Abstract
We present a systematic classification of counterterms of four-dimensional supersymmetric field theories on curved space, obtained as the rigid limit of new minimal supergravity. These are supergravity invariants constructed using the field theory background fields. We demonstrate that if the background preserves two supercharges of opposite chirality, then all dimensionless counterterms vanish, implying that in this case the supersymmetric partition function is free of ambiguities. When only one Euclidean supercharge is preserved, we describe the ambiguities that appear in the partition function, in particular in the dependence on marginal couplings.
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References
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353.
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [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].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [INSPIRE].
M. Sohnius and P.C. West, The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity, Nucl. Phys. B 198 (1982) 493 [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [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].
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere partition functions and the Zamolodchikov metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].
J. Gomis and N. Ishtiaque, Kähler potential and ambiguities in 4D N = 2 SCFTs, arXiv:1409.5325 [INSPIRE].
F. Brandt, Local BRST cohomology in minimal D = 4, N = 1 supergravity, Annals Phys. 259 (1997) 253 [hep-th/9609192] [INSPIRE].
S. Ferrara and S. Sabharwal, Structure of new minimal supergravity, Annals Phys. 189 (1989) 318 [INSPIRE].
D. Cassani and D. Martelli, Supersymmetry on curved spaces and superconformal anomalies, JHEP 10 (2013) 025 [arXiv:1307.6567] [INSPIRE].
S. Cecotti, S. Ferrara, M. Porrati and S. Sabharwal, New minimal higher derivative supergravity coupled to matter, Nucl. Phys. B 306 (1988) 160 [INSPIRE].
M. de Roo, A. Wiedemann and E. Zijlstra, The construction of R 2 actions in D = 4, N = 1 supergravity, Class. Quant. Grav. 7 (1990) 1181 [INSPIRE].
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
M. Dine, Supersymmetry phenomenology (with a broad brush), hep-ph/9612389 [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 3: supersymmetry, Cambridge University Press, Cambridge U.K. (2005).
C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on curved spaces and holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].
T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring curved superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, From rigid supersymmetry to twisted holomorphic theories, Phys. Rev. D 90 (2014) 085006 [arXiv:1407.2598] [INSPIRE].
D. Cassani, C. Klare, D. Martelli, A. Tomasiello and A. Zaffaroni, Supersymmetry in lorentzian curved spaces and holography, Commun. Math. Phys. 327 (2014) 577 [arXiv:1207.2181] [INSPIRE].
M. Muller, Supergravity in U(1) superspace with a two form gauge potential, Nucl. Phys. B 264 (1986) 292 [INSPIRE].
F. Farakos, C. Germani, A. Kehagias and E.N. Saridakis, A new class of four-dimensional N = 1 supergravity with non-minimal derivative couplings, JHEP 05 (2012) 050 [arXiv:1202.3780] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP 08 (2014) 123 [arXiv:1405.5144] [INSPIRE].
P. Gauduchon and L. Ornea, Locally conformally Kähler metrics on Hopf surfaces, Ann. Inst. Fourier 48 (1998) 1107.
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The geometry of supersymmetric partition functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on the Fayet-Iliopoulos term in field theory and supergravity, JHEP 06 (2009) 007 [arXiv:0904.1159] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3D dualities from 4D dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [INSPIRE].
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
T. Nishioka and I. Yaakov, Generalized indices for \( \mathcal{N}=1 \) theories in four-dimensions, arXiv:1407.8520 [INSPIRE].
C. Closset and I. Shamir, The \( \mathcal{N}=1 \) chiral multiplet on T 2 × S 2 and supersymmetric localization, JHEP 03 (2014) 040 [arXiv:1311.2430] [INSPIRE].
A. Cappelli and A. Coste, On the stress tensor of conformal field theories in higher dimensions, Nucl. Phys. B 314 (1989) 707 [INSPIRE].
C.P. Herzog and K.-W. Huang, Stress tensors from trace anomalies in conformal field theories, Phys. Rev. D 87 (2013) 081901 [arXiv:1301.5002] [INSPIRE].
K.-W. Huang, Weyl anomaly induced stress tensors in general manifolds, Nucl. Phys. B 879 (2014) 370 [arXiv:1308.2355] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in D = 4 and D = 6, arXiv:1407.6061 [INSPIRE].
T.T. Dumitrescu and G. Festuccia, Exploring curved superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].
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Assel, B., Cassani, D. & Martelli, D. Supersymmetric counterterms from new minimal supergravity. J. High Energ. Phys. 2014, 135 (2014). https://doi.org/10.1007/JHEP11(2014)135
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DOI: https://doi.org/10.1007/JHEP11(2014)135