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Register a new userHigher-Derivative Wess-Zumino Model in Three Dimensions
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Carlos Roberto Senise J\\'unior
Publication date
2012
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English
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We deform the well-known three dimensional $mathcal{N}=1$ Wess-Zumino model by adding higher derivative operators (Lee-Wick operators) to its action. The effects of these operators are investigated both at the classical and quantum levels.
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Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some of its important properties, both at the formal algebraic level (e.g., preserving the associativity of the deformed theory) as well as at the physical level (e.g., maintaining renormalizability). The Hopf algebra formalism allows the definition of algebraically consistent deformations of SUSY, but this algebraic consistency does not guarantee that physical models build upon these structures will be consistent from the physical point of view. We will investigate a deformation induced by a Drinfeld twist of the ${cal N}=1$ SUSY algebra in three space-time dimensions. The use of the Hopf algebra formalism allows the construction of deformed ${cal N}=1$ SUSY algebras that should still preserve a deformed version of supersymmetry. We will construct the simplest deformed version of the Wess-Zumino model in this context, but we will show that despite the consistent algebraic structure, the model in question is not invariant under SUSY transformation and is not renormalizable. We will comment on the relation of these results with previous ones discussed in the literature regarding similar four-dimensional constructions.
We develop geometric superspace settings to construct arbitrary higher derivative couplings (including R^n terms) in three-dimensional supergravity theories with N=1,2,3 by realising them as conformal supergravity coupled to certain compensators. For all known off-shell supergravity formulations, we construct supersymmetric invariants with up to and including four derivatives. As a warming-up exercise, we first give a new and completely geometric derivation of such invariants in N=1 supergravity. Upon reduction to components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952. We then carry out a similar construction in the case of N=2 supergravity for which there exist two minimal formulations that differ by the choice of compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet. For these formulations all four derivative invariants are constructed in completely general and gauge independent form. For a general supergravity model (in the N=1 and minimal N=2 cases) with curvature-squared and lower order terms, we derive the superfield equations of motion, linearise them about maximally supersymmetric backgrounds and obtain restrictions on the parameters that lead to models for massive supergravity. We use the non-minimal formulation for N = 2 supergravity (which corresponds to a complex linear compensator) to construct a novel consistent theory of massive supergravity. In the case of N = 3 supergravity, we employ the off-shell formulation with a vector multiplet as compensator to construct for the first time various higher derivative invariants. These invariants may be used to derive models for N = 3 massive supergravity. As a bi-product of our analysis, we also present superfield equations for massive higher spin multiplets in (1,0), (1,1) and (2,0) anti-de Sitter superspaces.
In this paper, kink scattering in the dimensional reduction of the bosonic sector of a one-parameter family of generalized Wess-Zumino models with three vacuum points is discussed. The value of the model parameter determines the specific location of the vacua. The influence of the vacuum arrangements (evolving from three collinear vacua to three vacua placed at the vertices of an equilateral triangle) on the kink scattering is investigated. Two different regimes can be distinguished: in the first one, two symmetric BPS kinks/antikinks arise whereas in the second one a new different BPS kink/antikink emerges, with the exception of a three-fold rotational symmetry case, where the three topological defects are identical. The scattering between the two symmetric kinks is thoroughly analyzed. Two different scattering channels have been found: kink-kink reflection and kink-kink hybridization. In the last case, the collision between the two symmetric kinks gives rise to the third different kink. Resonance phenomena also appear allowing a vibrating kink to split into two symmetric kinks moving away.
We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for our main result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the $varepsilon$-expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects we discuss some subtleties specific to the codimension two case. In particular, conformal blocks and the Lorentzian inversion formula have to be slightly modified in order to accommodate odd-spin operators that can have a non-zero one-point function. In the Wess-Zumino model we initiate the $varepsilon$-expansion bootstrap for four-point functions of chiral operators, with the goal of obtaining spectral information about the bulk theory. We then proceed to tackle the harder technical problem of analyzing monodromy defects in the presence of supersymmetry. We use inversion formula technology and spectral data coming from our four-point function analysis, in order to completely bootstrap two-point functions of chiral operators at leading order in $varepsilon$. Our result can be written in terms of novel special functions which we analyze in detail, and allows us to efficiently extract the CFT data that characterizes the correlator.
We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.
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