Abstract
We report a novel BPS jumping phenomenon of 5d \( \mathcal{N} \) = 1 supersymmetric gauge theories whose brane configuration is equipped with an O7-plane. The study of the relation between O7+-plane and O7−-plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU(2N + 8) gauge theory with a symmetric hypermultiplet converted to the SU(2N) gauge theory with an antisymmetric hypermultiplet. The other is pure SO(2N + 8) gauge theory jumping to pure Sp(N) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an Op-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions (p = 6, 5 respectively).
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References
J. Polchinski, Dirichlet Branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
J. Dai, R.G. Leigh and J. Polchinski, New Connections Between String Theories, Mod. Phys. Lett. A 4 (1989) 2073 [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. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
K. Landsteiner and E. Lopez, New curves from branes, Nucl. Phys. B 516 (1998) 273 [hep-th/9708118] [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov and D. Tsabar, Branes, orientifolds and chiral gauge theories, Nucl. Phys. B 524 (1998) 251 [hep-th/9801020] [INSPIRE].
A. Giveon and D. Kutasov, Brane Dynamics and Gauge Theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].
O. Bergman and G. Zafrir, 5d fixed points from brane webs and O7-planes, JHEP 12 (2015) 163 [arXiv:1507.03860] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Seiberg-Witten curves with O7±-planes, JHEP 11 (2023) 178 [arXiv:2306.11631] [INSPIRE].
H.-C. Kim, M. Kim, S.-S. Kim and G. Zafrir, Superconformal indices for non-Lagrangian theories in five dimensions, JHEP 03 (2024) 164 [arXiv:2307.03231] [INSPIRE].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
Y. Tachikawa, Frozen singularities in M and F theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
L.C. Jeffrey and F.C. Kirwan, Localization for nonabelian group actions, alg-geom/9307001 [INSPIRE].
M. Brion and M. Vergne, Arrangements of hyperplanes I: Rational functions and Jeffrey-Kirwan residue, math/9903178.
A. Szenes and M. Vergne, Toric reduction and a conjecture of Batyrev and Materov, math/0306311 [https://doi.org/10.1007/s00222-004-0375-2].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic Genera of 2d \( \mathcal{N} \) = 2 Gauge Theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [INSPIRE].
S. Nawata and R.-D. Zhu, Instanton counting and O-vertex, JHEP 09 (2021) 190 [arXiv:2107.03656] [INSPIRE].
Y. Chen, J. Jiang, S. Nawata and Y. Shao, Instantons on Young diagrams with matters, JHEP 03 (2023) 120 [arXiv:2301.02342] [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].
M.R. Douglas, S.H. Katz and C. Vafa, Small instantons, Del Pezzo surfaces and type I-prime theory, Nucl. Phys. B 497 (1997) 155 [hep-th/9609071] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, Discrete θ and the 5d superconformal index, JHEP 01 (2014) 079 [arXiv:1310.2150] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Complete prepotential for 5d \( \mathcal{N} \) = 1 superconformal field theories, JHEP 02 (2020) 074 [arXiv:1912.10301] [INSPIRE].
Q. Jia and P. Yi, Holonomy saddles and 5d BPS quivers, JHEP 10 (2022) 098 [arXiv:2208.14579] [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].
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].
E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
O.J. Ganor and A. Hanany, Small E(8) instantons and tensionless noncritical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003] [INSPIRE].
B. Haghighat et al., M-Strings, Commun. Math. Phys. 334 (2015) 779 [arXiv:1305.6322] [INSPIRE].
B. Haghighat, G. Lockhart and C. Vafa, Fusing E-strings to heterotic strings: E + E → H, Phys. Rev. D 90 (2014) 126012 [arXiv:1406.0850] [INSPIRE].
J. Kim et al., Elliptic Genus of E-strings, JHEP 09 (2017) 098 [arXiv:1411.2324] [INSPIRE].
W. Cai, M.-X. Huang and K. Sun, On the Elliptic Genus of Three E-strings and Heterotic Strings, JHEP 01 (2015) 079 [arXiv:1411.2801] [INSPIRE].
S.-S. Kim, M. Taki and F. Yagi, Tao Probing the End of the World, PTEP 2015 (2015) 083B02 [arXiv:1504.03672] [INSPIRE].
S.-S. Kim and F. Yagi, Topological vertex formalism with O5-plane, Phys. Rev. D 97 (2018) 026011 [arXiv:1709.01928] [INSPIRE].
