Aspects of massive ABJM models with inhomogeneous mass parameters
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Springer
Received: October 20, 2019 Accepted: December 11, 2019 Published: December 23, 2019
Kyung Kiu Kim,a Yoonbai Kim,b O-Kab Kwonb and Chanju Kimc a
Department of Physics, Sejong University, Seoul 05006, Korea b Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Korea c Department of Physics, Ewha Womans University, Seoul 03760 Korea
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Recently, N = 3 mass-deformed ABJM model with arbitrary mass-function depending on a spatial coordinate was constructed. In addition to the N = 3 case, we construct lower supersymmetric N = 1 and N = 2 inhomogeneously mass-deformed ABJM (ImABJM) models, which require three and two arbitrary mass-functions, respectively. We also construct general vacuum solutions of the N = 3 ImABJM model for any periodic mass-function. There are two classes of vacua, which are diagonal type and GRVV type according to reference value of mass-functions. We provide explicit examples of the vacuum solutions and discuss related operators. Keywords: Supersymmetric Effective Theories, Chern-Simons Theories, Gauge-gravity correspondence ArXiv ePrint: 1910.05044
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2019)153
JHEP12(2019)153
Aspects of massive ABJM models with inhomogeneous mass parameters
Contents 1 Introduction
1
2 N = 1, 2 ImABJM models 2.1 N = 3 deformation 2.2 N = 2 deformation 2.3 N = 1 deformation
3 5 6 7 8 8 9 10
4 Periodic vacuum solutions for N = 3 deformation 4.1 m(x) = m1 sin qx case 4.2 m(x) = m0 + m1 sin qx case 4.3 General structure of periodic vacuum solutions 4.4 Classical limit of vevs for general periodic vacuum solutions
13 13 14 15 16
5 Conclusion
18
A Derivation of (3.13)
19
B Various vacuum configurations with periodic mass-functions
20
1
Introduction
The low energy behavior of N M2-branes on Zk -orbifold is described by the N = 6 ABJM theory with Uk (N ) × U−k (N ) gauge group at level k [1]. Due to the non-dynamical nature of the Chern-Simons gauge fields, an interesting extension is realized by use of a supersymmetry-preserving mass deformation, which gives rise to the mass-deformed ABJM (mABJM) theory [2, 3]. The mass parameter is originated from the self-dual constant 4form field strength accompanied by the Wess-Zumino type coupling with M2 branes [4, 5] in the 11-dimensional supergravity. Gravity dual of the mABJM theory is identified as the LLM geometry [6] with Zk orbifold. It also turns out that the 4-form field strength with one spatial coordinate dependence allows an N = 3 supersymmetry maximally. Accordingly, the ABJM theory with spatially dependent mass-function was constructed [7]. We will call such a theory the inhomogeneously mass-deformed ABJM (ImABJM) model in what follows. The spatially varying mass-function m = m(x) whose functional form is arbitrary breaks a half supersymmetry of the original
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