Abstract
Using superspace techniques, we compute the mixed OPE between an \( \mathcal{N}=2 \) stress-tensor multiplet, a chiral multiplet and a flavor current multiplet. We perform a detailed analysis of the three-point function between two of the mentioned multiplets and a third arbitrary operator. We then solve all the constraints coming from the \( \mathcal{N}=2 \) superconformal symmetry and from the equations of motion and/or conservation equations, and obtain all the possible operators that can appear in the expansion. This calculation is the first step towards a more general superconformal block analysis of mixed correlators in \( \mathcal{N}=2 \) theories.
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References
L. Bhardwaj and Y. Tachikawa, Classification of 4d N = 2 gauge theories, JHEP 12 (2013) 100 [arXiv:1309.5160] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [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].
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].
A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [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].
F.A. Dolan, L. Gallot and E. Sokatchev, On four-point functions of 1/2-BPS operators in general dimensions, JHEP 09 (2004) 056 [hep-th/0405180] [INSPIRE].
A. Bissi and T. Lukowski, Revisiting N = 4 superconformal blocks, JHEP 02 (2016) 115 [arXiv:1508.02391] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, Z.U. Khandker, D. Li, D. Poland and D. Simmons-Duffin, Covariant approaches to superconformal blocks, JHEP 08 (2014) 129 [arXiv:1402.1167] [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].
P. Liendo, I. Ramirez and J. Seo, Stress-tensor OPE in N = 2 superconformal theories, JHEP 02 (2016) 019 [arXiv:1509.00033] [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. Lemos and P. Liendo, Bootstrapping N = 2 chiral correlators, JHEP 01 (2016) 025 [arXiv:1510.03866] [INSPIRE].
M. Lemos and P. Liendo, N = 2 central charge bounds from 2d chiral algebras, JHEP 04 (2016) 004 [arXiv:1511.07449] [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].
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].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with E n global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].
Y.-K.E. Cheung, O.J. Ganor and M. Krogh, Correlators of the global symmetry currents of 4D and 6D superconformal theories, Nucl. Phys. B 523 (1998) 171 [hep-th/9710053] [INSPIRE].
S. Rychkov, EPFL lectures on conformal field theory in D ≥ 3 dimensions, arXiv:1601.05000 [INSPIRE].
H. Osborn, N = 1 superconformal symmetry in four-dimensional quantum field theory, Annals Phys. 272 (1999) 243 [hep-th/9808041] [INSPIRE].
J.-H. Park, Superconformal symmetry and correlation functions, Nucl. Phys. B 559 (1999) 455 [hep-th/9903230] [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in D = 4,arXiv:1307.8092 [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in N = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs I: physical constraints on relevant deformations, arXiv:1505.04814 [INSPIRE].
P.C. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs II: construction of special Kähler geometries and RG flows, arXiv:1601.00011 [INSPIRE].
M.F. Sohnius, The multiplet of currents for N = 2 extended supersymmetry, Phys. Lett. B 81 (1979) 8 [INSPIRE].
D. Poland and D. Simmons-Duffin, Bounds on 4D conformal and superconformal field theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [INSPIRE].
J. Song, Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT, JHEP 02 (2016) 045 [arXiv:1509.06730] [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].
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].
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ArXiv ePrint: 1602.07269
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Ramírez, I.A. Mixed OPEs in \( \mathcal{N}=2 \) superconformal theories. J. High Energ. Phys. 2016, 43 (2016). https://doi.org/10.1007/JHEP05(2016)043
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DOI: https://doi.org/10.1007/JHEP05(2016)043