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Quantum Wall Crossing in \({{\mathcal N}=2}\) Gauge Theories

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Abstract

We study refined and motivic wall-crossing formulas in \({{\mathcal N}=2}\) supersymmetric gauge theories with SU(2) gauge group and N f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that “refined = motivic.”

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References

  1. Aganagic M., Bouchard V., Klemm A.: Topological strings and (almost) modular forms. Commun. Math. Phys. 277, 771–819 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Bilal A., Ferrari F.: Curves of marginal stability and weak and strong-coupling bps spectra in n = 2 supersymmetric qcd. Nucl. Phys. B480, 589–622 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  3. Cecotti, S., Vafa, C.: Bps wall crossing and topological strings (2009, preprint). arXiv:0910.2615

  4. Chiang T.M., Klemm A., Yau S.T., Zaslow E.: Local mirror symmetry: calculations and interpretations. Adv. Theor. Math. Phys. 3, 495–565 (1999)

    MATH  MathSciNet  Google Scholar 

  5. Denef, F., Moore, G.W.: Split states, entropy enigmas, holes and halos (2007)

  6. Diaconescu, E., Moore, G.W.: Crossing the wall: Branes vs. bundles (2007, preprint). arXiv:0706.3193

  7. Dimofte T., Gukov S.: Refined, motivic, and quantum. Lett. Math. Phys. 91(1), 1 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dimofte T., Gukov S., Lenells J., Zagier D.: Exact results for perturbative chern-simons theory with complex gauge group. Commun. Num. Thy. Phys. 3(2), 363–443 (2009)

    MATH  MathSciNet  Google Scholar 

  9. Dimofte, T., Jafferis, D.L.: Motivic wall crossing, moduli spaces, and invisible walls, in preparation (2010)

  10. Douglas M.R., Fiol B., Römelsberger C.: The spectrum of bps branes on a noncompact calabi-yau. JHEP 09, 057 (2005)

    Article  ADS  Google Scholar 

  11. Fiol, B.: The bps spectrum of n = 2 su(n) sym and parton branes (2000, preprint). hep-th/0012079

  12. Gaiotto, D., Moore, G.W., Neitzke, A.: Four-dimensional wall-crossing via three-dimensional field theory (2008, preprint). arXiv:0807.4723

  13. Gaiotto, D., Moore, G.W., Neitzke, A.: Wall-crossing, hitchin systems, and the wkb approximation (2009, preprint). arXiv:0907.3987

  14. Gross, M., Pandharipande, R., Siebert, B.: The tropical vertex (2009)

  15. Hanany A., Oz Y.: On the quantum moduli space of vacua of n = 2 supersymmetric su(n c ) gauge theories. Nucl. Phys. B452, 283–312 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  16. Katz S., Mayr P., Vafa C.: Mirror symmetry and exact solution of 4d n = 2 gauge theories i. Adv. Theor. Math. Phys. 1, 53–114 (1998)

    MathSciNet  Google Scholar 

  17. Katz S., Klemm A., Vafa C.: Geometric engineering of quantum field theories. Nucl. Phys. B497, 173–195 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  18. Klemm A., Lerche W., Vafa C., Warner N.: Self-dual strings and n = 2 supersymmetric field theory. Nucl. Phys. B477, 746–766 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  19. Kontsevich, M., Soibelman, Y.: Stability structures, motivic donaldson-thomas invariants and cluster transformations (2008, preprint). arXiv:0811.2435

  20. Kontsevich, M., Soibelman, Y.: Cohomological hall algebra, exponential Hodge structures, and motivic Donaldson-Thomas invariants (2009, preprint). arXiv:1006.2706

  21. Kontsevich, M., Soibelman, Y.: Motivic donaldson-thomas invariants: Summary of results (2009, preprint). arXiv:0910.4315

  22. Le Potier, J.: Lectures on vector bundles, Cambridge Studies in Advanced Mathematics, vol. 54. Cambridge University Press, Cambridge (1997)

  23. Lerche, W.: Introduction to Seiberg-witten theory and its stringy origin, Nucl. Phys. Proc. Suppl. 55B (1996)

  24. Reineke, M.: Poisson automorphisms and quiver moduli (2008, preprint). arXiv:0804. 3214

  25. Reineke, M.: Cohomology of quiver moduli, functional equations, and integrality of donaldson-thomas type invariants (2009, preprint). arXiv:0903.0261

  26. Seiberg N., Witten E.: Electric-magnetic duality, monopole condensation, and confinement in n = 2 supersymmetric yang-mills theory. Nucl. Phys. B426, 19–52 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  27. Seiberg N., Witten E.: Monopoles, duality and chiral symmetry breaking in n = 2 supersymmetric qcd. Nucl. Phys. B431, 484–550 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  28. Witten E.: Solutions of four-dimensional field theories via M-theory. Nucl. Phys. B500, 3–42 (1997)

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, USA

    Tudor Dimofte & Sergei Gukov

  2. University of California, Santa Barbara, CA, 93106, USA

    Sergei Gukov

  3. Department of Mathematics, KSU, Manhattan, KS, 66506, USA

    Yan Soibelman

Authors
  1. Tudor Dimofte
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  2. Sergei Gukov
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  3. Yan Soibelman
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Correspondence to Tudor Dimofte.

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Dimofte, T., Gukov, S. & Soibelman, Y. Quantum Wall Crossing in \({{\mathcal N}=2}\) Gauge Theories. Lett Math Phys 95, 1–25 (2011). https://doi.org/10.1007/s11005-010-0437-x

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  • DOI: https://doi.org/10.1007/s11005-010-0437-x

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