Abstract
We analyze S-duality of orientifolds of the Calabi-Yau cone over the first del Pezzo surface (dP 1). The S-duals of known phases, described by quiver gauge theories, contain intrinsically strongly-coupled sectors. These sectors are realized by a higher multiplicity intersection of NS5 branes and D5 branes atop an O5 plane, and can be thought of as stuck at the infinite coupling point between two Seiberg-dual gauge theories. We argue that such sectors appear generically in orientifolds of non-orbifold singularities, where in many examples every orientifold phase contains such a sector. Understanding such sectors is therefore key to understanding orientifolds of Calabi-Yau singularities. We construct the strongly-coupled sectors for dP 1 orientifolds using deconfinement, and show that they have interesting, non-trivial properties. Using this construction, we verify the predictions of S-duality for dP 1.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
P.C. Argyres, K.A. Intriligator, R.G. Leigh and M.J. Strassler, On inherited duality in N = 1 D = 4 supersymmetric gauge theories, JHEP 04 (2000) 029 [hep-th/9910250] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
N. Seiberg, The power of duality: exact results in 4D SUSY field theory, Int. J. Mod. Phys. A 16 (2001) 4365 [hep-th/9506077] [INSPIRE].
I. Garcia-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part I. Field theory, JHEP 10 (2013) 007 [arXiv:1210.7799] [INSPIRE].
M. Bianchi, G. Inverso, J.F. Morales and D.R. Pacifici, Unoriented quivers with flavour, JHEP 01 (2014) 128 [arXiv:1307.0466] [INSPIRE].
I. García-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part II. String theory, JHEP 10 (2013) 006 [arXiv:1307.1701] [INSPIRE].
A.M. Uranga, Comments on nonsupersymmetric orientifolds at strong coupling, JHEP 02 (2000) 041 [hep-th/9912145] [INSPIRE].
S. Sugimoto, Confinement and dynamical symmetry breaking in non-SUSY gauge theory from S-duality in string theory, Prog. Theor. Phys. 128 (2012) 1175 [arXiv:1207.2203] [INSPIRE].
A. Hook and G. Torroba, S-duality of nonsupersymmetric gauge theories, Phys. Rev. D 89 (2014) 025006 [arXiv:1309.5948] [INSPIRE].
D. Gaiotto and S.S. Razamat, N = 1 theories of class S k , JHEP 07 (2015) 073 [arXiv:1503.05159] [INSPIRE].
S. Franco, H. Hayashi and A. Uranga, Charting class S k territory, Phys. Rev. D 92 (2015) 045004 [arXiv:1504.05988] [INSPIRE].
A. Hanany and K. Maruyoshi, Chiral theories of class S, arXiv:1505.05053 [INSPIRE].
S. Franco and G. Torroba, Gauge theories from D7-branes over vanishing 4-cycles, JHEP 01 (2011) 017 [arXiv:1010.4029] [INSPIRE].
M. Berkooz, The dual of supersymmetric SU(2K) with an antisymmetric tensor and composite dualities, Nucl. Phys. B 452 (1995) 513 [hep-th/9505067] [INSPIRE].
P. Pouliot, Duality in SUSY SU(N) with an antisymmetric tensor, Phys. Lett. B 367 (1996) 151 [hep-th/9510148] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
P.A. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York U.S.A. (1978).
D. Malyshev, Del Pezzo singularities and SUSY breaking, Adv. High Energy Phys. 2011 (2011) 630892 [arXiv:0705.3281] [INSPIRE].
A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [INSPIRE].
S. Franco, A. Hanany, K.D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].
S. Franco, A. Hanany, D. Krefl, J. Park, A.M. Uranga and D. Vegh, Dimers and orientifolds, JHEP 09 (2007) 075 [arXiv:0707.0298] [INSPIRE].
K.D. Kennaway, Brane tilings, Int. J. Mod. Phys. A 22 (2007) 2977 [arXiv:0706.1660] [INSPIRE].
M. Yamazaki, Brane tilings and their applications, Fortsch. Phys. 56 (2008) 555 [arXiv:0803.4474] [INSPIRE].
A. Ishii and K. Ueda, On moduli spaces of quiver representations associated with dimer models, RIMS Kôkyûroku Bessatsu B 9 (2008) 127 [arXiv:0710.1898].
A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, JHEP 10 (2007) 029 [hep-th/0511063] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 [hep-th/0003085] [INSPIRE].
C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [INSPIRE].
Y. Imamura, K. Kimura and M. Yamazaki, Anomalies and O-plane charges in orientifolded brane tilings, JHEP 03 (2008) 058 [arXiv:0801.3528] [INSPIRE].
C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y. Stanev, Chiral asymmetry in four-dimensional open string vacua, Phys. Lett. B 385 (1996) 96 [hep-th/9606169] [INSPIRE].
J.D. Lykken, E. Poppitz and S.P. Trivedi, M(ore) on chiral gauge theories from D-branes, Nucl. Phys. B 520 (1998) 51 [hep-th/9712193] [INSPIRE].
Z. Kakushadze, Gauge theories from orientifolds and large-N limit, Nucl. Phys. B 529 (1998) 157 [hep-th/9803214] [INSPIRE].
