Abstract
We analyze the conformal bootstrap constraints in theories with four super-charges and a global O(N ) × U(1) flavor symmetry in 3 ≤ d ≤ 4 dimensions. In particular, we consider the 4-point function of O(N )-fundamental chiral operators Z i that have no chiral primary in the O(N )-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of N + 1 chiral super-fields with superpotential W = X∑ N i = 1 Z 2 i as well as general bounds on SCFTs where ∑ N i = 1 Z 2 i vanishes in the chiral ring.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [INSPIRE].
S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [INSPIRE].
G. Mack, Duality in quantum field theory, Nucl. Phys. B 118 (1977) 445 [INSPIRE].
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].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising model with the conformal bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising model with the conformal bootstrap II. c-minimization and precise critical exponents, J. Stat. Phys. 157 (2014) 869 [arXiv:1403.4545] [INSPIRE].
F. Gliozzi and A. Rago, Critical exponents of the 3d Ising and related models from conformal bootstrap, JHEP 10 (2014) 042 [arXiv:1403.6003] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping mixed correlators in the 3D Ising model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D conformal field theories with global symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N ) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
S.M. Chester, S.S. Pufu and R. Yacoby, Bootstrapping O(N ) vector models in 4 ≤ d ≤ 6, Phys. Rev. D 91 (2015) 086014 [arXiv:1412.7746] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N ) archipelago, JHEP 11 (2015) 106 [arXiv:1504.07997] [INSPIRE].
L.F. Alday and A. Bissi, The superconformal bootstrap for structure constants, JHEP 09 (2014) 144 [arXiv:1310.3757] [INSPIRE].
D. Bashkirov, Bootstrapping the N = 1 SCFT in three dimensions, arXiv:1310.8255 [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The N = 4 superconformal bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, The N = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, Exact correlators of BPS operators from the 3d superconformal bootstrap, JHEP 03 (2015) 130 [arXiv:1412.0334] [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. Berkooz, R. Yacoby and A. Zait, Bounds on N = 1 superconformal theories with global symmetries, JHEP 08 (2014) 008 [Erratum ibid. 01 (2015) 132] [arXiv:1402.6068] [INSPIRE].
L.F. Alday and A. Bissi, Generalized bootstrap equations for N = 4 SCFT, JHEP 02 (2015) 101 [arXiv:1404.5864] [INSPIRE].
C. Beem, M. Lemos, L. Rastelli and B.C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping the three-dimensional supersymmetric Ising model, Phys. Rev. Lett. 115 (2015) 051601 [arXiv:1502.04124] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping SCFTs with four supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
S.M. Chester, S. Giombi, L.V. Iliesiu, I.R. Klebanov, S.S. Pufu and R. Yacoby, Accidental symmetries and the conformal bootstrap, JHEP 01 (2016) 110 [arXiv:1507.04424] [INSPIRE].
D. Poland and A. Stergiou, Exploring the minimal 4D N = 1 SCFT, JHEP 12 (2015) 121 [arXiv:1509.06368] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping the three-dimensional supersymmetric Ising model, Phys. Rev. Lett. 115 (2015) 051601 [arXiv:1502.04124] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping SCFTs with four supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact terms, unitarity and F-maximization in three-dimensional superconformal theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric field theories on three-manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
S. Giombi and I.R. Klebanov, Interpolating between a and F , JHEP 03 (2015) 117 [arXiv:1409.1937] [INSPIRE].
D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [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].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY gauge theories on three-sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY gauge theories on squashed three-spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
P.M. Ferreira, I. Jack and D.R.T. Jones, The quasiinfrared fixed point at higher loops, Phys. Lett. B 392 (1997) 376 [hep-ph/9610296] [INSPIRE].
P.M. Ferreira and J.A. Gracey, Nonzeta knots in the renormalization of the Wess-Zumino model?, Phys. Lett. B 424 (1998) 85 [hep-th/9712140] [INSPIRE].
I. Jack, D.R.T. Jones and A. Pickering, The soft scalar mass β-function, Phys. Lett. B 432 (1998) 114 [hep-ph/9803405] [INSPIRE].
I. Jack and D.R.T. Jones, Quasiinfrared fixed points and renormalization group invariant trajectories for nonholomorphic soft supersymmetry breaking, Phys. Rev. D 61 (2000) 095002 [hep-ph/9909570] [INSPIRE].
L.V. Avdeev, S.G. Gorishnii, A. Yu. Kamenshchik and S.A. Larin, Four loop β-function in the Wess-Zumino model, Phys. Lett. B 117 (1982) 321 [INSPIRE].
D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [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: 1511.07552
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
Chester, S.M., Iliesiu, L.V., Pufu, S.S. et al. Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4. J. High Energ. Phys. 2016, 103 (2016). https://doi.org/10.1007/JHEP05(2016)103
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)103