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Scalar field theories with polynomial shift symmetries. (English) Zbl 1328.81152

Due to Geradus ’t Hooft theoretical physics often needs to explore questions that may be formulated as puzzles of naturalness. Actually, there are many landscapes of naturalness. Why is the Higgs mass so small? Why is the cosmological constant so small? One area is nonrelativistic gravity theory, an approach to quantum gravity which has recently attracted attention, mainly due to many achieved improvements with regard to short distance behavior. The four authors of the present paper considered in a previous paper [“Multicritical symmetry breaking and naturalness of slow Nambu-Goldstone bosons”, Phys. Rev. D 88, No. 10, Article ID 101701, 6 p. (2013; doi:10.1103/PhysRevD.88.101701)] related subjects as multicritical symmetry breaking and naturalness of slow Nambu-Goldstone bosons. They now continue their study of naturalness in the context of nonrelativistic QFT of the Lifshitz type. Their focus is on scalar field theories, multicritical Nambu-Goldstone bosons, and polynomial shift symmetries. Section 1 provides an introduction. In Section 2 the physics background is reviewed and in Section 3 the polynomial-shift invariants are considered, but also Galileon invariants. In Section 4 new invariants are introduced via the graphical approach. The reader will find conclusions as well as an outlook in Section 5 and I myself am convinced that the four authors handled the problem with wide knowledge and deep insight.

MSC:

81T10 Model quantum field theories
81T99 Quantum field theory; related classical field theories
81V17 Gravitational interaction in quantum theory
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