Superfield Supergravity Research Articles

Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors TABC, and curvature supertensors RABcd in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, mathcal{N} = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, mathcal{N} = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, mathcal{N} = 1 superspace

For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, mathcal{N} = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, mathcal{N} = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, mathcal{N} = 1 superfield supergravity. We find the 11D, mathcal{N} = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.

A detailed discussion of superfield supergravity prepotential perturbations

This paper presents a detailed discussion of the issue of supergravity perturbations around the flat five dimensional superspace required for manifest superspace formulations of the supergravity side of the AdS5/CFT4 correspondence.

Different representations for the action principle in 4D 𝒩 = 2 supergravity

Within the superspace formulation for four-dimensional = 2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate two approaches to reduce the superfield action to components. One of them is based on the principle of projective invariance which is a purely = 2 concept having no analogue in simple supergravity. In this approach, the component reduction of the action is performed without imposing any Wess-Zumino gauge condition, that is by keeping intact all the gauge symmetries of the superfield action, including the super-Weyl invariance. As a simple application, the c-map is derived for the first time from superfield supergravity. Our second approach to component reduction is based on the method of normal coordinates around a submanifold in a curved superspace, which we develop in detail. We derive differential equations which are obeyed by the vielbein and the connection in normal coordinates, and which can be used to reconstruct these objects, in principle in closed form. A separate equation is found for the super-determinant of the vielbein E = Ber(EMA), which allows one to reconstruct E without a detailed knowledge of the vielbein. This approach is applicable to any supergravity theory in any number of space-time dimensions. As a simple application of this construction, we reduce an integral over the curved = 2 superspace to that over the chiral subspace of the full superspace. We also give a new representation for the curved projective-superspace action principle as a chiral integral.

Five-dimensional superfield supergravity

We present a projective superspace formulation for matter-coupled simple supergravity in five dimensions. Our starting point is the superspace realization for the minimal supergravity multiplet proposed by Howe in 1981. We introduce various off-shell supermultiplets (i.e. hypermultiplets, tensor and vector multiplets) that describe matter fields coupled to supergravity. A projective-invariant action principle is given, and specific dynamical systems are constructed including supersymmetric nonlinear sigma-models. We believe that this approach can be extended to other supergravity theories with eight supercharges in D⩽6 space–time dimensions, including the important case of 4D N=2 supergravity.

Field Strengths of Linearized 5D,N= 1 Superfield Supergravity On a 3-Brane

Recently a description of linearized 5D supergravity in 4D, N =1 superspace was presented. By analyzing the on-shell component Lagrangian, this description was proven to be Lorentz invariant in five dimensions. This paper describes a geometric formulation of the 5D supergravity in 4D, N =1 superspace. Using this new formalism, the on-shell structure of the previous description is verified from purely superspace methods. This geometric description provides a connection to dimensionally reduced manifestly supersymmetric 5D supergravity.

D=4supergravity dynamically coupled to superstring in a superfield Lagrangian approach

We elaborate a full superfield description of the interacting system of dynamical $D=4,$ $N=1$ supergravity and a dynamical superstring. As far as a minimal formulation of simple supergravity is used, such a system should contain as well the tensor (real linear) multiplet which describes the dilaton and the two-superform gauge field whose pullback provides the Wess-Zumino term for the superstring. The superfield action is given by the sum of the Wess-Zumino action for $D=4,$ $N=1$ superfield supergravity, the superfield action for the tensor multiplet in curved superspace, and the Green-Schwarz superstring action. The latter includes the coupling to the tensor multiplet both in the Nambu-Goto and in the Wess-Zumino terms. We derive superfield equations of motion including, besides the superfield supergravity equations with the source, the source-full superfield equations for the linear multiplet. The superstring equations keep the same form as for the superstring in supergravity and 2-superform background. The analysis of gauge symmetries shows that the superfield description of the interacting system is gauge equivalent to the dynamical system described by the sum of the spacetime, component action for supergravity interacting with the tensor multiplet, and of the purely bosonic string action.

Complete solution of 2D superfield supergravity from graded Poisson-sigma models, and the super point particle

Recently an alternative description of 2D supergravities in terms of graded Poisson-sigma models (GPSM) has been given. As pointed out previously by the present authors a certain subset of GPSMs can be interpreted as ``genuine'' supergravity, satisfying the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of GPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the GPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the GPSM frame, where ``supergeodesics'' can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications such as the (almost) trivial quantization are mentioned.

