Marco Matone3, Luca Mazzucato4 anil Yu Nakayama5 1 School of Natural Sciences, Institute for Advanced StudyEinstein Drive. Princeton. NJ 08540. USA2 Scuola Normale Superiorep.zza Dei Cavalieri 7, 56126 Pisa. Italy, and INFN sezione di. Pisa. Italy 3Dipartimento di Fisica “G. Galilei"’, ưniversit The liouville geometry of 2 instantons a à di PadovaVia Marzolo 8. 35131 Padova. Italy, and INFN se.zione di Padova, Italy ’International School for Advanced Studies (SISSA/ISAS)Via Beirut 2The liouville geometry of 2 instantons a
- 4- 34014 Trieste, Italy, and INFN, sezione di Trieste. Italy ’■Department of Physics, Faculty of Science, University of TokyoHongo 7-3-1, Bunkyo-ku,arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a ed to the moduli space of punctured spheres. Due to the recursive structure of the boundary in the Deligne-Knudsen-Mumford stable compactification, this leads to a new recursion relation for the instanton coefficients, which is bilinear. Instanton contributions are expressed as integrals on .Mo,n in The liouville geometry of 2 instantons a the framework of the Lionville F-models. This also suggests considering instanton contributions as a kind of Hurwitz numbers and also provides a predThe liouville geometry of 2 instantons a
iction on the asymptotic form of the Gromov-Witten invariants. We also interpret this map in terms of the geometric engineering approach to the gauge arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a al background and its relation to the uniformization program. Finally we point out an intriguing analogy with the self-dual YM equations for the gravitational version of SU(2) where surprisingly the same Haupt-modulc of the SW solution appears.38108Contents1Introduction ............................. The liouville geometry of 2 instantons a .......................................21.1.Instantons, moduli of punctured spheres and recursion relations .............21.2.The Stringy- point of ViThe liouville geometry of 2 instantons a
ew...................................................41.3.Outline of the Paper ........................................................62Classical LioarXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a 82.2.Deligne-Knudsen-Mumford compactfication ....................................102.3.Weil-Petersson volume recursion relation ...................................112.4.The equation for the Weil-Petersson volume generating function .............132.5.A surprising similarity ......................... The liouville geometry of 2 instantons a ...........................143The Lionville F-models and the master equation..................................153.1.The Lionville background..........The liouville geometry of 2 instantons a
..........................................1G3.2.Intersection theory and the bootstrap.......................................183.3.The master equation arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a moduli space and Aio.n ...............................................214.1.Stable compactification and the bubble tree.................................224.2.The Hurwitz moduli space....................................................234.3.The geometry of Weil-Petersson recursion relations......... The liouville geometry of 2 instantons a .................255AT = 2 gauge theory as Liouville F-models ......................................265.1.A master equation in A'1’ = 2 SYM?..........The liouville geometry of 2 instantons a
................................265.2.Relation to ADHM construction...............................................286The bilinear relation............arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano Bolognesi The liouville geometry of 2 instantons a to bilinear .................................................31arXiv:hep-th/0405117v3 13 Jun 2004The Lionville Geometry of J\f = 2 Instantons and the Moduli of Punctured SpheresGaetano Bertoldi1, Stefano BolognesiGọi ngay
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