Abstract
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M . We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism [1-3], we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed \( \mathcal{N} \) = 4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Osborn, Derivation of a Four-dimensional c Theorem, Phys. Lett. B 222 (1989) 97 [INSPIRE].
I. Jack and H. Osborn, Analogs for the c Theorem for Four-dimensional Renormalizable Field Theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].
H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
M.A. Luty and R. Sundrum, Supersymmetry breaking and composite extra dimensions, Phys. Rev. D 65 (2002) 066004 [hep-th/0105137] [INSPIRE].
M. Luty and R. Sundrum, Anomaly mediated supersymmetry breaking in four-dimensions, naturally, Phys. Rev. D 67 (2003) 045007 [hep-th/0111231] [INSPIRE].
P. Meade, N. Seiberg and D. Shih, General Gauge Mediation, Prog. Theor. Phys. Suppl. 177 (2009) 143 [arXiv:0801.3278] [INSPIRE].
S. Dimopoulos and G.F. Giudice, Multimessenger theories of gauge mediated supersymmetry breaking, Phys. Lett. B 393 (1997) 72 [hep-ph/9609344] [INSPIRE].
R. Argurio and D. Redigolo, Tame D-tadpoles in gauge mediation, JHEP 01 (2013) 075 [arXiv:1206.7037] [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].
Z. Komargodski and N. Seiberg, Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets, JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].
L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
J.A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP 04 (2000) 009 [hep-th/9911029] [INSPIRE].
S. Weinberg, The quantum theory of fields. Vol. 3: Supersymmetry, Cambridge University Press, Cambridge U.K. (2000).
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
T.T. Dumitrescu and G. Festuccia, Exploring Curved Superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].
F. D’Eramo, J. Thaler and Z. Thomas, The Two Faces of Anomaly Mediation, JHEP 06 (2012) 151 [arXiv:1202.1280] [INSPIRE].
F. D’Eramo, J. Thaler and Z. Thomas, Anomaly Mediation from Unbroken Supergravity, JHEP 09 (2013) 125 [arXiv:1307.3251] [INSPIRE].
Y. Nakayama, Consistency of local renormalization group in d = 3, Nucl. Phys. B 879 (2014) 37 [arXiv:1307.8048] [INSPIRE].
F. Baume, B. Keren-Zur, R. Rattazzi and L. Vitale, The local Callan-Symanzik equation: structure and applications, arXiv:1401.5983 [INSPIRE].
M. Dine and N. Seiberg, Comments on quantum effects in supergravity theories, JHEP 03 (2007) 040 [hep-th/0701023] [INSPIRE].
M. Dine and P. Draper, Anomaly Mediation in Local Effective Theories, JHEP 02 (2014) 069 [arXiv:1310.2196] [INSPIRE].
Y. Imamura, Relation between the 4d superconformal index and the S 3 partition function, JHEP 09 (2011) 133 [arXiv:1104.4482] [INSPIRE].
O. Aharony, M. Berkooz, D. Tong and S. Yankielowicz, Confinement in Anti-de Sitter Space, JHEP 02 (2013) 076 [arXiv:1210.5195] [INSPIRE].
B. Gripaios, H.D. Kim, R. Rattazzi, M. Redi and C. Scrucca, Gaugino mass in AdS space, JHEP 02 (2009) 043 [arXiv:0811.4504] [INSPIRE].
N. Arkani-Hamed and H. Murayama, Holomorphy, rescaling anomalies and exact β-functions in supersymmetric gauge theories, JHEP 06 (2000) 030 [hep-th/9707133] [INSPIRE].
M. Dine et al., Supersymmetric QCD: Exact Results and Strong Coupling, JHEP 05 (2011) 061 [arXiv:1104.0461] [INSPIRE].
K. Yonekura, On the Trace Anomaly and the Anomaly Puzzle in N = 1 Pure Yang-Mills, JHEP 03 (2012) 029 [arXiv:1202.1514] [INSPIRE].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calculus, Nucl. Phys. B 229 (1983) 381 [INSPIRE].
M.A. Shifman and A.I. Vainshtein, Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion, Nucl. Phys. B 277 (1986) 456 [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: 1402.3385
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
Di Pietro, L., Dine, M. & Komargodski, Z. (Non-)decoupled supersymmetric field theories. J. High Energ. Phys. 2014, 73 (2014). https://doi.org/10.1007/JHEP04(2014)073
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)073