Supersymmetric Galileons and auxiliary fields in 2+1 dimensions

Abstract

In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories.We classify all possible models without derivative terms of the auxiliary field in the fermionic sector and find that scalar field theories of the form P (X, φ), where X = −(∂φ) 2 /2, belong to this kind of models. A ghost-free supersymmetric extension of Galileon models is found in three spacetime dimensions. Finally, the auxiliary field problem is discussed.

Renormalization group improvement of the superpotential for the N=2 Chern-Simons-matter model

“…As an important example, due to non-trivial anomalous dimension of the matter superfield, we computed the complete leading log effective superpotential in the N = 1 Wess-Zumino model and the N = 2 supersymmetric Chern-Simons-matter theory and demonstrated that they have an expected form Φ 4 Φ 2 µ α and ΦD 2 Φ Φ 2 µ α . We discussed the vacuum properties of the quantum effective superpotential in such model, and showed that no mass is generated by radiative corrections, differently from what happens for the N = 1 version of the model [15,[22][23][24][25]. We argued that the supersymmetry is preserved by quantum corrections.…”

“…Using the renormalization group functions given in the literature [20], β λ = 5λ 3 24π 2 and γ Φ = λ 2 192π 2 , substituting (27) into (25) and performing the sum, we obtain…”

Non-uniqueness of the supersymmetric extension of the O(3) σ-model

“…If the absence of higher-derivative contributions is imposed it turns out that such a term is unique (for dim M T = 2) up to an overall function depending on the superfields but not on derivatives. Besides, it does not contain derivatives acting on the auxiliary field (although the appearance of the derivative of the auxiliary field not always implies that F becomes dynamical -it leads usually to the generation of higher-derivative terms for the physical fields [19]). …”

“…If we substitute (2.9) in (2.3), we get 19) where g(Φ, Φ † ) = 1/(1 + Φ † Φ) 2 is the CP 1 metric. The action (2.19) constitutes the N = 1 CP 1 formulation of the model.…”

“…However, the fermionic part of the supersymmetric models contains potentially dangerous higherderivative terms. A different proposal was made in [15,16] (in four dimensions) and in [17][18][19] (in three dimensions) with N = 1 and N = 2 SUSY. In these cases, the fermionic part of the non-equivalent supersymmetric extensions suffers from the appearance of derivative terms involving the auxiliary field.…”