Junctions of mass-deformed nonlinear sigma models on SO(2 N )/U( N ) and Sp( N )/U( N ). Part II
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Springer
Received: March 9, Revised: July 16, Accepted: August 5, Published: September 4,
2020 2020 2020 2020
Taegyu Kima and Sunyoung Shinb,c a
Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea b Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Republic of Korea c Department of Physics, Kangwon National University, Chuncheon 24341, Republic of Korea
E-mail: [email protected], [email protected] Abstract: We construct three-pronged junctions of mass-deformed nonlinear sigma models on SO(2N )/U(N ) and Sp(N )/U(N ) for generic N . We study the nonlinear sigma models on the Grassmann manifold or on the complex projective space. We discuss the relation between the nonlinear sigma model constructed in the harmonic superspace formalism and the nonlinear sigma model constructed in the projective superspace formalism by comparing each model with the N = 2 nonlinear sigma model constructed in the N = 1 superspace formalism. Keywords: Extended Supersymmetry, Sigma Models ArXiv ePrint: 2002.01923
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)042
JHEP09(2020)042
Junctions of mass-deformed nonlinear sigma models on SO(2N )/U(N ) and Sp(N )/U(N ). Part II
Contents 1 Introduction
1
2 Models
3
4 Three-pronged junctions of the mass-deformed nonlinear sigma model on Sp(N )/U(N ) 13 4.1 N = 4m − 1 14 4.2 N = 4m 17 5 N = 2 nonlinear sigma models on the Grassmann manifold 5.1 N = 1 superspace formalism 5.2 Harmonic superspace formalism 5.3 Projective superspace formalism
20 21 23 26
6 Summary and discussion
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A Lagrangian in section 2
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B SO(2N )/U(N ) with N = 4m
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C SO(2N )/U(N ) with N = 4m + 1
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D Sp(N )/U(N ) with N = 4m − 1
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E Sp(N )/U(N ) with N = 4m
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1
Introduction
Topological solitons of supersymmetric theories are Bogomol’nyi-Prasad-Sommerfield (BPS) states, which preserve a fraction of supersymmetry [1]. Walls and junctions preserve 1/2 supersymmetry [2, 3] and 1/4 supersymmetry respectively [4–6]. Potential terms and various wall configurations are discussed in [7–12]. The moduli matrix formalism is proposed in [13, 14] to analyse walls in the N = 2 supersymmetric U(NC ) gauge theory. In the strong coupling limit, it becomes the massdeformed N = 2 nonlinear sigma model on the Grassmann manifold GNF ,NC , which is
–1–
JHEP09(2020)042
3 Three-pronged junctions of the mass-deformed nonlinear sigma model on SO(2N )/U(N ) 6 3.1 N = 4m 7 3.2 N = 4m + 1 10
U(N +M ) defined by GN +M,M = U(N )×U(M ) . Wall solutions are exact in the strong coupling limit. There is a bundle structure in the N = 2 nonlinear sigma model on the Grassmann manifold with the Fayet-Iliopoulos (FI) parameters ca = (0, 0, c) so that only one of the chiral fields in the hypermultiplet contributes to the configuration of vacua and walls. Walls are built from elementary walls in the moduli matrix formalism. Elementary walls can be identified with the simple roots of the flavour symmetry [15]. Hermitian symmetric spaces SO(2N )/U(
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