General Superfield Research Articles

Two-loop effective potential for general higher-derivative superfield models

For a three-dimensional higher-derivative scalar superfield model, and a four-dimensional higher-derivative chiral superfield model, where which the higher-derivative operators are described by polynomials of arbitrary degrees, we explicitly calculate the two-loop effective potential.

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.

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.

Peakon Solutions to Supersymmetric Camassa—Holm Equation and Degasperis—Procesi Equation

In this paper, the supersymmetric Camassa—Holm equation and Degasperis—Procesi equation are derived from a general superfield equations by choosing different parameters. Their peakon-type solutions are shown in weak sense. At the same time, the dynamic behaviors are analyzed particularly when the two peakons collide elastically, and some results are compared with each other between the two equations.

The Explicit Pure Vector Superfield in Gauge Theories

An explicit expression of the pure vector superfield is derived in gauge theories in the Wess-Zumino gauge. A pure vector superfield means that the theta independent part of the superfield transforms as a Lorentz vector. This is to be contrasted with the so-called general scalar superfield, whose theta independent part is a scalar, as well as with the known spinor superfield, whose theta independent part is a spinor, which both contain a vector field. In contrast to the latter two superfields, the action of supersymmetric gauge theories follows directly from the theory of a pure vector superfield from a so-called D-term. As the construction of a supersymmetric gauge theory of Yang-Mills vector Bosons, is more naturally generated out of a pure vector supersfield and not of a scalar or a spinor, the importance of a pure vector superfield cannot be overemphasized.

ON INVARIANTS AND SCALAR CHIRAL CORRELATION FUNCTIONS IN ${\mathcal N} = 1$ SUPERCONFORMAL FIELD THEORIES

A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in [Formula: see text] superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.

Supersymmetric classical cosmology

In this work a supersymmetric cosmological model is analyzed in which we consider a general superfield action of a homogeneous scalar field supermultiplet interacting with the scale factor in a supersymmetric FRW model. There appear fermionic superpartners associated with both the scale factor and the scalar field, and classical equations of motion are obtained from the super-Wheeler-DeWitt equation through the usual WKB method. The resulting supersymmetric Einstein-Klein-Gordon equations contain extra radiation and stiff matter terms, and we study their solutions in flat space for different scalar field potentials. The solutions are compared to the standard case, in particular those corresponding to the exponential potential, and their implications for the dynamics of the early Universe are discussed in turn.

A supersymmetric Lagrangian for fermionic fields with mass dimension one

We present the derivation of a supersymmetric model for fermionic fields with integer-valued mass dimension based on a general superfield with one free spinor index. First, we develop a formalism based on a general superfield with one free spinor index. Then, we systematically derive all associated chiral and antichiral superfields up to third order in covariant derivatives. Using this formalism we are able to construct a supersymmetric on-shell Lagrangian that contains a kinetic term for the fermionic fields with mass dimension one. We then derive the corresponding on-shell supercurrent and succeed in formulating a consistent second quantization for the component fields. Finally, we present our result for a supersymmetric Hamiltonian. As the Lagrangian is by construction supersymmetric and the Hamiltonian was derived from the Lagrangian using supersymmetry algebra the Hamiltonian must be positive definite.

Supertranslations to All Orders*

We calculate the transformation laws of the general linear superfield and chiral superfields under supertranslations to all orders in the translation parameters . We use the superfield formalism with complete expansions of the component fields in the coordinate shifts . The results show in particular how a general supertranslation transforms each component field of a supermultiplet into a complete superfield. The results also provide complete parametri-zations of orbits of component fields under supertranslations.

On Wess–Zumino gauge

In the relation between the linear (L) supersymmetry (SUSY) representation and the nonlinear (NL) SUSY representation we discuss the role of the Wess–Zumino gauge. We show in two-dimensional spacetime that a spontaneously broken LSUSY theory with mass and Yukawa interaction terms for a minimal off-shell vector supermultiplet is obtained from a general superfield without imposing any special gauge conditions in N=2 NL/L SUSY relation.

Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory

We derive the nilpotent (anti-)BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^\mu (with \mu = 0,1,2,3) and a couple of Grassmannian variables \theta and \bar{\theta}. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4, 1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism.

Formula omitted] non-linear supersymmetric mechanics

We construct a new two-dimensional N=8 supersymmetric mechanics with non-linear chiral supermultiplet. Being intrinsically non-linear this multiplet describes 2 physical bosonic and 8 fermionic degrees of freedom. We construct the most general superfield action of the sigma-model type and propose its simplest extension by a Fayet–Iliopoulos term. The most interesting property of the constructed system is a new type of geometry in the bosonic subsector, which is different from the special Kähler one characterizing the case of the linear chiral N=8 supermultiplet.

