Quantum consistency in supersymmetric theories with R-symmetry in curved space
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Springer
Received: February 19, Revised: May 2, Accepted: May 6, Published: May 23,
2019 2019 2019 2019
Ok Song An,a Jin U. Kang,b,a Jong Chol Kima and Yong Hae Koa a
Department of Physics, Kim Il Sung University, Ryongnam Dong, TaeSong District, Pyongyang, DPR Korea b International Centre for Theoretical Physics, Strada Costiera 11, Trieste 34151, Italy
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We discuss consistency at the quantum level in the rigid N = 1 supersymmetric field theories with a U(1)R symmetry in four-dimensional curved space which are formulated via coupling to the new-minimal supergravity background fields. By analyzing correlation functions of the current operators in the R-multiplet, we show that the quantum consistency with the (unbroken) supersymmetry requires the U(1)R anomaly coefficient, which depends only on the field content of the theory, to vanish. This consistency condition is obtained under the assumption that the supercurrent Ward identity is non-anomalous and that the vacuum is supersymmetric. Keywords: Anomalies in Field and String Theories, Supersymmetric Effective Theories, Supergravity Models, Supersymmetric Gauge Theory ArXiv ePrint: 1902.04525
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)146
JHEP05(2019)146
Quantum consistency in supersymmetric theories with R-symmetry in curved space
Contents 1
2 New minimal supergravity and Killing spinor
3
3 Ward identities and correlation functions 3.1 Ward identities 3.2 Higher-point correlation functions
5 5 6
4 Rigid supersymmetry algebra
9
5 Quantum consistency
13
6 Discussions
16
A Conventions
17
B An example: N = 1 with a free chiral multiplet on R × Sr3
18
1
Introduction
Supersymmetric field theories in curved space have attracted many interests in recent years. For such theories supersymmetric localization technique [1, 2] allows the non-perturbative exact computation of some interesting physical quantities such as the partition function and BPS Wilson loops, which can be used to test the duality conjectures like the AdS/CFT correspondence [3–5]. In this paper we focus on supersymmetric field theories with a U(1)R symmetry on curved manifolds in 3+1 dimensions. According to [6–8] (see also [9] for a recent review), one can formulate a N = 1 theory with a U(1)R symmetry in 4D curved space via coupling to the new-minimal supergravity [10, 11]: one first couples the R-multiplet to the new-minimal supergravity multiplet and then take a rigid limit sending the Newton’s constant to zero, so that the supergravity is decoupled while the fields in the supergravity multiplet are sent to fixed backgrounds. In constructing supersymmetric field theories in curved space, background fields are typically chosen to be bosonic, and consistency with supersymmetry requires the supersymmetry variation of the gravitino in the gravity multiplet to vanish, which leads to a generalized Killing spinor (GKS) equation. For eac
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