Abstract
We classify the first few brane tilings on a genus 2 Riemann surface and identify their toric Calabi-Yau moduli spaces. These brane tilings are extensions of tilings on the 2-torus, which represent one of the largest known classes of 4d \( \mathcal{N}=1 \) superconformal field theories for D3-branes. The classification consists of 16 distinct genus 2 brane tilings with up to 8 quiver fields and 4 superpotential terms. The Higgs mechanism is used to relate the different theories.
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References
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. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: the Plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].
A. Butti, D. Forcella, A. Hanany, D. Vegh and A. Zaffaroni, Counting Chiral Operators in Quiver Gauge Theories, JHEP 11 (2007) 092 [arXiv:0705.2771] [INSPIRE].
L. Grant and K. Narayan, Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory, Class. Quant. Grav. 25 (2008) 045010 [hep-th/0701189] [INSPIRE].
J. Davey, A. Hanany and J. Pasukonis, On the Classification of Brane Tilings, JHEP 01 (2010) 078 [arXiv:0909.2868] [INSPIRE].
A. Ishii and K. Ueda, On moduli spaces of quiver representations associated with dimer models, arXiv:0710.1898.
D. Forcella, Operators and vacua of N = 1 field theories, Nuovo Cim. B 125 (2010) 905 [arXiv:0912.3444] [INSPIRE].
A. Hanany, Counting BPS operators in the chiral ring: the plethystic story, AIP Conf. Proc. 939 (2007) 165 [INSPIRE].
A. Hanany and A. Zaffaroni, The master space of supersymmetric gauge theories, Adv. High Energy Phys. 2010 (2010) 427891.
A. Zaffaroni, The master space of N=1 quiver gauge theories: Counting BPS operators, prepared for 8 τη Workshop on Continuous Advances in QCD (CAQCD-08), Minneapolis, Minnesota, U.S.A., 15-18 May 2008.
D. Forcella, Master Space and Hilbert Series for N = 1 Field Theories, arXiv:0902.2109 [INSPIRE].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, Mastering the Master Space, Lett. Math. Phys. 85 (2008) 163 [arXiv:0801.3477] [INSPIRE].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, The Master Space of N = 1 Gauge Theories, JHEP 08 (2008) 012 [arXiv:0801.1585] [INSPIRE].
B. Feng, S. Franco, A. Hanany and Y.-H. He, Symmetries of toric duality, JHEP 12 (2002) 076 [hep-th/0205144] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, JHEP 08 (2001) 040 [hep-th/0104259] [INSPIRE].
B. Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as Seiberg duality and brane diamonds, JHEP 12 (2001) 035 [hep-th/0109063] [INSPIRE].
C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [INSPIRE].
A. Butti and A. Zaffaroni, R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization, JHEP 11 (2005) 019 [hep-th/0506232] [INSPIRE].
S. Franco, A. Hanany and P. Kazakopoulos, Hidden exceptional global symmetries in 4 − D CFTs, JHEP 07 (2004) 060 [hep-th/0404065] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
J. Bagger and N. Lambert, Modeling Multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].
A. Gustavsson, Selfdual strings and loop space Nahm equations, JHEP 04 (2008) 083 [arXiv:0802.3456] [INSPIRE].
A. Hanany and A. Zaffaroni, Tilings, Chern-Simons Theories and M2 Branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [INSPIRE].
A. Hanany, D. Vegh and A. Zaffaroni, Brane Tilings and M2 Branes, JHEP 03 (2009) 012 [arXiv:0809.1440] [INSPIRE].
K. Ueda and M. Yamazaki, Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories, JHEP 12 (2008) 045 [arXiv:0808.3768] [INSPIRE].
J. Davey, A. Hanany, N. Mekareeya and G. Torri, Higgsing M2-brane Theories, JHEP 11 (2009) 028 [arXiv:0908.4033] [INSPIRE].
J. Davey, A. Hanany, N. Mekareeya and G. Torri, M2-Branes and Fano 3-folds, J. Phys. A 44 (2011) 405401 [arXiv:1103.0553] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3, JHEP 09 (2011) 005 [arXiv:1105.2299] [INSPIRE].
C. Closset and S. Cremonesi, Toric Fano varieties and Chern-Simons quivers, JHEP 05 (2012) 060 [arXiv:1201.2431] [INSPIRE].
