Superfield Action Research Articles

Supersymmetric higher-derivative models in quantum cosmology

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.

Unconstrained off-shell superfield formulation of 4D, mathcal{N} = 2 supersymmetric higher spins

We present, for the first time, the complete off-shell 4D, mathcal{N} = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the mathcal{N} = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields {h}_{alpha left(s-1right)dot{alpha}left(s-1right)}^{++} , {h}_{alpha left(s-2right)dot{alpha}left(s-2right)}^{++} and two conjugated complex analytic spinor superfields {h}_{alpha left(s-1right)dot{alpha}left(s-1right)}^{+3} , {h}_{alpha left(s-2right)dot{alpha}left(s-1right)}^{+3} , where α(s) := (α1. . . αs), dot{alpha} (s) := ( dot{alpha} 1. . . dot{alpha} s). Like in the harmonic superspace formulations of mathcal{N} = 2 Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content (s,s−1/2,s−1/2,s−1) is restored. For s = 2 the action describes the linearized version of “minimal” mathcal{N} = 2 Einstein supergravity.

Formula omitted] supersymmetric d = 1 sigma models on group manifolds

We construct manifestly N=4 supersymmetric off-shell superfield actions for the HKT d=1 sigma models on the group manifolds U(2) and SU(3), using the harmonic d=1 approach. The underlying (4,4,0) and (4,4,0)⊕(4,4,0) multiplets are described, respectively, by one and two harmonic analytic superfields q+ satisfying the appropriate nonlinear harmonic constraints. The invariant actions in both cases are bilinear in the superfields. We present the corresponding superfield realizations of the U(2) and SU(3) isometries and show that in fact they are enlarged to the products U(2)×SU(2) and SU(3)×U(2). We prove the corresponding invariances at both the superfield and component levels and present the bosonic d=1 sigma model actions, as integral over t in the U(2) case and over t and SU(2) harmonics in the SU(3) case. In the U(2) case we also give a detailed comparison with the general harmonic approach to HKT models and establish a correspondence with a particular action of the off-shell nonlinear multiplet (3,4,1). A possible way of generalizing U(2) model to the matrix U(2n) case is suggested.

Quaternion-K\xe4hler mathcal{N} = 4 supersymmetric mechanics

Using the mathcal{N} = 4, 1D harmonic superspace approach, we construct a new type of mathcal{N} = 4 supersymmetric mechanics involving 4n-dimensional Quaternion-Kähler (QK) 1D sigma models as the bosonic core. The basic ingredients of our construction are local mathcal{N} = 4,1D supersymmetry realized by the appropriate transformations in 1D harmonic superspace, the general mathcal{N} = 4, 1D superfield vielbein and a set of 2(n + 1) analytic “matter” superfields representing (n + 1) off-shell supermultiplets (4, 4, 0). Both superfield and component actions are given for the simplest QK models with the manifolds ℍHn = Sp(1, n)/[Sp(1) × Sp(n)] and ℍPn = Sp(1 + n)/[Sp(1) × Sp(n)] as the bosonic targets. For the general case the relevant superfield action and constraints on the (4, 4, 0) “matter” superfields are presented. Further generalizations are briefly discussed.

Ghost-free vector superfield actions in supersymmetric higher-derivative theories

We systematically construct ghost-free higher-derivative actions of Abelian vector supermultiplets in four-dimensional mathcal{N}=1 global supersymmetric theories. After giving a simple example which illustrates that a naive introduction of a higher-derivative term gives rise to a ghost, we discuss possible building blocks for a ghost-free action and explicitly show that their bosonic parts have no ghost mode and the auxiliary field D does not propagate. Higher-derivative terms yield higher powers of the auxiliary field D in the actions, and the D-term equations of motion consequently admit multiple solutions in general. We confirm that the well-known supersymmetric Dirac-Born-Infeld action falls into this class. We further give another example in which the standard quadratic kinetic term (Maxwell term) is corrected by a quartic term of the field strength. We also discuss possible couplings to matter fields and a deformed D-term potential.

Induced effective action in 6D hypermultiplet theory on a vector/tensor background

We consider the six dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. Manifestly a (1,0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contributions to the effective action is calculated.

Long N = 2, 4 multiplets in supersymmetric mechanics

We define SU(2|1) supermultiplets described by chiral superfields having non-zero external spins with respect to SU(2) ⊂ SU(2|1) and show that their splitting into N = 2, d = 1 multiplets contains the so called “long” indecomposable N = 2, d = 1 multiplets (2, 4, 2)l. We give superfield formulation for this type of N = 2 long multiplets and construct their most general superfield action. A simple example of long N = 4, d = 1 multiplet is also considered, both in the superfield and the component formulations.

SU(2|2) supersymmetric mechanics

We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various worldline $SU(2|2)$ superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell $SU(2|2)$ multiplets $({\bf 3,8,5})$, $({\bf 4,8,4})$ and $({\bf 5,8,3})$, we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group $OSp(4^*|4)$ in the conformal cases. For the simplest $({\bf 5, 8, 3})$ model the quantization is performed.

Bi-HKT and bi-Kähler supersymmetric sigma models

We study Clifford Kähler with torsion (or bi-HKT) N=4 supersymmetric quantum mechanical sigma models. They are characterized by the usual and the mirror sectors displaying each HKT geometry. When the metric involves isometries, a Hamiltonian reduction is possible. The most natural such reduction with respect to a half of bosonic target space coordinates produces an N=4 model, related to the twisted Kähler model due to Gates, Hull and Rocek, but including certain extra F-terms in the superfield action.

