Abstract
We discuss Type IIB 5-brane configurations for 5d \( \mathcal{N}=1 \) gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
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References
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].
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132] [INSPIRE].
A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [INSPIRE].
N.C. Leung and C. Vafa, Branes and toric geometry, Adv. Theor. Math. Phys. 2 (1998) 91 [hep-th/9711013] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
I. Brunner and A. Karch, Branes and six-dimensional fixed points, Phys. Lett. B 409 (1997) 109 [hep-th/9705022] [INSPIRE].
O. Bergman and G. Zafrir, 5d fixed points from brane webs and O7-planes, JHEP 12 (2015) 163 [arXiv:1507.03860] [INSPIRE].
F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and N = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-brane webs, symmetry enhancement and duality in 5d supersymmetric gauge theory, JHEP 03 (2014) 112 [arXiv:1311.4199] [INSPIRE].
O. Bergman and G. Zafrir, Lifting 4d dualities to 5d, JHEP 04 (2015) 141 [arXiv:1410.2806] [INSPIRE].
G. Zafrir, Brane webs and O5-planes, JHEP 03 (2016) 109 [arXiv:1512.08114] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, 5-brane webs for 5d \( \mathcal{N}=1 \) G 2 gauge theories, JHEP 03 (2018) 125 [arXiv:1801.03916] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Dualities and 5-brane webs for 5d rank 2 SCFTs, JHEP 12 (2018) 016 [arXiv:1806.10569] [INSPIRE].
P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On Geometric Classification of 5d SCFTs, JHEP 04 (2018) 103 [arXiv:1801.04036] [INSPIRE].
Y. Tachikawa and S. Terashima, Seiberg-Witten geometries revisited, JHEP 09 (2011) 010 [arXiv:1108.2315] [INSPIRE].
K. Ohmori, Y. Tachikawa and G. Zafrir, Compactifications of 6d N = (1, 0) SCFTs with non-trivial Stiefel-Whitney classes, JHEP 04 (2019) 006 [arXiv:1812.04637] [INSPIRE].
P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards classification of 5d SCFTs: single gauge node, arXiv:1705.05836 [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Discrete theta angle from an O5-plane, JHEP 11 (2017) 041 [arXiv:1707.07181] [INSPIRE].
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
C. Closset, M. Del Zotto and V. Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys. 6 (2019) 052 [arXiv:1812.10451] [INSPIRE].
H. Hayashi, H.-C. Kim and T. Nishinaka, Topological strings and 5d T N partition functions, JHEP 06 (2014) 014 [arXiv:1310.3854] [INSPIRE].
H. Hayashi and G. Zoccarato, Exact partition functions of Higgsed 5d T N theories, JHEP 01 (2015) 093 [arXiv:1409.0571] [INSPIRE].
S.-S. Kim, M. Taki and F. Yagi, Tao probing the end of the world, PTEP 2015 (2015) 083B02 [arXiv:1504.03672] [INSPIRE].
H. Hayashi and G. Zoccarato, Topological vertex for Higgsed 5d T N theories, JHEP 09 (2015) 023 [arXiv:1505.00260] [INSPIRE].
S.-S. Kim and F. Yagi, Topological vertex formalism with O5-plane, Phys. Rev. D 97 (2018) 026011 [arXiv:1709.01928] [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].
D. Kutasov, Orbifolds and solitons, Phys. Lett. B 383 (1996) 48 [hep-th/9512145] [INSPIRE].
A. Sen, Duality and orbifolds, Nucl. Phys. B 474 (1996) 361 [hep-th/9604070] [INSPIRE].
A. Kapustin, D(n) quivers from branes, JHEP 12 (1998) 015 [hep-th/9806238] [INSPIRE].
A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2N) global symmetry, JHEP 07 (1999) 009 [hep-th/9903242] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee, M. Taki and F. Yagi, A new 5d description of 6d D-type minimal conformal matter, JHEP 08 (2015) 097 [arXiv:1505.04439] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, 6d SCFTs, 5d dualities and Tao web diagrams, arXiv:1509.03300 [INSPIRE].
H. Hayashi et al., More on 5d descriptions of 6d SCFTs, JHEP 10 (2016) 126 [arXiv:1512.08239] [INSPIRE].
M.R. Gaberdiel and B. Zwiebach, Exceptional groups from open strings, Nucl. Phys. B 518 (1998) 151 [hep-th/9709013] [INSPIRE].
M.R. Gaberdiel, T. Hauer and B. Zwiebach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117 [hep-th/9801205] [INSPIRE].
O. DeWolfe, A. Hanany, A. Iqbal and E. Katz, Five-branes, seven-branes and five-dimensional E(n) field theories, JHEP 03 (1999) 006 [hep-th/9902179] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Equivalence of several descriptions for 6d SCFT, JHEP 01 (2017) 093 [arXiv:1607.07786] [INSPIRE].
G. Zafrir, Brane webs, 5d gauge theories and 6d \( \mathcal{N}=\left(1,0\right) \) SCFT’s, JHEP 12 (2015) 157 [arXiv:1509.02016] [INSPIRE].
O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Uncovering infinite symmetries on [p, q] 7-branes: Kac-Moody algebras and beyond, Adv. Theor. Math. Phys. 3 (1999) 1835 [hep-th/9812209] [INSPIRE].
K. Ohmori and H. Shimizu, S 1 /T 2 compactifications of 6d \( \mathcal{N}=\left(1,0\right) \) theories and brane webs, JHEP 03 (2016) 024 [arXiv:1509.03195] [INSPIRE].
H. Hayashi and K. Ohmori, 5d/6d DE instantons from trivalent gluing of web diagrams, JHEP 06 (2017) 078 [arXiv:1702.07263] [INSPIRE].
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Hayashi, H., Kim, SS., Lee, K. et al. Rank-3 antisymmetric matter on 5-brane webs. J. High Energ. Phys. 2019, 133 (2019). https://doi.org/10.1007/JHEP05(2019)133
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DOI: https://doi.org/10.1007/JHEP05(2019)133