Abstract
We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, \( \mathcal{N} \) = 1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
G. Aldazabal, L.E. Ibáñez, F. Quevedo and A.M. Uranga, D-branes at singularities: A Bottom up approach to the string embedding of the standard model, JHEP 08 (2000) 002 [hep-th/0005067] [INSPIRE].
D. Berenstein, V. Jejjala and R.G. Leigh, The Standard model on a D-brane, Phys. Rev. Lett. 88 (2002) 071602 [hep-ph/0105042] [INSPIRE].
H. Verlinde and M. Wijnholt, Building the standard model on a D3-brane, JHEP 01 (2007) 106 [hep-th/0508089] [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. Martelli, J. Sparks, D. Vegh et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [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. Forcella, I. Garcia-Etxebarria and A. Uranga, E3-brane instantons and baryonic operators for D3-branes on toric singularities, JHEP 03 (2009) 041 [arXiv:0806.2291] [INSPIRE].
S. Franco, Bipartite Field Theories: from D-brane Probes to Scattering Amplitudes, JHEP 11 (2012) 141 [arXiv:1207.0807] [INSPIRE].
D. Xie and M. Yamazaki, Network and Seiberg Duality, JHEP 09 (2012) 036 [arXiv:1207.0811] [INSPIRE].
S. Franco, Cluster Transformations from Bipartite Field Theories, arXiv:1301.0316 [INSPIRE].
A.B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, arXiv:1107.5588 [INSPIRE].
S. Franco, Dimer Models, Integrable Systems and Quantum Teichmüller Space, JHEP 09 (2011) 057 [arXiv:1105.1777] [INSPIRE].
R. Eager, S. Franco and K. Schaeffer, Dimer Models and Integrable Systems, JHEP 06 (2012) 106 [arXiv:1107.1244] [INSPIRE].
S. Franco, D. Galloni and Y.-H. He, Towards the Continuous Limit of Cluster Integrable Systems, JHEP 09 (2012) 020 [arXiv:1203.6067] [INSPIRE].
A. Amariti, D. Forcella and A. Mariotti, Integrability on the Master Space, JHEP 06 (2012) 053 [arXiv:1203.1616] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A.B. Goncharov, A. Postnikov et al., Scattering Amplitudes and the Positive Grassmannian, arXiv:1212.5605 [INSPIRE].
S. Franco, D. Galloni and R.-K. Seong, New Directions in Bipartite Field Theories, JHEP 06 (2013) 032 [arXiv:1211.5139] [INSPIRE].
A. Amariti and D. Forcella, Scattering Amplitudes and Toric Geometry, JHEP 09 (2013) 133 [arXiv:1305.5252] [INSPIRE].
J.J. Heckman, C. Vafa, D. Xie and M. Yamazaki, String Theory Origin of Bipartite SCFTs, JHEP 05 (2013) 148 [arXiv:1211.4587] [INSPIRE].
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].
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].
O. Aharony, A. Hanany and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams, JHEP 01 (1998) 002 [hep-th/9710116] [INSPIRE].
S. Krippendorf, M.J. Dolan, A. Maharana and F. Quevedo, D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics, JHEP 06 (2010) 092 [arXiv:1002.1790] [INSPIRE].
M.J. Dolan, S. Krippendorf and F. Quevedo, Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity, JHEP 10 (2011) 024 [arXiv:1106.6039] [INSPIRE].
M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, The Web of D-branes at Singularities in Compact Calabi-Yau Manifolds, JHEP 05 (2013) 114 [arXiv:1304.2771] [INSPIRE].
P. Ouyang, Holomorphic D7 branes and flavored N = 1 gauge theories, Nucl. Phys. B 699 (2004) 207 [hep-th/0311084] [INSPIRE].
S. Kuperstein, Meson spectroscopy from holomorphic probes on the warped deformed conifold, JHEP 03 (2005) 014 [hep-th/0411097] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
D.R. Morrison and M.R. Plesser, Nonspherical horizons. 1., Adv. Theor. Math. Phys. 3 (1999) 1 [hep-th/9810201] [INSPIRE].
S.S. Gubser and I.R. Klebanov, Baryons and domain walls in an N = 1 superconformal gauge theory, Phys. Rev. D 58 (1998) 125025 [hep-th/9808075] [INSPIRE].
D. Berenstein, C.P. Herzog and I.R. Klebanov, Baryon spectra and AdS /CFT correspondence, JHEP 06 (2002) 047 [hep-th/0202150] [INSPIRE].
C.E. Beasley, BPS branes from baryons, JHEP 11 (2002) 015 [hep-th/0207125] [INSPIRE].
A. Butti, D. Forcella and A. Zaffaroni, Counting BPS baryonic operators in CFTs with Sasaki-Einstein duals, JHEP 06 (2007) 069 [hep-th/0611229] [INSPIRE].
D. Forcella, A. Hanany and A. Zaffaroni, Baryonic Generating Functions, JHEP 12 (2007) 022 [hep-th/0701236] [INSPIRE].
R.G. Leigh and M. Rozali, Brane boxes, anomalies, bending and tadpoles, Phys. Rev. D 59 (1999) 026004 [hep-th/9807082] [INSPIRE].
M. Wijnholt, Large volume perspective on branes at singularities, Adv. Theor. Math. Phys. 7 (2004) 1117 [hep-th/0212021] [INSPIRE].
C.P. Herzog, Exceptional collections and del Pezzo gauge theories, JHEP 04 (2004) 069 [hep-th/0310262] [INSPIRE].
