Scalar Superfield Research Articles

EmbeddingR+R2inflation in supergravity

We find the natural embedding of the (R+R^2)-inflationary model into the recently constructed N=1 F(\cal R)-supergravity. It gives a simple and viable realization of chaotic inflation in supergravity. The only requirement for a slow-roll inflation is the existence of the (\cal R)^3-term with an anomalously large coefficient in Taylor expansion of the F(\cal R) function, where \cal R is the covariantly-chiral scalar supercurvature superfield.

D = 11 SUPERGRAVITY WITH MANIFEST SUPERSYMMETRY

The complete supersymmetric classical Batalin–Vilkovisky action for 11-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.

NewN=4supersymmetric Yang-Mills path integral

Using Lorentz covariant spinor helicity formalism we reorganize the unitary scalar superfield light-cone path integral for the N=4 supersymmetric Yang-Mills theory. In new variables in the chiral Fourier superspace the quadratic and cubic parts of the classical action have manifest Lorentz, kinematical and dynamical supersymmetry, with the exception of terms which contribute only to the contact terms in the supergraphs with propagators shrinking to a point. These terms have the same structure as supergraphs with quartic light-cone vertices, which break dynamical supersymmetry. We present evidence that all complicated terms breaking dynamical supersymmetry have to cancel and therefore can be omitted. It is plausible that the new form of the path integral leads to a set of relatively simple unitarity based rules with manifest N=4 supersymmetry.

$ \mathcal{N} = 2 $ supergravity and supercurrents

We address the problem of classifying all N=2 supercurrent multiplets in four space-time dimensions. For this purpose we consider the minimal formulation of N=2 Poincare supergravity with a tensor compensator, and derive its linearized action in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, a vector multiplet, and a tensor multiplet. Such an action was ruled out to exist in the past. Using the action constructed, one can derive other models for linearized N=2 supergravity by applying N=2 superfield duality transformations. The action depends parametrically on a constant non-vanishing real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the tensor compensator. Upon reduction to N=1 superfields, we show that the model describes two dually equivalent formulations for the massless multiplet (1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0, the action describes (i) new minimal N=1 supergravity; and (ii) the Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0, on the other hand, the action describes (i) old minimal N=1 supergravity; and (ii) the Ogievetsky-Sokatchev gravitino multiplet.

Coleman-Weinberg mechanism in a three-dimensional supersymmetric Chern-Simons-matter model

Using the superfield formalism, we study the dynamical breaking of gauge symmetry in the N=1 three-dimensional supersymmetric Chern-Simons model, coupled to a complex scalar superfield with a quartic self-coupling. This is an analogue of the conformally invariant Coleman-Weinberg model in four spacetime dimensions. We show that a mass for the gauge and matter superfields are dynamically generated after two-loop corrections to the effective superpotential. We also discuss the N=2 extension of our work, showing that the Coleman-Weinberg mechanism in such model is not feasible, because it is incompatible with perturbation theory.

2D $ \mathcal{N} = \left( {4,4} \right) $ superspace supergravity and bi-projective superfields

We propose a new superspace formulation for $ \mathcal{N} = \left( {4,4} \right) $ conformal supergravity in two dimensions. This is based on a geometry where the structure group of the curved superspace is chosen to be SO(1,1) × SU(2) L × SU(2) R . The off-shell supergravity multiplet possesses super-Weyl transformations generated by an unconstrained real scalar superfield. The new supergravity formulation turns out to be an extension of the minimal multiplet introduced in 1988 by Gates et. al. and it allows the existence of various off-shell matter supermultiplets. Covariant twisted-II and twisted-I multiplets respectively describe the field strength of an Abelian vector multiplet and its prepotential. Moreover, we introduce covariant bi-projective superfields. These define a large class of matter multiplets coupled to 2D $ \mathcal{N} = \left( {4,4} \right) $ conformal supergravity. They are the analogue of the covariant projective superfields recently introduced for 4D and 5D matter-coupled supergravity but they differ by the fact that bi-projective superfields are defined with the use of two $ \mathbb{C}{P^1} $ instead of one. We conclude by giving a manifestly locally supersymmetric and super-Weyl invariant action principle in bi-projective superspace.

On the renormalization of theories of a scalar chiral superfield

An exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action, it is shown that the nonperturbative nonrenormalization theorem follows, quite simply, from the flow equation. Next, it is argued that there do not exist any physically acceptable non-trivial fixed points. Finally, the Wess-Zumino model is considered, as a low energy effective theory. Following an evaluation of the one and two loop β-function coefficients, to illustrate the ease of use of the formalism, it is shown that the β-function in the massless case does not receive any nonperturbative power corrections.

