Abstract
Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), \( {\mathcal{T}}_{3,\frac{3}{2}} \), emerging in this duality splits into a free piece and an interacting piece, \( {\mathcal{T}}_X \), even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about \( {\mathcal{T}}_X \) by bootstrapping its chiral algebra, \( {}_{\mathcal{X}}\left({\mathcal{T}}_X\right) \), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for \( {\mathcal{T}}_X \) and, by studying this quantity in the limit of small S 1, we make contact with a proposed S 1 reduction. Along the way, we discuss various properties of \( {\mathcal{T}}_X \) : as an \( \mathcal{N} \) = 1 theory, it has flavor symmetry SU(3) × SU(2) × U(1), the central charge of \( {}_{\mathcal{X}}\left({\mathcal{T}}_X\right) \) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of \( {\mathcal{T}}_X \) theories (giving us a surprisingly close AD relative of Gaiotto’s T N theories), but it does lead to some open questions in the context of the chiral algebra/4D \( \mathcal{N} \) =2SCFT correspondence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
M. Buican, S. Giacomelli, T. Nishinaka and C. Papageorgakis, Argyres-Douglas theories and S-duality, JHEP 02 (2015) 185 [arXiv:1411.6026] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
M. Buican, Minimal distances between SCFTs, JHEP 01 (2014) 155 [arXiv:1311.1276] [INSPIRE].
E. Witten, An SU(2) anomaly, Phys. Lett. 117B (1982) 324 [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].
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite chiral symmetry in four dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
M. Buican and T. Nishinaka, On the superconformal index of Argyres-Douglas theories, J. Phys. A 49 (2016) 015401 [arXiv:1505.05884] [INSPIRE].
C. Cordova and S.-H. Shao, Schur indices, BPS particles and Argyres-Douglas theories, JHEP 01 (2016) 040 [arXiv:1506.00265] [INSPIRE].
D. Xie, W. Yan and S.-T. Yau, Chiral algebra of Argyres-Douglas theory from M5 brane, arXiv:1604.02155 [INSPIRE].
V.G. Kac and M. Wakimoto, A remark on boundary level admissible representations, Compt. Rend. Math. 355 (2017) 128.
V.P. Spiridonov and S.O. Warnaar, Inversions of integral operators and elliptic beta integrals on root systems, Adv. Math. 207 (2006) 91.
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The superconformal index of the E 6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [INSPIRE].
M. Lemos and W. Peelaers, Chiral algebras for Trinion theories, JHEP 02 (2015) 113 [arXiv:1411.3252] [INSPIRE].
V.K. Dobrev and V.B. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. 162B (1985) 127 [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].
M. Buican and T. Nishinaka, Argyres-Douglas theories, S 1 reductions and topological symmetries, J. Phys. A 49 (2016) 045401 [arXiv:1505.06205] [INSPIRE].
L. Fredrickson, D. Pei, W. Yan and K. Ye, Argyres-Douglas theories, chiral algebras and wild Hitchin characters, arXiv:1701.08782 [INSPIRE].
C. Beem, M. Lemos, P. Liendo, L. Rastelli and B.C. van Rees, The N = 2 superconformal bootstrap, JHEP 03 (2016) 183 [arXiv:1412.7541] [INSPIRE].
M. Buican and T. Nishinaka, Argyres-Douglas theories, the Macdonald index and an RG inequality, JHEP 02 (2016) 159 [arXiv:1509.05402] [INSPIRE].
T. Creutzig, W-algebras for Argyres-Douglas theories, arXiv:1701.05926 [INSPIRE].
M. Buican and T. Nishinaka, Conformal manifolds in four dimensions and chiral algebras, J. Phys. A 49 (2016) 465401 [arXiv:1603.00887] [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in N = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
A. Arabi Ardehali, High-temperature asymptotics of supersymmetric partition functions, JHEP 07 (2016) 025 [arXiv:1512.03376] [INSPIRE].
L. Di Pietro and M. Honda, Cardy formula for 4d SUSY theories and localization, JHEP 04 (2017) 055 [arXiv:1611.00380] [INSPIRE].
M. Buican and T. Nishinaka, On irregular singularity wave functions and superconformal indices, arXiv:1705.07173 [INSPIRE].
T. Nishioka, Y. Tachikawa and M. Yamazaki, 3d partition function as overlap of wavefunctions, JHEP 08 (2011) 003 [arXiv:1105.4390] [INSPIRE].
D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled N = 2 theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [INSPIRE].
S. Benvenuti and S. Giacomelli, Compactification of dualities with decoupled operators and 3d mirror symmetry, arXiv:1706.02225 [INSPIRE].
P. Liendo, I. Ramirez and J. Seo, Stress-tensor OPE in N = 2 superconformal theories, JHEP 02 (2016) 019 [arXiv:1509.00033] [INSPIRE].
I.A. Ramírez, Mixed OPEs in N = 2 superconformal theories, JHEP 05 (2016) 043 [arXiv:1602.07269] [INSPIRE].
P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs III: enhanced Coulomb branches and central charges, arXiv:1609.04404 [INSPIRE].
S. Cecotti, J. Song, C. Vafa and W. Yan, Superconformal index, BPS monodromy and chiral algebras, arXiv:1511.01516 [INSPIRE].
J. Song, D. Xie and W. Yan, Vertex operator algebras of Argyres-Douglas theories from M 5-branes, arXiv:1706.01607 [INSPIRE].
J. Song, Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT, JHEP 02 (2016) 045 [arXiv:1509.06730] [INSPIRE].
D. Xie and S.-T. Yau, Argyres-Douglas matter and N = 2 dualities, arXiv:1701.01123 [INSPIRE].
A. Gadde, S.S. Razamat and B. Willett, “Lagrangian” for a non-Lagrangian field theory with N = 2 supersymmetry, Phys. Rev. Lett. 115 (2015) 171604 [arXiv:1505.05834] [INSPIRE].
K. Maruyoshi and J. Song, Enhancement of supersymmetry via renormalization group flow and the superconformal index, Phys. Rev. Lett. 118 (2017) 151602 [arXiv:1606.05632] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Coulomb branch and the moduli space of instantons, JHEP 12 (2014) 103 [arXiv:1408.6835] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY gauge theories on three-sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [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. Cremonesi, A. Hanany and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories, JHEP 01 (2014) 005 [arXiv:1309.2657] [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: 1706.03797
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
Buican, M., Laczko, Z. & Nishinaka, T. \( \mathcal{N} \) = 2 S-duality revisited. J. High Energ. Phys. 2017, 87 (2017). https://doi.org/10.1007/JHEP09(2017)087
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)087