A. Hanany and A. Zaffaroni, On the realization of chiral four-dimensional gauge theories using branes, JHEP 05 (1998) 001 [hep-th/9801134] [INSPIRE].
S. Franco, Bipartite Field Theories: from D-brane Probes to Scattering Amplitudes, JHEP 11 (2012) 141 [arXiv:1207.0807] [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. Hanany and R.-K. Seong, Brane Tilings and Reflexive Polygons, Fortsch. Phys. 60 (2012) 695 [arXiv:1201.2614] [INSPIRE].
A. Hanany and R.-K. Seong, Brane Tilings and Specular Duality, JHEP 08 (2012) 107 [arXiv:1206.2386] [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].
D. Forcella, A. Hanany and A. Zaffaroni, Master Space, Hilbert Series and Seiberg Duality, JHEP 07 (2009) 018 [arXiv:0810.4519] [INSPIRE].
A. Hanany, D. Orlando and S. Reffert, Sublattice Counting and Orbifolds, JHEP 06 (2010) 051 [arXiv:1002.2981] [INSPIRE].
J. Davey, A. Hanany and R.-K. Seong, Counting Orbifolds, JHEP 06 (2010) 010 [arXiv:1002.3609] [INSPIRE].
J. Davey, A. Hanany and R.-K. Seong, An Introduction to Counting Orbifolds, Fortsch. Phys. 59 (2011) 677 [arXiv:1102.0015] [INSPIRE].
A. Hanany, V. Jejjala, S. Ramgoolam and R.-K. Seong, Calabi-Yau Orbifolds and Torus Coverings, JHEP 09 (2011) 116 [arXiv:1105.3471] [INSPIRE].
A. Hanany and R.-K. Seong, Symmetries of Abelian Orbifolds, JHEP 01 (2011) 027 [arXiv:1009.3017] [INSPIRE].
S. Franco et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [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].
D.R. Gulotta, Properly ordered dimers, R-charges and an efficient inverse algorithm, JHEP 10 (2008) 014 [arXiv:0807.3012] [INSPIRE].
R. Bocklandt, Consistency conditions for dimer models, arXiv:1104.1592 [INSPIRE].
V. Jejjala, S. Ramgoolam and D. Rodriguez-Gomez, Toric CFTs, Permutation Triples and Belyi Pairs, JHEP 03 (2011) 065 [arXiv:1012.2351] [INSPIRE].
K.D. Kennaway, Brane Tilings, Int. J. Mod. Phys. A 22 (2007) 2977 [arXiv:0706.1660] [INSPIRE].
A. Butti and A. Zaffaroni, From toric geometry to quiver gauge theory: the Equivalence of a-maximization and Z-minimization, Fortsch. Phys. 54 (2006) 309 [hep-th/0512240] [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].
D. Martelli, J. Sparks and S.-T. Yau, The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds, Commun. Math. Phys. 268 (2006) 39 [hep-th/0503183] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
B. Feng, S. Franco, A. Hanany and Y.-H. He, UnHiggsing the del Pezzo, JHEP 08 (2003) 058 [hep-th/0209228] [INSPIRE].
S. Franco and D. Vegh, Moduli spaces of gauge theories from dimer models: proof of the correspondence, JHEP 11 (2006) 054 [hep-th/0601063] [INSPIRE].
D. Martelli and J. Sparks, Moduli spaces of Chern-Simons quiver gauge theories and AdS 4 /CFT 3, Phys. Rev. D 78 (2008) 126005 [arXiv:0808.0912] [INSPIRE].
P. Kasteleyn, The statistics of dimers on a lattice: I. the number of dimer arrangements on a quadratic lattice, Physica 27 (1961) 1209.
P.W. Kasteleyn, Graph theory and crystal physics, Graph theory and theoretical physics 1 (1967) 43.
R. Kenyon, A. Okounkov and S. Sheffield, Dimers and amoebae, math-ph/0311005 [INSPIRE].
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Cremonesi, S., Hanany, A. & Seong, RK. Double handled brane tilings. J. High Energ. Phys. 2013, 1 (2013). https://doi.org/10.1007/JHEP10(2013)001
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DOI: https://doi.org/10.1007/JHEP10(2013)001