Long multiplets in supersymmetric mechanics

The ``long'' indecomposable $\mathcal{N}=2$, $d=1$ multiplet $(\mathbf{2},\mathbf{4},\mathbf{2})$ defined in B. Assel et al. [J. High Energy Phys. 07 (2015) 043] as a deformation of the pair of chiral multiplets $(\mathbf{2},\mathbf{2},\mathbf{0})$ and $(\mathbf{0},\mathbf{2},\mathbf{2})$ by a number of the mass-dimension parameters is described in the superfield approach. We present its most general superfield and component actions as well as a generalization to the case with the superfields of the opposite Grassmann parities and dimensionless deformation parameter. We show that the long $\mathcal{N}=2$, $d=1$ multiplets are naturally embedded into the chiral $SU(2|1)$, $d=1$ superfields having nonzero external spins with respect to $SU(2)\ensuremath{\subset}SU(2|1)$. A superfield with spin $s$ contains $2s$ long multiplets and two short multiplets $(\mathbf{2},\mathbf{2},\mathbf{0})$ and $(\mathbf{0},\mathbf{2},\mathbf{2})$. Two possible $\mathcal{N}=4$, $d=1$ generalizations of the $\mathcal{N}=2$ long multiplet in the superfield approach are also proposed.

N = 1 $$ \mathcal{N}=1 $$ superfield description of six-dimensional supergravity

We express the action of six-dimensional supergravity in terms of four-dimensional $$ \mathcal{N}=1 $$ superfields, focusing on the moduli dependence of the action. The gauge invariance of the action in the tensor-vector sector is realized in a quite nontrivial manner, and it determines the moduli dependence of the action. The resultant moduli dependence is intricate, especially on the shape modulus. Our result is reduced to the known superfield actions of six-dimensional global SUSY theories and of five-dimensional supergravity by replacing the moduli superfields with their background values and by performing the dimensional reduction, respectively.

New realizations of the supergroup D(2, 1; α) in N = 4 $$ \mathcal{N}=4 $$ superconformal mechanics

We present new explicit realizations of the most general $$ \mathcal{N}=4 $$ , d = 1 superconformal symmetry D(2, 1; α) in the models of $$ \mathcal{N}=4 $$ superconformal mechanics based on the reducible multiplets (1 , 4 , 3) ⊕ (0 , 4 , 4), (3 , 4 , 1) ⊕ (0 , 4 , 4) and (4 , 4 , 0) ⊕ (0 , 4 , 4). We start from the manifestly supersymmetric superfield actions for these systems and then descend to the relevant off- and on-shell component actions from which we derive the D(2, 1; α) (super)charges by the Noether procedure. Some peculiarities of these realizations of D(2, 1; α) are discussed. We also construct a new D(2, 1; α) invariant system by joining the multiplets (3 , 4 , 1) and (4 , 4 , 0) in such a way that they interact with each other through an extra (0 , 4 , 4) multiplet. New fermionic conformal couplings appear as the result of elimination of the appropriate auxiliary fields.

N =1 superfield description of vector-tensor couplings in six dimensions

We express supersymmetric couplings among the vector and the tensor multiplets in six dimensions (6D) in terms of N=1 superfields. The superfield description is derived from the invariant action in the projective superspace. The obtained expression is consistent with the known superfield actions of 6D supersymmetric gauge theory and 5D Chern-Simons theory after the dimensional reduction. Our result provides a crutial clue to the N=1 superfield description of 6D supergravity.

Construction of 6D supersymmetric field models in [formula omitted] harmonic superspace

We consider the six-dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. The actions for free (2,0) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure.

Harmonic superfield action for $$\mathcal{N}$$ = 4 SYM theory with central charge

We develop a superfield formulation of N = 4 supersymmetric Yang-Mills theory with the rigid central charge in USp(4) harmonic superspace. Component formulation of this theory was given by Sohnius, Stelle and West [1] but its superfield formulation has not been constructed so far. We construct the superfield action, corresponding to this model, and show that it reproduces the component action from [1].

Supergravity actions with integral forms

Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincaré dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates' so-called “Ectoplasmic Integration Theorem”, relating superfield actions to component actions.

Gauge and matter superfield theories on S 2

We develop a superfield formulation of gauge and matter field theories on a two-dimensional sphere with rigid $$ \mathcal{N}=\left(2,2\right) $$ as well as extended supersymmetry. The construction is based on a supercoset $$ \frac{\mathrm{SU}\left(\left.2\right|1\right)}{\mathrm{U}(1)\times \mathrm{U}(1)} $$ containing S 2 as the bosonic subspace. We derive an explicit form of supervielbein and covariant derivatives on this coset, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace.

Superfield theories on S 3 and their localization

We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid $ \mathcal{N} $ = 2 supersymmetry, as well as with $ \mathcal{N} $ > 2. The construction is based on a supercoset SU(2|1)/U(1) containing S 3 as the bosonic subspace. We derive an explicit form of SU(2|1)/U(1) supervielbein and covariant derivatives, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace.

Quasicomplex N=2, d=1 Supersymmetric Sigma Models

We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1) multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0) and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry.

Towards harmonic superfield formulation of [formula omitted], [formula omitted] SYM theory with the central charge

We develop a superfield formulation of N=4 supersymmetric Yang–Mills theory with the rigid central charge in USp(4) harmonic superspace. The component formulation of this theory was given by Sohnius, Stelle and West [1], but its superfield formulation has not been constructed so far. We construct the superfield action, corresponding to this model, and show that it reproduces the component action from [1].