Dynamical supersymmetry in maximally supersymmetric gauge theories

Maximally supersymmetric theories can be described by a single scalar superfield in light-cone superspace. When they are also (super)conformally invariant, they are uniquely specified by the form of the dynamical supersymmetry. We present an explicit derivation of the light-cone superspace form of the dynamical supersymmetry in the cases of ten- and four-dimensional super-Yang–Mills, and the three-dimensional Bagger–Lambert–Gustavsson theory, starting from the covariant formulation of these theories.

Towards a manifestly supersymmetric action for 11-dimensional supergravity

We investigate the possibility of writing a manifestly supersymmetric action for 11-dimensional supergravity. The construction involves an explicit relation between the fields in the super-vielbein and the super-3-form, and uses non-minimal pure spinors. A simple cubic interaction term for a single scalar superfield is found.

N=8supergravity on the light cone

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.

Seeking the loop quantum gravity Barbero-Immirzi parameter and field in 4D,N=1supergravity

We embed the loop quantum gravity Barbero-Immirzi parameter and field within an action describing 4D, $\mathcal{N}=1$ supergravity and thus within a low-energy effective action of superstring/M theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the loop quantum gravity action. This suggest the possibility of a relation between loop quantum gravity and supersymmetric string theory, where the Barbero-Immirzi parameter and field of the former play the role of the supersymmetric axion in the latter. Adding matter fermions in loop quantum gravity may require the extension of the Holst action through the Nieh-Yan topological invariant, while in pure, matter-free supergravity their supersymmetric extensions are the same. We show that, when the Barbero-Immirzi parameter is promoted to a field in the context of 4D supergravity, it is equivalent to adding a dynamical complex chiral (dilaton-axion) superfield with a nontrivial kinetic term (or K\ahler potential), coupled to supergravity.

Equivalence between supersymmetric self-dual and Maxwell–Chern–Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell–Chern–Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss.

UV properties of 𝒩 = 8 supergravity

AbstractWe discuss here the recent developments in 𝒩 = 8 supergravity. In particular, we propose to use the light‐cone superspace with an unconstrained chiral scalar superfield for the studies of the UV structure of the perturbative 𝒩 = 8 supergravity. For this purpose we construct the generating functional for the light‐cone momentum space superfield amplitudes. We prove an 𝒩 = 8 equivalence theorem for the light‐cone and covariant on‐shell amplitudes. We point out an interesting relation between our light‐cone formalism and Nair' s construction and supertwistors. We also point out the importance of the non‐linearly realized E(7,7), symmetry for these studies and argue that this symmetry may be anomaly‐free.

Superstring-inspired supergravity as the universal source of inflation and quintessence

We prove (in superspace) the equivalence between the higher-derivative N=1 supergravity, defined by a holomorphic function F of the chiral scalar curvature superfield, and the standard theory of a chiral scalar superfield with a chiral superpotential W, coupled to the (minimal) Poincaré supergravity in four spacetime dimensions. The relation between the holomorphic functions F and W is found. It can be used as the technical framework for the possible scenario unifying the early Universe inflation and the present Universe acceleration. We speculate on the possible origin of our model as the effective supergravity generated by quantum superstrings, with a dilaton–axion field as the leading field component of the chiral superfield.

Dynamical breaking of gauge symmetry in supersymmetric quantum electrodynamics in three-dimensional spacetime

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term A{sup {alpha}}A{sub {alpha}} through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

Three-dimensional nonanticommutative superspace

We propose two alternative formulations for a three-dimensional non-anticommutative superspace in which some of the fermionic coordinates obey Clifford anticommutation relations. For this superspace, we construct the supersymmetry generators satisfying standard anticommutation relations and the corresponding supercovariant derivatives. We formulate a scalar superfield theory in such a superspace and calculate its propagator. We also suggest a prescription for the introduction of interactions in such theories.

A note on N=(2,2) superfields in two dimensions

Abstract Motivated by the results in hep-th/0508228 , we perform a careful analysis of the allowed linear constraints on N = ( 2 , 2 ) scalar superfields. We show that only chiral, twisted-chiral and semi-chiral superfields are possible. Various subtleties are discussed.

6D supersymmetric nonlinear sigma-models in 4D, Script N = 1 superspace

Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.

On the construction of linearized N = 1 supergravities coupled to matter

We present a modified formulation of minimal N = 1 linearized supergravity coupled to generic N = 1 supersymmetric matter. The formalism is based on the superprojectors, superspin-transition operators, vector and scalar superfield. Such approach has some advantages for finding superpropagators.

BRST–VSUSY SUPERSPACE AND TWISTED SUPERFIELDS FOR D=4 BF SYSTEMS

We propose to construct the off-shell supersymmetric structure present in quantized D=4 BF theories in terms of a BRST–VSUSY superspace formalism. The method is based on the introduction of constrained scalar superfields. We also discuss how to find the D=4 BF action from D=N=4 supersymmetric action by an appropriate twisting process.