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Gauge theory dynamics and Kähler potential for Calabi-Yau complex moduli

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Abstract

We compute the exact two-sphere partition function and matrix of two-point functions of operators in the chiral ring with their complex conjugates in two-dimensional supersymmetric gauge theories. For gauge theories that flow in the infrared to a CalabiYau nonlinear sigma model, these renormalization group invariant observables determine the exact Kähler potential and associated Zamolodchikov metric in the complex structure moduli space of the Calabi-Yau manifold.

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References

  1. E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. E. Witten, Mirror manifolds and topological field theory, hep-th/9112056 [INSPIRE].

  4. V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [ar**v:0712.2824] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, JHEP 05 (2013) 093 [ar**v:1206.2606] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. F. Benini and S. Cremonesi, Partition functions of N = (2,2) gauge theories on S 2 and vortices, ar**v:1206.2356 [INSPIRE].

  7. H. Jockers, V. Kumar, J.M. Lapan, D.R. Morrison and M. Romo, Two-Sphere Partition Functions and Gromov-Witten Invariants, ar**v:1208.6244 [INSPIRE].

  8. J. Gomis and S. Lee, Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP 04 (2013) 019 [ar**v:1210.6022] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  9. L.J. Dixon, Some world-sheet properties of superstring compactifications, on orbifolds and otherwise, lectures at the 1987 ICTP summer Workshop in High Energy Physics and Cosmology, Triest, 1987.

  10. W. Lerche, C. Vafa and N.P. Warner, Chiral Rings in N = 2 Superconformal Theories, Nucl. Phys. B 324 (1989) 427 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. S. Sugishita and S. Terashima, Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries, JHEP 11 (2013) 021 [ar**v:1308.1973] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. D. Honda and T. Okuda, Exact results for boundaries and domain walls in 2d supersymmetric theories, ar**v:1308.2217 [INSPIRE].

  14. K. Hori and M. Romo, Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary, ar**v:1308.2438 [INSPIRE].

  15. N. Doroud, J. Gomis, Kähler Potential for Complex Moduli in Non-Abelian Calabi-Yau Quotients, work in progress.

  16. J. Gates, S.J., C. Hull and M. Roček, Twisted Multiplets and New Supersymmetric Nonlinear σ-models, Nucl. Phys. B 248 (1984) 157 [INSPIRE].

  17. G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [ar**v:1105.0689] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. A. Strominger and E. Witten, New Manifolds for Superstring Compactification, Commun. Math. Phys. 101 (1985) 341 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  19. P. Candelas, A. Dale, C. Lütken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds, Nucl. Phys. B 298 (1988) 493 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222 [INSPIRE].

  21. P. Berglund, P. Candelas, X. De La Ossa, A. Font, T. Hubsch et al., Periods for Calabi-Yau and Landau-Ginzburg vacua, Nucl. Phys. B 419 (1994) 352 [hep-th/9308005] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press, 1998.

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Correspondence to Nima Doroud.

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ArXiv ePrint: 1309.2305

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Doroud, N., Gomis, J. Gauge theory dynamics and Kähler potential for Calabi-Yau complex moduli. J. High Energ. Phys. 2013, 99 (2013). https://doi.org/10.1007/JHEP12(2013)099

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