M. Wijnholt, Large volume perspective on branes at singularities, Adv. Theor. Math. Phys. 7 (2004) 1117 [hep-th/0212021] [INSPIRE].
M. Wijnholt, Geometry of particle physics, Adv. Theor. Math. Phys. 13 (2009) [hep-th/0703047] [INSPIRE].
B. Heidenreich, Dimer models and involutions of the quiver, unpublished notes.
J. Evslin, What does(n’t) k-theory classify?, hep-th/0610328 [INSPIRE].
A. Hanany and B. Kol, On orientifolds, discrete torsion, branes and M-theory, JHEP 06 (2000) 013 [hep-th/0003025] [INSPIRE].
A. Hatcher, Algebraic topology, http://www.math.cornell.edu/~hatcher/AT/ATpage.html, Cambridge University Press, Cambridge U.K. (2002).
C.-H. Liu, On the isolated singularity of a seven space obtained by rolling Calabi-Yau threefolds through extremal transitions, hep-th/9801175 [INSPIRE].
R. Kenyon, An introduction to the dimer model, math/0310326.
B. Feng, Y.-H. He, K.D. Kennaway and C. Vafa, Dimer models from mirror symmetry and quivering amoebae, Adv. Theor. Math. Phys. 12 (2008) 489 [hep-th/0511287] [INSPIRE].
I. Garcia-Etxebarria, F. Saad and A.M. Uranga, Quiver gauge theories at resolved and deformed singularities using dimers, JHEP 06 (2006) 055 [hep-th/0603108] [INSPIRE].
I. García-Etxebarria and B. Heidenreich, Charting the wilderness of orientifolds, to appear.
N.J. Evans, C.V. Johnson and A.D. Shapere, Orientifolds, branes and duality of 4D gauge theories, Nucl. Phys. B 505 (1997) 251 [hep-th/9703210] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].
Y. Imamura, Global symmetries and ’t Hooft anomalies in brane tilings, JHEP 12 (2006) 041 [hep-th/0609163] [INSPIRE].
K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(N c ) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
N. Broomhead, Dimer models and Calabi-Yau algebras, arXiv:0901.4662 [INSPIRE].
A. Hanany, C.P. Herzog and D. Vegh, Brane tilings and exceptional collections, JHEP 07 (2006) 001 [hep-th/0602041] [INSPIRE].
J. Davey, A. Hanany and J. Pasukonis, On the classification of brane tilings, JHEP 01 (2010) 078 [arXiv:0909.2868] [INSPIRE].
J.P. Davey, Brane tilings, M2-branes and orbifolds, arXiv:1110.6658 [INSPIRE].
S. Franco and A.M. . Uranga, Dynamical SUSY breaking at meta-stable minima from D-branes at obstructed geometries, JHEP 06 (2006) 031 [hep-th/0604136] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly marginal deformations and global symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
Y. Imamura, H. Isono, K. Kimura and M. Yamazaki, Exactly marginal deformations of quiver gauge theories as seen from brane tilings, Prog. Theor. Phys. 117 (2007) 923 [hep-th/0702049] [INSPIRE].
F.A. Dolan and H. Osborn, Applications of the superconformal index for protected operators and q-hypergeometric identities to N = 1 dual theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [INSPIRE].
M.A. Luty, M. Schmaltz and J. Terning, A sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter, Phys. Rev. D 54 (1996) 7815 [hep-th/9603034] [INSPIRE].
T. Sakai, Duality in supersymmetric SU(N) gauge theory with a symmetric tensor, Mod. Phys. Lett. A 12 (1997) 1025 [hep-th/9701155] [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(N c ) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
C. Csáki, M. Schmaltz and W. Skiba, Confinement in N = 1 SUSY gauge theories and model building tools, Phys. Rev. D 55 (1997) 7840 [hep-th/9612207] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
C. Romelsberger, Calculating the superconformal index and Seiberg duality, arXiv:0707.3702 [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, Commun. Math. Phys. 304 (2011) 797 [arXiv:0910.5944] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Superconformal indices of N = 4 SYM field theories, Lett. Math. Phys. 100 (2012) 97 [arXiv:1005.4196] [INSPIRE].
R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy, Cohomology of line bundles: a computational algorithm, J. Math. Phys. 51 (2010) 103525 [arXiv:1003.5217] [INSPIRE].
S.-Y. Jow, Cohomology of toric line bundles via simplicial Alexander duality, J. Math. Phys. 52 (2011) 033506 [arXiv:1006.0780].
T. Rahn and H. Roschy, Cohomology of line bundles: proof of the algorithm, J. Math. Phys. 51 (2010) 103520 [Publisher’s note ibid. 51 (2010) 129901] [arXiv:1006.2392] [INSPIRE].
M.A.A. van Leeuwen, A.M. Cohen and B. Lisser, LiE, a computer algebra package for Lie group computations webpage, http://www-math.univ-poitiers.fr/~maavl/LiE, (1992).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1506.03090
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
García-Etxebarria, I., Heidenreich, B. Strongly coupled phases of \( \mathcal{N}=1 \) S-duality. J. High Energ. Phys. 2015, 32 (2015). https://doi.org/10.1007/JHEP09(2015)032
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)032