A. Hanany, C.P. Herzog and D. Vegh, Brane tilings and exceptional collections, JHEP 07 (2006) 001 [hep-th/0602041] [INSPIRE].
A.M. Uranga, Local models for intersecting brane worlds, JHEP 12 (2002) 058 [hep-th/0208014] [INSPIRE].
A.M. Uranga, D-brane probes, RR tadpole cancellation and k-theory charge, Nucl. Phys. B 598 (2001) 225 [hep-th/0011048] [INSPIRE].
L.E. Ibáñez, R. Rabadán and A.M. Uranga, Anomalous U(1)’s in type-I and type IIB D = 4, N =1 string vacua, Nucl. Phys. B 542 (1999) 112 [hep-th/9808139][INSPIRE].
G. Aldazabal, D. Badagnani, L.E. Ibáñez and A.M. Uranga, Tadpole versus anomaly cancellation in D = 4, D = 6 compact IIB orientifolds, JHEP 06 (1999) 031 [hep-th/9904071] [INSPIRE].
S. Cremonesi, A. Hanany and R.-K. Seong, Double Handled Brane Tilings, JHEP 10 (2013) 001 [arXiv:1305.3607] [INSPIRE].
J. Park, R. Rabadán and A.M. Uranga, Orientifolding the conifold, Nucl. Phys. B 570 (2000) 38 [hep-th/9907086] [INSPIRE].
A.M. Uranga, Brane configurations for branes at conifolds, JHEP 01 (1999) 022 [hep-th/9811004] [INSPIRE].
K. Dasgupta and S. Mukhi, Brane constructions, conifolds and M-theory, Nucl. Phys. B 551 (1999) 204 [hep-th/9811139] [INSPIRE].
J.H. Brodie and A. Hanany, Type IIA superstrings, chiral symmetry and N = 1 4 − D gauge theory dualities, Nucl. Phys. B 506 (1997) 157 [hep-th/9704043] [INSPIRE].
A. Hanany and A. Zaffaroni, Chiral symmetry from type IIA branes, Nucl. Phys. B 509 (1998) 145 [hep-th/9706047] [INSPIRE].
A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, JHEP 10 (2007) 029 [hep-th/0511063] [INSPIRE].
N. Broomhead, Dimer models and Calabi-Yau algebras, arXiv:0901.4662 [INSPIRE].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen, D.B. Kaplan, A. Karch and L. Motl, Deconstructing (2,0) and little string theories, JHEP 01 (2003) 083 [hep-th/0110146] [INSPIRE].
K.D. Kennaway, Brane Tilings, Int. J. Mod. Phys. A 22 (2007) 2977 [arXiv:0706.1660] [INSPIRE].
K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
S. Benvenuti, S. Franco, A. Hanany, D. Martelli and J. Sparks, An Infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP 06 (2005) 064 [hep-th/0411264] [INSPIRE].
S. Elitzur, A. Giveon and D. Kutasov, Branes and N = 1 duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [INSPIRE].
H. Ooguri and Y. Ookouchi, Meta-Stable Supersymmetry Breaking Vacua on Intersecting Branes, Phys. Lett. B 641 (2006) 323 [hep-th/0607183] [INSPIRE].
S. Franco, I. Garcia-Etxebarria and A.M. Uranga, Non-supersymmetric meta-stable vacua from brane configurations, JHEP 01 (2007) 085 [hep-th/0607218] [INSPIRE].
I. Bena, E. Gorbatov, S. Hellerman, N. Seiberg and D. Shih, A Note on (Meta)stable Brane Configurations in MQCD, JHEP 11 (2006) 088 [hep-th/0608157] [INSPIRE].
O.J. Ganor, A Note on zeros of superpotentials in F-theory, Nucl. Phys. B 499 (1997) 55 [hep-th/9612077] [INSPIRE].
M. Buican and S. Franco, SUSY breaking mediation by D-brane instantons, JHEP 12 (2008) 030 [arXiv:0806.1964] [INSPIRE].
D. Baumann, A. Dymarsky, I.R. Klebanov, J.M. Maldacena, L.P. McAllister et al., On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [INSPIRE].
D. Baumann, A. Dymarsky, I.R. Klebanov, L. McAllister and P.J. Steinhardt, A Delicate universe, Phys. Rev. Lett. 99 (2007) 141601 [arXiv:0705.3837] [INSPIRE].
F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, Phys. Rev. Lett. 104 (2010) 231601 [arXiv:0910.5496] [INSPIRE].
A. Font, L.E. Ibáñez, F. Marchesano and D. Regalado, Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification, JHEP 03 (2013) 140 [Erratum ibid. 1307 (2013) 036] [arXiv:1211.6529] [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].
A. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The Baryonic branch of Klebanov-Strassler solution: A supersymmetric family of SU(3) structure backgrounds, JHEP 03 (2005) 069 [hep-th/0412187] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
S. Franco, A. Hanany and A.M. Uranga, Multi-flux warped throats and cascading gauge theories, JHEP 09 (2005) 028 [hep-th/0502113] [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].
S. Benvenuti and A. Hanany, Conformal manifolds for the conifold and other toric field theories, JHEP 08 (2005) 024 [hep-th/0502043] [INSPIRE].
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: 1306.6331
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
Franco, S., Uranga, A. Bipartite field theories from D-branes. J. High Energ. Phys. 2014, 161 (2014). https://doi.org/10.1007/JHEP04(2014)161
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)161