H.-C. Kim, M. Kim, S.-S. Kim and K.-H. Lee, Bootstrapping BPS spectra of 5d/6d field theories, JHEP 04 (2021) 161 [arXiv:2101.00023] [INSPIRE].
S.-S. Kim and X.-Y. Wei, Refined topological vertex with ON-planes, JHEP 08 (2022) 006 [arXiv:2201.12264] [INSPIRE].
C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5d SCFT, JHEP 07 (2015) 063 [Addendum ibid. 04 (2016) 094] [arXiv:1406.6793] [INSPIRE].
D. Gaiotto and H.-C. Kim, Duality walls and defects in 5d \( \mathcal{N} \) = 1 theories, JHEP 01 (2017) 019 [arXiv:1506.03871] [INSPIRE].
J. Chen et al., E-string quantum curve, Nucl. Phys. B 973 (2021) 115602 [arXiv:2103.16996] [INSPIRE].
S. Shadchin, On certain aspects of string theory/gauge theory correspondence, hep-th/0502180 [INSPIRE].
H.-C. Kim, S.-S. Kim and K. Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].
U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multiinstanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108] [INSPIRE].
H.-C. Kim et al., Probing Hanany-Witten Transitions of 5d SCFTs via Supersymmetric Defects, in progress.
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].
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].
A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d Topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The Superconformal Index of the E6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge Theories and Macdonald Polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].
D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
S. Benvenuti and S. Pasquetti, 3D-partition functions on the sphere: exact evaluation and mirror symmetry, JHEP 05 (2012) 099 [arXiv:1105.2551] [INSPIRE].
S. Nawata, M. Sperling, H.E. Wang and Z. Zhong, Magnetic quivers and line defects — On a duality between 3d \( \mathcal{N} \) = 4 unitary and orthosymplectic quivers, JHEP 02 (2022) 174 [arXiv:2111.02831] [INSPIRE].
S.S. Razamat and B. Willett, Down the rabbit hole with theories of class \( \mathcal{S} \), JHEP 10 (2014) 099 [arXiv:1403.6107] [INSPIRE].
L. Rozansky and E. Witten, HyperKahler geometry and invariants of three manifolds, Selecta Math. 3 (1997) 401 [hep-th/9612216] [INSPIRE].
C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [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].
M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld and Y.I. Manin, Construction of Instantons, Phys. Lett. A 65 (1978) 185 [INSPIRE].
G.W. Moore, N. Nekrasov and S. Shatashvili, Integrating over Higgs branches, Commun. Math. Phys. 209 (2000) 97 [hep-th/9712241] [INSPIRE].
N. Nekrasov and S. Shadchin, ABCD of instantons, Commun. Math. Phys. 252 (2004) 359 [hep-th/0404225] [INSPIRE].
Acknowledgments
We thank Jin Chen, Hirotaka Hayashi, Chiung Hwang, Jiaqun Jiang, Hee-Cheol Kim, Minsung Kim, Kimyeong Lee, Yiwen Pan, Marcus Sperling, Kaiwen Sun, Hao Wang, Yi-Nan Wang, Xin Wang, Piljin Yi, Gabi Zafrir, Xinyu Zhang, Jiahao Zheng, Zhenghao Zhong and Rui-Dong Zhu for valuable discussions. SK thanks KIAS for hosting “Autumn Symposium on String Theory 2022,” “Recent Trends in Supersymmetric Field Theories 2023” where part of the work is presented and the organizers of “2023 East Asia Joint Workshop on Fields and Strings” for the invitation and hospitality. SK, XL, and FY thank Fudan university for hosting “String Theory and Quantum Field Theory 2024” where part of the work is done. SK is supported by NSFC grant No. 12250610188. XL is supported by NSFC grant No. 11501470, No. 11426187, No. 11791240561, the Fundamental Research Funds for the Central Universities 2682021ZTPY043 and partially supported by NSFC grant No. 11671328. The work of SN was supported by NSFC Grant No.11850410428 and Shanghai Foreign Expert grant No. 22WZ2502100. FY is supported by the NSFC grant No. 11950410490 and by Start-up research grant YH1199911312101 and also partially supported by the Fundamental Research Funds for the Central Universities 2682021ZTPY043.
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Kim, SS., Li, X., Nawata, S. et al. Freezing and BPS jumping. J. High Energ. Phys. 2024, 340 (2024). https://doi.org/10.1007/JHEP05(2024)340
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DOI: https://doi.org/10.1007/JHEP05(2024)340