Abstract
We study certain higher-spin chiral operators in \( \mathcal{N}=2 \) superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality (“type A” theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is independent of the details of the superconformal index. We then use the index to show that if a theory is not of type A but has an \( \mathcal{N}=2 \)-preserving deformation by a relevant operator that takes it to a theory of this type in the infrared, the ultraviolet theory cannot have these higher-spin operators either. As an application of this discussion, we give a simple prescription to extract the 2a − c conformal anomaly directly from the superconformal index. We also comment on how this procedure works in the holographic limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
C. Beem et al., Infinite chiral symmetry in four dimensions, arXiv:1312.5344 [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, W symmetry in six dimensions, arXiv:1404.1079 [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [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].
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].
S. Cecotti, A. Neitzke and C. Vafa, R-twisting and 4D/2D correspondences, arXiv:1006.3435 [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [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].
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].
F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory, JHEP 12 (2002) 071 [hep-th/0211170] [INSPIRE].
V.K. Dobrev and V.B. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. B 162 (1985) 127 [INSPIRE].
V.K. Dobrev and V.B. Petkova, On the group theoretical approach to extended conformal supersymmetry: classification of multiplets, Lett. Math. Phys. 9 (1985) 287 [INSPIRE].
V.K. Dobrev and V.B. Petkova, Group theoretical approach to extended conformal supersymmetry: function space realizations and invariant differential operators, Fortsch. Phys. 35 (1987) 537 [INSPIRE].
H. Osborn, N = 1 superconformal symmetry in four-dimensional quantum field theory, Annals Phys. 272 (1999) 243 [hep-th/9808041] [INSPIRE].
M. Buican, Minimal distances between SCFTs, JHEP 01 (2014) 155 [arXiv:1311.1276] [INSPIRE].
J.-F. Fortin, K. Intriligator and A. Stergiou, Current OPEs in superconformal theories, JHEP 09 (2011) 071 [arXiv:1107.1721] [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].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
O. Aharony et al., The Hagedorn-deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. B 864 (2012) 884] [arXiv:0903.4172] [INSPIRE].
S. Nawata, Localization of N = 4 superconformal field theory on S 1 × S 3 and index, JHEP 11 (2011) 144 [arXiv:1104.4470] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The geometry of supersymmetric partition functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP 08 (2014) 123 [arXiv:1405.5144] [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. Hanany and C. Romelsberger, Counting BPS operators in the chiral ring of N = 2 supersymmetric gauge theories or N = 2 braine surgery, Adv. Theor. Math. Phys. 11 (2007) 1091 [hep-th/0611346] [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].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with E(n) global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].
K. Kodaira, On compact analytic surfaces. II, Ann. Math. 77 (1963) 563.
K. Kodaira, On compact analytic surfaces. III, Ann. Math. 78 (1963) 1.
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].
A.D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, 1/N 2 corrections to the holographic Weyl anomaly, JHEP 01 (2014) 002 [arXiv:1310.2611] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, The shortened KK spectrum of IIB supergravity on Y p,q, JHEP 02 (2014) 064 [arXiv:1311.4550] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in D = 4 and D = 6, arXiv:1407.6061 [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometric integrals and ’t Hooft anomaly matching conditions, JHEP 06 (2012) 016 [arXiv:1203.5677] [INSPIRE].
A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].
E. Witten, On S duality in Abelian gauge theory, Selecta Math. 1 (1995) 383 [hep-th/9505186] [INSPIRE].
G.W. Moore and E. Witten, Integration over the u plane in Donaldson theory, Adv. Theor. Math. Phys. 1 (1997) 298 [hep-th/9709193] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477-478] [hep-th/9906070] [INSPIRE].
V.I. Arnold, S.M. Gusein-Zade and A.N. Varěncko, Singularities of differentiable maps, Birkhäuser, Boston U.S.A. (1988).
D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled N = 2 theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [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: 1407.2835
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., Nishinaka, T. & Papageorgakis, C. Constraints on chiral operators in \( \mathcal{N}=2 \) SCFTs. J. High Energ. Phys. 2014, 95 (2014). https://doi.org/10.1007/JHEP12(2014)095
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)095