Formula omitted] mechanics in [formula omitted] harmonic superspace

The N = 8 , 1D analytic bi-harmonic superspace is shown to provide a natural setting for N = 8 supersymmetric mechanics associated with the off-shell multiplet ( 4 , 8 , 4 ) . The latter is described by an analytic superfield q 1 , 1 , and we construct the general superfield and component actions for any number of such multiplets. The set of transformations preserving the flat superspace constraints on q 1 , 1 constitutes N = 8 extension of the two-dimensional Heisenberg algebra h ( 2 ) , with an operator central charge. The corresponding invariant q 1 , 1 action is constructed. It is unique and breaks 1D scale invariance. We also find a one-parameter family of scale-invariant q 1 , 1 actions which, however, are not invariant under the full N = 8 Heisenberg supergroup. Based on preserving the bi-harmonic Grassmann analyticity, we formulate N = 8 , 1D supergravity in terms of the appropriate analytic supervielbeins. For its truncated version we construct, both at the superfield and component levels, the first example of off-shell q 1 , 1 action with local N = 8 , 1D supersymmetry. This construction can be generalized to any number of self-interacting q 1 , 1 .

Two-dimensional [formula omitted] supersymmetric mechanics in superspace

We construct a two-dimensional N=8 supersymmetric quantum mechanics which inherits the most interesting properties of N=2, d=4 supersymmetric Yang–Mills theory. Analyzing the superfield constraints, we show that only complex scalar fields from the N=2,d=4 vector multiplet become physical bosons in d=1. The rest of the bosonic components are reduced to auxiliary fields, thus giving rise to the (2,8,6) supermultiplet in d=1. We construct the most general superfield action for this supermultiplet and demonstrate that it possesses duality symmetry extended to the fermionic sector of theory. We also explicitly present the Dirac brackets for the canonical variables and construct the supercharges and Hamiltonian which form a N=8 super-Poincaré algebra with central charges. Finally, we discuss the duality transformations which relate the (2,8,6) supermultiplet with the (4,8,4) one.

DUALITY PROPERTIES OF SUPER D-BRANE ACTIONS IN GENERAL TYPE IIB SUPERGRAVITY BACKGROUND

We examine duality transformations of supersymmetric and κ-symmetric Dp-brane actions in a general type IIB supergravity background where in particular the dilaton and the axion are not supposed to be zero or a constant but a general superfield. Due to nonconstant dilaton and axion, we can explicitly show that the dilaton and the axion as well as the two two-form gauge potentials transform as doublets under the SL (2,R) transformation from the point of view of the world volume field theory.

Superfield effective action within the general chiral superfield model

The chiral superfield model associated with the low-energy limit of superstring theory and characterized by the Kahler and the chiral potential [K(Φ, \(\overline \Phi\)) and W(Φ), respectively] is analyzed. An approach to solving a general problem is developed, and quantum loop corrections at arbitrary K(Φ, \(\overline \Phi\)) and W(Φ) are found. Various aspects of a supergraph technique that are associated with calculating perturbative contributions to the superfield effective action are analyzed. Explicit expressions for the one-and two-loop corrections to the Kahler potential are calculated. The leading two-loop correction to the chiral potential is obtained, and it is shown that, irrespective of the form of K(Φ, \(\overline \Phi\)) and W(Φ), counterterms are not needed for deducing this correction.

On the structure of effective action in four-dimensional quantum dilaton supergravity

A general structure of effective action in a new chiral superfield model associated with N = 1, D = 4 supergravity is investigated. This model corresponds to finite quantum field theory and does not demand the regularization and renormalization of the effective action calculation. It is shown that in a local approximation the effective action is defined by two objects called the general superfield effective Lagrangian and the chiral superfield effective Lagrangian. A proper-time method is generalized for calculation of these two effective Lagrangians in a superfield manner. A power expansion of the effective action in supercovariant derivatives is formulated and the lower terms of such an expansion are calculated in explicit superfield form.

Topological amplitudes in heterotic superstring theory

We show that certain heterotic string amplitudes are given in terms of correlators of the twisted topological (2,0) SCFT, corresponding to the internal sector of the N = 1 space-time supersymmetric background. The genus g topological partition function F g corresponds to a term in the effective action of the form W 2 g , where W is the gauge or gravitational superfield. We study also recursion relations related to holomorphic anomalies, showing that, contrary to the type II case, they involve correlators of anti-chiral superfields. The corresponding terms in the effective action are of the form W 2 g Π n , where Π is a chiral superfield obtained by chiral projection of a general superfield. We observe that the structure of the recursion relations is that of N = 1 spacetime supersymmetry Ward identity. We give also a solution of the tree-level recursion relations and discuss orbifold examples.

Geometric superfield approach to superconformal mechanics

The new general geometric approach to d=1 conformally invariant systems, previously elaborated by the authors with an example of conformal mechanics, is applied in the supersymmetry case. The authors construct a manifestly invariant superfield description of the superconformal mechanics (SCM) models for arbitrary even N, N being a number of independent real d=1 Poincare supersymmetries. These systems are shown to result from nonlinear realisations of d=1 superconformal groups SU(1,1 mod N/2) in the cosets SU(1,1 mod N/2)/U(N/2). For the N=4 case, which has previously been worked out only on shell, they find two different off-shell formulations related via a duality transformation. The systems with higher N are essentially new. An effect of creating the U(1) central charge in the d=1, N=4 superconformal algebra su(1,1 mod 2) by the duality transformation is revealed. By extending the procedure employed in the bosonic case they derive general superfield solutions of the N=2 and N=4 SCM equations.