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Multiple D4-D2-D0 on the conifold and wall-crossing with the flop

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Abstract

We study the wall-crossing phenomena of D4-D2-D0 bound states with two units of D4-branechargeontheresolvedconifold. We identify the walls of marginal stability and evaluate the discrete changes of the BPS indices by using the Kontsevich-Soibelman wall-crossing formula. In particular, we find that the field theories on D4-branes in two large radius limits are properly connected by the wall-crossings involving the flop transition of the conifold. We also find that in one of the large radius limits there are stable bound states of two D4-D2-D0 fragments.

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References

  1. B. Szendroi, Non-commutative Donaldson-Thomas theory and the conifold, Geom. Topol. 12 (2008) 1171 [arXiv:0705.3419] [SPIRES].

    Article  MathSciNet  Google Scholar 

  2. E. Diaconescu and G.W. Moore, Crossing the wall: branes vs. bundles, arXiv:0706.3193 [SPIRES].

  3. D.L. Jafferis and N. Saulina, Fragmenting D4 branes and coupled q-deformed Yang-Mills, arXiv:0710.0648 [SPIRES].

  4. M.C.N. Cheng and E.P. Verlinde, Wall crossing, discrete attractor flow and Borcherds algebra, SIGMA 4 (2008) 068 [arXiv:0806.2337] [SPIRES].

    MathSciNet  Google Scholar 

  5. E. Andriyash and G.W. Moore, Ample D4-D2-D0 decay, arXiv:0806.4960 [SPIRES].

  6. K. Nagao and H. Nakajima, Counting invariant of perverse coherent sheaves and its wall-crossing, arXiv:0809. 2992 [SPIRES].

  7. K. Nagao, Derived categories of small toric Calabi-Yau 3-folds and counting invariants, arXiv:0809.2994.

  8. G.L. Cardoso, J.R. David, B. de Wit and S. Mahapatra, The mixed black hole partition function for the STU model, JHEP 12 (2008) 086 [arXiv:0810.1233] [SPIRES].

    Article  ADS  Google Scholar 

  9. A. Collinucci and T. Wyder, The elliptic genus from split flows and Donaldson-Thomas invariants, JHEP 05 (2010) 081 [arXiv:0810.4301] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. D.L. Jafferis and G.W. Moore, Wall crossing in local Calabi Yau manifolds, arXiv:0810.4909 [SPIRES].

  11. W.-y. Chuang and D.L. Jafferis, Wall crossing of BPS states on the conifold from Seiberg duality and pyramid partitions, Commun. Math. Phys. 292 (2009) 285 [arXiv:0810.5072] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. H. Ooguri and M. Yamazaki, Crystal melting and toric Calabi-Yau manifolds, Commun. Math. Phys. 292 (2009) 179 [arXiv:0811.2801] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. A. Collinucci, P. Soler and A.M. Uranga, Non-perturbative effects and wall-crossing from topological strings, JHEP 11 (2009) 025 [arXiv:0904.1133] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. T. Dimofte and S. Gukov, Refined, motivic and quantum, Lett. Math. Phys. 91 (2010) 1 [arXiv:0904.1420] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  15. J.R. David, On walls of marginal stability in N =2 string theories, JHEP 08 (2009) 054 [arXiv:0905.4115] [SPIRES].

    Article  ADS  Google Scholar 

  16. J. Manschot, Stability and duality in N =2 supergravity, Commun. Math. Phys. 299 (2010) 651 [arXiv:0906.1767] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. W.-y. Chuang and G. Pan, BPS state counting in local obstructed curves from quiver theory and Seiberg duality, J. Math. Phys. 51 (2010) 052305 [arXiv:0908.0360] [SPIRES].

  18. M. Aganagic, H. Ooguri, C. Vafa and M. Yamazaki, W all crossing and M-theory, arXiv:0908.1194 [SPIRES].

  19. W. Van Herck and T. Wyder, Black hole meiosis, JHEP 04 (2010) 047 [arXiv: 0909.0508] [SPIRES].

    Article  Google Scholar 

  20. K. Nagao and M. Yamazaki, The non-commutative topological vertex and wall crossing phenomena, arXiv:0910.5479 [SPIRES].

  21. P. Sulkowski, Wall-crossing, free fermions and crystal melting, Commun. Math. Phys. 301 (2011) 517 [arXiv:0910.5485] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. S. Lee and P. Yi, A study of wall-crossing: flavored kinks in D =2 QED, JHEP 03 (2010) 055 [arXiv:0911.4726] [SPIRES].

