S-duality and topological strings

In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- and B-model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.

[1]  A. Okounkov,et al.  Gromov–Witten theory and Donaldson–Thomas theory, II , 2004, Compositio Mathematica.

[2]  C. Vafa,et al.  Topological Strings and Integrable Hierarchies , 2003, hep-th/0312085.

[3]  R. Pandharipande,et al.  Gromov–Witten theory and Donaldson–Thomas theory, I , 2003, Compositio Mathematica.

[4]  Thomas W. Grimm,et al.  The e ective action of N = 1 Calabi - Yau orientifolds , 2004, hep-th/0403067.

[5]  C. Vafa,et al.  N=2 strings and the twistorial Calabi-Yau , 2004, hep-th/0402128.

[6]  E. Witten.  Perturbative Gauge Theory as a String Theory in Twistor Space , 2003, hep-th/0312171.

[7]  A. Okounkov,et al.  Quantum Calabi-Yau and Classical Crystals , 2003, hep-th/0309208.

[8]  N. Nekrasov,et al.  Small Instantons, Little Strings and Free Fermions , 2003, hep-th/0302191.

[9]  P. Tripathy,et al.  New supersymmetric string compactifications , 2002, hep-th/0211182.

[10]  S. Gurrieri,et al.  Mirror symmetry in generalized Calabi–Yau compactifications ☆ , 2002, hep-th/0211102.

[11]  E. Witten,et al.  Erratum to: “CFT's from Calabi–Yau four-folds” , 2001 .

[12]  C. Vafa.  Superstrings and topological strings at large N , 2000, hep-th/0008142.

[13]  C. Vafa,et al.  RR flux on Calabi–Yau and partial supersymmetry breaking , 1999, hep-th/9912152.

[14]  E. Witten,et al.  CFT's from Calabi–Yau four-folds , 1999, hep-th/9906070.

[15]  G. Cardoso,et al.  Deviations from the Area Law for Supersymmetric Black Holes , 1999, hep-th/9904005.

[16]  R. Gopakumar,et al.  M-Theory and Topological Strings--II , 1998, hep-th/9812127.

[17]  S. A. Huggett,et al.  The geometric universe : science, geometry, and the work of Roger Penrose , 1998 .

[18]  H. Ooguri,et al.  Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes , 1993, hep-th/9309140.

[19]  I. Antoniadis,et al.  Topological amplitudes in string theory , 1993, hep-th/9307158.

[20]  Yoshihisa Kitagawa.  Perspectives of String Theory , 1993 .

[21]  E. Witten.  Chern-Simons gauge theory as a string theory , 1992, hep-th/9207094.

[22]  C. Taubes.  The existence of anti-self-dual conformal structures , 1992 .

[23]  S. Donaldson,et al.  Connected sums of self-dual manifolds and deformations of singular spaces , 1989 .

[24]  A. Strominger.  Vacuum Topology and Incoherence in Quantum Gravity , 1984 .

[25]  M. Atiyah,et al.  Self-duality in four-dimensional Riemannian geometry , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.