Abstract
We study the supergravity dual of four-dimensional \( \mathcal{N}=1 \) superconformal field theories arising from wrapping M5-branes on a Kähler two-cycle inside a Calabi-Yau threefold. We derive an effective three-dimensional theory living on the cobordism between the infrared and ultraviolet Riemann surfaces, describing the renormalization group flows between AdS7 and AdS5 as well as between different AdS5 fixed points. The realization of this system as an effective theory is convenient to make connections to known theories, and we show that upon imposing (physical) infrared boundary conditions, the effective three-dimensional theory further reduces to two-dimensional SU(2) Yang-Mills theory on the Riemann surface.
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References
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems and the WKB Approximation, arXiv:0907.3987 [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic Uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].
M. Fluder, Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes, arXiv:1710.09479 [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-Dimensional SCFTs from M5-Branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].
J.T. Liu and R. Minasian, Black holes and membranes in AdS 7, Phys. Lett. B 457 (1999) 39 [hep-th/9903269] [INSPIRE].
C. Beem and A. Gadde, The N = 1 superconformal index for class S fixed points, JHEP 04 (2014) 036 [arXiv:1212.1467] [INSPIRE].
M.F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. Lond. A 308 (1982) 523 [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4d Superconformal Index from q-deformed 2d Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
I. Bah and B. Wecht, New N = 1 Superconformal Field Theories In Four Dimensions, JHEP 07 (2013) 107 [arXiv:1111.3402] [INSPIRE].
J.P. Gauntlett, Branes, calibrations and supergravity, in Strings and geometry. Proceedings, Summer School, Cambridge, U.K., March 24 – April 20, 2002, pp. 79–126, hep-th/0305074 [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11-D supergravity on AdS 7 × S 4 and selfduality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS 7 × S 4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged Maximally Extended Supergravity in Seven-dimensions, Phys. Lett. B 143 (1984) 103 [INSPIRE].
C. Beasley and E. Witten, Non-Abelian localization for Chern-Simons theory, J. Diff. Geom. 70 (2005) 183 [hep-th/0503126] [INSPIRE].
N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara and R.J. Szabo, Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles, Adv. Theor. Math. Phys. 12 (2008) 981 [hep-th/0609129] [INSPIRE].
Y. Tachikawa, Five-dimensional supergravity dual of a-maximization, Nucl. Phys. B 733 (2006) 188 [hep-th/0507057] [INSPIRE].
D. Gaiotto and J. Maldacena, The Gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
I. Bah, M. Gabella and N. Halmagyi, Punctures from probe M5-branes and \( \mathcal{N}=1 \) superconformal field theories, JHEP 07 (2014) 131 [arXiv:1312.6687] [INSPIRE].
I. Bah, AdS5 solutions from M5-branes on Riemann surface and D6-branes sources, JHEP 09 (2015) 163 [arXiv:1501.06072] [INSPIRE].
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Fluder, M. 4d \( \mathcal{N}=1/2d \) Yang-Mills duality in holography. J. High Energ. Phys. 2018, 38 (2018). https://doi.org/10.1007/JHEP08(2018)038
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DOI: https://doi.org/10.1007/JHEP08(2018)038