    Article  ADS  Google Scholar 

  23. M. Aganagic and M. Yamazaki, Open BPS wall crossing and M-theory, Nucl. Phys. B 834 (2010) 258 [arXiv:0911.5342] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. T. Dimofte, S. Gukov and Y. Soibelman, Quantum wall crossing in N =2 gauge theories, Lett. Math. Phys. 95 (2011) 1 [arXiv:0912.1346] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. R.J. Szabo, Instantons, topological strings and enumerative geometry, Adv. Math. Phys. 2010 (2010) 107857 [arXiv:0912.1509] [SPIRES].

    Google Scholar 

  26. D. Krefi, Wall crossing phenomenology of orientifolds, arXiv:1001. 5031 [SPIRES].

  27. W.-y. Chuang, D.-E. Diaconescu and G. Pan, Rank two ADHM invariants and wallcrossing, arXiv:1002.0579 [SPIRES].

  28. J. Manschot, W all-crossing of D 4-branes using flow trees, arXiv:1003.1570 [SPIRES].

  29. W.-y. Chuang, D.-E. Diaconescu and G. Pan, Wallcrossing and cohomology of the moduli space of Hitchin pairs, arXiv:1004.4195 [SPIRES].

  30. H. Ooguri, P. Sulkowski and M. Yamazaki, Wall crossing as seen by matrix models, arXiv:1005.1293 [SPIRES].

  31. M. Aganagic and K. Schaeffer, W all crossing, quivers and crystals, arXiv:1006.2113 [SPIRES].

  32. T. Nishinaka and S. Yamaguchi, Wall-crossing of D4-D2-D0 and flop of the conifold, JHEP 09 (2010) 026 [arXiv:1007.2731] [SPIRES];

    Article  MathSciNet  ADS  Google Scholar 

  33. F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [SPIRES];

  36. J. de Boer, F. Denef, S. El-Showk, I. Messamah and D. Van den Bleeken, Black hole bound states in AdS 3 × S 2, JHEP 11 (2008) 050 [arXiv:0802.2257] [SPIRES].

    Article  Google Scholar 

  37. J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N =2 multicenter solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [SPIRES];

    Article  Google Scholar 

  38. M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435.

  39. M. Kontsevich and Y. Soibelman, Motivic Donaldson-Thomas invariants: summary of results, arXiv:0910.4315 [SPIRES];

  40. D. Gaiotto, G.W. Moore and A. Neitzke, Four-dimensional wall-crossing via three-dimensional field theory, Commun. Math. Phys. 299 (2010) 163 [arXiv:0807.4723] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [SPIRES].

  42. S. Cecotti and C. Vafa, BPS wall crossing and topological strings, arXiv:0910.2615 [SPIRES].

  43. D. Gaiotto, G.W. Moore and A. Neitzke, Framed BPS states, arXiv:1006.0146 [SPIRES].

  44. E. Andriyash, F. Denef, D.L. Jafferis and G.W. Moore, Wall-crossing from supersymmetric galaxies, arXiv:1008.0030 [SPIRES].

  45. E. Andriyash, F. Denef, D.L. Jafferis and G.W. Moore, Bound state transformation walls, arXiv:1008.3555 [SPIRES];

  46. P.S. Aspinwall, D-branes on Calabi-Yau manifolds, hep-th/0403166 [SPIRES].

  47. R. Gopakumar and C. Vafa, M-theory and topological strings. I, hep-th/9809187 [SPIRES].

  48. R. Gopakumar and C. Vafa, M-theory and topological strings. II, hep-th/9812127 [SPIRES];

  49. M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, Black holes, q-deformed 2 d Yang-Mills and non-perturbative topological strings, Nucl. Phys. B 715 (2005) 304 [hep-th/0411280] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. C. Vafa, Two dimensional Yang-Mills, black holes and topological strings, hep-th/0406058 [SPIRES].

  52. J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  53. H. Nakajima, Instantons on ALE spaces, quiver varieties and Kac-Moody algebras, Duke Math. J. 76 (1994) 365.

    Article  MathSciNet  MATH  Google Scholar 

  54. D. Jafferis, Crystals and intersecting branes, hep-th/0607032 [SPIRES].

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  1. Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560–0043, Japan

    Takahiro Nishinaka

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  1. Takahiro Nishinaka
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ArXiv ePrint:1010.6002

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Nishinaka, T. Multiple D4-D2-D0 on the conifold and wall-crossing with the flop. J. High Energ. Phys. 2011, 65 (2011). https://doi.org/10.1007/JHEP06(2011)065

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