Abstract
We study indices for 5d gauge theories on S 1 × S 4 /ℤ n . In the large orbifold limit, n → ∞, we find evidence that the indices become 4d indices in the presence of a ’t Hooft line operator. The non-perturbative part of the index poses some subtleties when being compared to the 4d monopole bubbling which happens in the presence of ’t Hooft line operators. We study such monopole bubbling indices and find an interesting connection to the Hilbert series of the moduli space of instantons on an auxiliary ALE space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Källén and M. Zabzine, Twisted supersymmetric 5D Yang-Mills theory and contact geometry, JHEP 05 (2012) 125 [arXiv:1202.1956] [INSPIRE].
J. Källén, J. Qiu and M. Zabzine, The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere, JHEP 08 (2012) 157 [arXiv:1206.6008] [INSPIRE].
J. Källén, J. Minahan, A. Nedelin and M. Zabzine, N 3 -behavior from 5D Yang-Mills theory, JHEP 10 (2012) 184 [arXiv:1207.3763] [INSPIRE].
J.A. Minahan, A. Nedelin and M. Zabzine, 5D super Yang-Mills theory and the correspondence to AdS 7 /CFT 6, J. Phys. A 46 (2013) 355401 [arXiv:1304.1016] [INSPIRE].
J. Qiu and M. Zabzine, 5D Super Yang-Mills on Y p,q Sasaki-Einstein manifolds, arXiv:1307.3149 [INSPIRE].
H.-C. Kim, J. Kim and S. Kim, Instantons on the 5-sphere and M5-branes, arXiv:1211.0144 [INSPIRE].
H.-C. Kim and K. Lee, Supersymmetric M5 Brane Theories on R x CP2, JHEP 07 (2013) 072 [arXiv:1210.0853] [INSPIRE].
H.-C. Kim, S. Kim, S.-S. Kim and K. Lee, The general M5-brane superconformal index, arXiv:1307.7660 [INSPIRE].
T. Kawano and N. Matsumiya, 5D SYM on 3D Sphere and 2D YM, Phys. Lett. B 716 (2012) 450 [arXiv:1206.5966] [INSPIRE].
Y. Fukuda, T. Kawano and N. Matsumiya, 5D SYM and 2D q-Deformed YM, Nucl. Phys. B 869 (2013) 493 [arXiv:1210.2855] [INSPIRE].
J. Yagi, 3d TQFT from 6d SCFT, JHEP 08 (2013) 017 [arXiv:1305.0291] [INSPIRE].
S. Lee and M. Yamazaki, 3d Chern-Simons Theory from M5-branes, arXiv:1305.2429 [INSPIRE].
C. Cordova and D.L. Jafferis, Complex Chern-Simons from M5-branes on the Squashed Three-Sphere, arXiv:1305.2891 [INSPIRE].
C. Cordova and D.L. Jafferis, Five-Dimensional Maximally Supersymmetric Yang-Mills in Supergravity Backgrounds, arXiv:1305.2886 [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].
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].
A. Iqbal and C. Vafa, BPS Degeneracies and Superconformal Index in Diverse Dimensions, arXiv:1210.3605 [INSPIRE].
A. Brandhuber and Y. Oz, The D-4-D-8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
O. Bergman and D. Rodriguez-Gomez, 5d quivers and their AdS 6 duals, JHEP 07 (2012) 171 [arXiv:1206.3503] [INSPIRE].
A. Passias, A note on supersymmetric AdS 6 solutions of massive type IIA supergravity, JHEP 01 (2013) 113 [arXiv:1209.3267] [INSPIRE].
Y. Lozano, E.O. Colgain, D. Rodriguez-Gomez and K. Sfetsos, New Supersymmetric AdS 6 via T-duality, Phys. Rev. Lett. 110 (2013) 231601 [arXiv:1212.1043] [INSPIRE].
D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, arXiv:1207.4359 [INSPIRE].
O. Bergman and D. Rodriguez-Gomez, Probing the Higgs branch of 5d fixed point theories with dual giant gravitons in AdS 6, JHEP 12 (2012) 047 [arXiv:1210.0589] [INSPIRE].
B. Assel, J. Estes and M. Yamazaki, Wilson Loops in 5d N = 1 SCFTs and AdS/CFT, arXiv:1212.1202 [INSPIRE].
O. Bergman, D. Rodriguez-Gomez and G. Zafrir, 5d superconformal indices at large-N and holography, JHEP 08 (2013) 081 [arXiv:1305.6870] [INSPIRE].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [INSPIRE].
S.S. Razamat and B. Willett, Global Properties of Supersymmetric Theories and the Lens Space, arXiv:1307.4381 [INSPIRE].
F. Benini, T. Nishioka and M. Yamazaki, 4d Index to 3d Index and 2d TQFT, Phys. Rev. D 86 (2012) 065015 [arXiv:1109.0283] [INSPIRE].
Y. Ito, T. Okuda and M. Taki, Line operators on S 1 × R 3 and quantization of the Hitchin moduli space, JHEP 04 (2012) 010 [arXiv:1111.4221] [INSPIRE].
D. Gang, E. Koh and K. Lee, Line Operator Index on S 1 × S 3, JHEP 05 (2012) 007 [arXiv:1201.5539] [INSPIRE].
P. Kronheimer, Monopoles and taub-nut metrics, Transfer Thesis, Oxford University, Oxford U.K. (1985).
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
A. Dey, A. Hanany, N. Mekareeya, D. Rodríguez-Gómez and R.-K. Seong, Hilbert Series for Moduli Spaces of Instantons on ℂ2 /ℤ n , arXiv:1309.0812 [INSPIRE].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
Y. Ito, K. Maruyoshi and T. Okuda, Scheme dependence of instanton counting in ALE spaces, JHEP 05 (2013) 045 [arXiv:1303.5765] [INSPIRE].
G. Bonelli, K. Maruyoshi, A. Tanzini and F. Yagi, N = 2 gauge theories on toric singularities, blow-up formulae and W-algebrae, JHEP 01 (2013) 014 [arXiv:1208.0790] [INSPIRE].
A. Hanany, N. Mekareeya and S.S. Razamat, Hilbert series for moduli spaces of two instantons, JHEP 01 (2013) 070 [arXiv:1205.4741] [INSPIRE].
D. Rodriguez-Gomez and G. Zafrir, On the 5d instanton index as a Hilbert series, arXiv:1305.5684 [INSPIRE].
R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176] [INSPIRE].
U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multiinstanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Multi instanton calculus on ALE spaces, Nucl. Phys. B 703 (2004) 518 [hep-th/0406243] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Instanton on toric singularities and black hole countings, JHEP 12 (2006) 073 [hep-th/0610154] [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].
A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
S. Benvenuti, A. Hanany and N. Mekareeya, The Hilbert series of the one instanton moduli space, JHEP 06 (2010) 100 [arXiv:1005.3026] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1309.1213
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Mekareeya, N., Rodríguez-Gómez, D. 5d gauge theories on orbifolds and 4d ’t Hooft line indices. J. High Energ. Phys. 2013, 157 (2013). https://doi.org/10.1007/JHEP11(2013)157
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2013)157