D-type fiber-base duality

Journal of High Energy Physics, Sep 2018

Abstract M5 branes probing D-type singularities give rise to 6d (1,0) SCFTs with SO × SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits.

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D-type fiber-base duality

Journal of High Energy Physics September 2018, 2018:60 | Cite as D-type fiber-base duality AuthorsAuthors and affiliations Babak HaghighatJoonho KimWenbin YanShing-Tung Yau Open Access Regular Article - Theoretical Physics First Online: 12 September 2018 Received: 23 July 2018 Accepted: 07 September 2018 6 Downloads Abstract M5 branes probing D-type singularities give rise to 6d (1,0) SCFTs with SO × SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits. Keywords Brane Dynamics in Gauge Theories Field Theories in Higher Dimensions String Duality Supersymmetric Gauge Theory  ArXiv ePrint: 1806.10335 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] J.J. Heckman, D.R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE]. [2] J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic Classification of 6D SCFTs, Fortsch. Phys. 63 (2015) 468 [arXiv:1502.05405] [INSPIRE]. [3] M. Del Zotto, C. Vafa and D. Xie, Geometric engineering, mirror symmetry and \( 6{\mathrm{d}}_{\left(1,0\right)}\to\ 4{\mathrm{d}}_{\left(\mathcal{N} = 2\right)} \), JHEP 11 (2015) 123 [arXiv:1504.08348] [INSPIRE]. [4] K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,0\right) \) theories on T 2 and class S theories: Part I, JHEP 07 (2015) 014 [arXiv:1503.06217] [INSPIRE]. [5] K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,0\right) \) theories on S 1 /T 2 and class S theories: part II, JHEP 12 (2015) 131 [arXiv:1508.00915] [INSPIRE]. [6] B. Haghighat, A. Iqbal, C. Kozçaz, G. Lockhart and C. Vafa, M-Strings, Commun. Math. Phys. 334 (2015) 779 [arXiv:1305.6322] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar [7] B. Haghighat, C. Kozçaz, G. Lockhart and C. Vafa, Orbifolds of M-strings, Phys. Rev. D 89 (2014) 046003 [arXiv:1310.1185] [INSPIRE]. [8] B. Haghighat, G. Lockhart and C. Vafa, Fusing E-strings to heterotic strings: E + E → H, Phys. Rev. D 90 (2014) 126012 [arXiv:1406.0850] [INSPIRE]. [9] J. Kim, S. Kim, K. Lee, J. Park and C. Vafa, Elliptic Genus of E-strings, JHEP 09 (2017) 098 [arXiv:1411.2324] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [10] B. Haghighat, A. Klemm, G. Lockhart and C. Vafa, Strings of Minimal 6d SCFTs, Fortsch. Phys. 63 (2015) 294 [arXiv:1412.3152] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [11] A. Gadde, B. Haghighat, J. Kim, S. Kim, G. Lockhart and C. Vafa, 6d String Chains, JHEP 02 (2018) 143 [arXiv:1504.04614] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [12] J. Kim, S. Kim and K. Lee, Higgsing towards E-strings, arXiv:1510.03128 [INSPIRE]. [13] H.-C. Kim, S. Kim and J. Park, 6d strings from new chiral gauge theories, arXiv:1608.03919 [INSPIRE]. [14] M. Del Zotto and G. Lockhart, On Exceptional Instanton Strings, JHEP 09 (2017) 081 [arXiv:1609.00310] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar [15] H.-C. Kim, J. Kim, S. Kim, K.-H. Lee and J. Park, 6d strings and exceptional instantons, arXiv:1801.03579 [INSPIRE]. [16] J. Kim, K. Lee and J. Park, On elliptic genera of 6d string theories, arXiv:1801.01631 [INSPIRE]. [17] M. Zotto and G. Lockhart, Universal Features of BPS Strings in Six-dimensional SCFTs, JHEP 08 (2018) 173 [arXiv:1804.09694] [INSPIRE].CrossRefGoogle Scholar [18] B. Haghighat, W. Yan and S.-T. Yau, ADE String Chains and Mirror Symmetry, JHEP 01 (2018) 043 [arXiv:1705.05199] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [19] N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math. 244 (2006) 525 [hep-th/0306238] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar [20] N. Nekrasov and V. Pestun, Seiberg-Witten geometry of four dimensional N = 2 quiver gauge theories, arXiv:1211.2240 [INSPIRE]. [21] M. Jardim and A. Maciocia, A Fourier-Mukai approach to spectral data for instantons, math/0006054 [INSPIRE]. [22] L. Bhardwaj, M. Del Zotto, J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, F-theory and the (...truncated)


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Babak Haghighat, Joonho Kim, Wenbin Yan, Shing-Tung Yau. D-type fiber-base duality, Journal of High Energy Physics, 2018, pp. 60, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)060