(4,4) superfield supergravity

We present the N = 4 superspace constraints for the two-dimensional off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N = 4 super-Weyl transformations, whose N = 4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose an ansatz which makes the N = 4 superconformal flatness of the N = 4 supergravity curved superspace manifest. Locally (4,4) supersymmetric TM-I matter couplings are constructed, with potential terms resulting from spontaneous supersymmetry breaking. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.

Quantum dynamics of N = 1, D = 4 supergravity compensator

A new $N=1$ superfield theory in $D=4$ flat superspace is suggested. It describes dynamics of supergravity compensator and can be considered as a low-energy limit for $N=1$, $D=4$ superfield supergravity. The theory is shown to be renormalizable in infrared limit and infrared free. A quantum effective action is investigated in infrared domain.

ON QUANTUM MODEL OF SUPERGRAVITY COMPENSATOR

A new N=1 superfield model in D=4 flat superspace is suggested. This model describes dynamics of chiral compensator and can be treated as a low-energy limit of D=4, N=1 quantum superfield supergravity. Renormalization structure of this model is studied and one-loop counterterms are calculated. It is shown that the theory is infrared-free. An effective action for the model under consideration is investigated in the infrared domain. The lower contributions to the one-loop effective action are computed in explicit form.

N = 2 super-Weyl symmetry, super-Liouville theory and super-Riemannian surfaces

The finite form of the N=2 super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional N=2 superfield supergravity are found in N=2 superspace. The super-Weyl anomaly of the N=2 extended fermionic string theory is computed in terms of the N=2 superfields, by using a short-time expansion of the N=2 chiral heat kernel. The super-Weyl invariant N=2 superconformal structure is introduced, and a new definition of the N=2 super-Riemannian surfaces is proposed.

Heterotic-string anomalies in (1,0) superspace

The supergravitational and super-Weyl anomalies of the heterotic string are computed using the background field method for (1,0) superfield supergravity. The cancellation, at the critical dimension, of the full super-Weyl anomaly is an automatic consequence of our supergraph calculation. The (1,0) superfield action is also given for the “bosonic formulation” of the heterotic string.

D=2 superfield supergravity, local (supersymmetry)2 and non-linear Σ models

The authors construct the unconstrained superfield formulation of D=2, N=1 supergravity and give general matter couplings. A new type of non-linear sigma model that possesses (local supersymmetry)(X)(local supersymmetry) is described.

Quantum superfield supergravity

The quantization of superfield supergravity is described.

Superspace formulation of new non-linear sigma models

The superspace formulation of two classes of supersymmetric non-linear σ-models are presented. Two alternative N = 1 superspace formulations are given for the d = 2 supersymmetric non-linear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N = 2 vector multiplet is used to construct a new class of d = 4 non-linear σ-models which when reduced to d = 2 possess N = 4 supersymmetry. Implications of these two classes of non-linear σ-models for N 4 superfield supergravity are discussed.

Quantum superfield supergravity with off-shell background fields

We describe the quantization of superfield supergravity in the presence of off-shell background fields. For simplicity we work only to first in off-shell quantities, but this is sufficient for computing quantum properties of the supergravity supercurrent such as its supertrace.

Linearized N = 2 superfield supergravity

We present the formulation of linearized SU(2) supergravity and U(2) conformal supergravity in terms of unconstrained N = 2 superfields: the gauge superfield, compensating superfields, gauge transformations, supertensors, actions and covariant derivatives.

Linearised N=2 superfield supergravity

The authors present a formulation of linearised N=2 supergravity in superfield form by solving linearised torsion constraints in superspace and identifying the irreducible supergravity. After building the linearised Lagrangians for N=1 supergravity (minimal and non-minimal) from the respective irreducible representations, they construct an unconstrained linearised superfield Lagrangian for the N=2 case.

Supergraphity: (I). Background field formalism

We describe the background field formalism in superfield supergravity. This formalism makes calculations of one-loop quantities no more difficult than corresponding calculations in QCD. Unlike component methods, which violate manifest global supersymmetry with non-supersymmetric gauge conditions, our techniques, in conjunction with those described in previous papers, also allow the straightforward calculation of higher loops.