Superspace Action Research Articles

Remarks on the Integral Form of D=11 Supergravity

We make some considerations and remarks on D = 11 supergravity and its integral form. We start from the geometrical formulation of supergravity and by means of the integral form technique we provide a superspace action that reproduces (at the quadratic level) the recent formulation of supergravity in pure spinor framework. We also make some remarks on Chevalley-Eilenberg cocycles and their Hodge duals.

Supersymmetrizing the Pasti-Sorokin-Tonin action

In this paper the harmonic superspace action of the tensor multiplet of N = (1, 0), d = 6 supersymmetry is constructed which in the bosonic limit reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field. The action involves, besides the potential containing the dynamical fields, also an auxiliary tensor multiplet and a set of analytic superfields with gauge PST scalar among them. For each of gauge symmetries of the PST action, a superfield analog is found. The equations of motion are calculated and it is shown that no extra degrees of freedom appear.

Spin-3/2 and spin-2 charged massive states in a constant electromagnetic background

We develop in components the superspace action obtained in [1] describing the first massive level of the open charged superstring in a flat four-dimensional spacetime. In the absence of an electromagnetic background, we show how the Rarita-Schwinger and Fierz-Pauli Lagrangians are retrieved for spin-3/2 and 2, respectively. We then write different forms of the action in the presence of the electromagnetic background. The resulting equations of motion describe the propagation of fields of charged spin-3/2 and spin-1/2 on the one hand, and spin-2, 1 and 0 on the other.

Nonlinear [formula omitted] supersymmetry and 3D supersymmetric Born-Infeld theory

Dp-branes acquire effective nonlinear descriptions whose bosonic part is related to the Born-Infeld action. This nonlinearity has been proven to be a consequence of the partial N=2→N=1 supersymmetry breaking, originating from the solitonic nature of the branes. In this work, we focus on the effective descriptions of D2-branes. Using the Goldstone multiplet interpretation of the action and the method of nilpotent N=2 superfields, we construct the 3D, N=1 superspace effective action which makes the first supersymmetry manifest and realizes the second, spontaneously broken, supersymmetry nonlinearly. We show that there are two such supersymmetric extensions of the 3D Born-Infeld action which correspond to the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these results are derived by applying the constrained superfield approach on the N=2,D=3 vector and chiral multiplets after expanding them around a nontrivial vacuum. We find that these two descriptions are related by a duality transformation which results in the inversion of a dimensionless parameter. For both descriptions we derive the explicit bosonic and fermionic parts of the 3D super Born-Infeld action. Finally, consider the deformation of the Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like, gauge invariant, mass term.

Towards non-Archimedean superstrings

An action for a prospect of a p-adic open superstring on a target Minkowski space is proposed. The action is constructed for ‘worldsheet’ fields taking values in the p-adic field Qp, but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analogue of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for N vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on p-adic superstring amplitudes.

Superspace first order formalism, trivial symmetries and electromagnetic interactions of linearized supergravity

We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.

Higher spin supermultiplets in three dimensions: (2,0) AdS supersymmetry

Within the framework of (2,0) anti-de Sitter (AdS) supersymmetry in three dimensions, we propose a multiplet of higher-spin currents. Making use of this supercurrent, we construct two off-shell gauge formulations for a massless multiplet of half-integer superspin (s+12), for every integer s>0. In the s=1 case, one formulation describes the linearised action for (2,0) anti-de Sitter supergravity, while the other gives the type III minimal supergravity action in (2,0) AdS superspace, with both linearised supergravity actions originally derived in arXiv:1109.0496. We formulate topologically massive higher-spin supermultiplets in (2,0) AdS superspace. Our results admit a natural extension to the case of S3.

Equations of motion from Cederwall\u2019s pure spinor superspace actions

Using non-minimal pure spinor superspace, Cederwall has constructed BRST-invariant actions for D = 10 super-Born-Infeld and D = 11 supergravity which are quartic in the superfields. But since the superfields have explicit dependence on the non-minimal pure spinor variables, it is non-trivial to show these actions correctly describe super-Born-Infeld and supergravity. In this paper, we expand solutions to the equations of motion from Cederwall’s actions to leading order around the linearized solutions and show that they correctly describe the interactions of D = 10 super-Born-Infeld and D = 11 supergravity.

Wess-Zumino and super Yang-Mills theories in D=4 integral superspace

We reconstruct the action of N = 1, D = 4 Wess-Zumino and N = 1, 2, D = 4 super-Yang-Mills theories, using integral top forms on the supermanifold {mathrm{mathcal{M}}}^{left(left.4right|4right)} . Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.

Generalized K\xe4hler structures on group manifolds and T-duality

We study generalized Kähler structures on N = (2, 2) supersymmetric WessZumino-Witten models; we use the well known case of SU(2) × U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the highly nontrivial structure of the hitherto unexplored case of SU(3); these tools should be useful for studying many other examples. We find that different generalized Kähler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models can be found by T-duality transformations along affine isometries.

Pure spinor superspace action for D = 6, N = 1 super-Yang-Mills theory

A Batalin-Vilkovisky action for D = 6, N = 1 super-Yang-Mills theory, including coupling to hypermultiplets, is given. The formalism involves pure spinor superfields. The geometric properties of the D = 6, N = 1 pure spinors (which differ from Cartan pure spinors) are examined. Unlike the situation for maximally supersymmetric models, the fields and antifields (including ghosts) of the vector multiplet reside in separate superfields. The formalism provides an off-shell superspace formulation for matter hypermultiplets, which in a traditional treatment are on-shell.

String Sigma Models on Curved Supermanifolds

We use the techniques of integral forms to analyze the easiest example of two-dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D = 2 supermanifold, and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds, and we show that the definitions used for flat supermanifolds can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield E.

Supergravity in the Group‐Geometric Framework: A Primer

AbstractWe review the group‐geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of off‐shell supergravities and Chern‐Simons supergravity are discussed in detail. A cursory account of supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians d‐forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in dimensions are summarized in Appendices.

Super-Quantum Mechanics in the Integral Form Formalism

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincar\'e duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.

Soft-collinear supersymmetry

Soft-Collinear Effective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with super-symmetry (SUSY). Explicitly, the effective Lagrangian for mathcal{N}=1 SUSY Yang-Mills is cconstructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the effective Lagrangian for chiral SUSY theories with Yukawa couplings, specifically the single flavor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian — to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding fields along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. Defining the theory with respect to a specific frame obfuscates Lorentz invariance — given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence be-tween SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang-Mills in “collinear superspace”, a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of superfields. As a byproduct, bootstrapping up to the full theory yields the first algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. This work paves the way toward discovering the effective theory for the collinear limit of mathcal{N}=4 SUSY Yang-Mills.

The integral form of supergravity

By using integral forms we derive the superspace action of D=3, N=1 supergravity as an integral on a supermanifold. The construction is based on target space picture changing operators, here playing the role of Poincare' duals to the lower-dimensional spacetime surfaces embedded into the supermanifold. We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, thus providing another proof of their equivalence.

Brane induced supersymmetry breaking and de Sitter supergravity

We obtain a four-dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua by coupling a superspace action of minimal N=1, D=4 supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action describing the dynamics of a space-filling non-BPS 3-brane in N=1, D=4 superspace. To the quadratic order in the goldstino field the obtained action coincides with earlier constructions of supergravities with nilpotent superfields, while matching the higher-order contributions will require a non-linear redefinition of fields. In the unitary gauge, in which the goldstino field is set to zero, the action coincides with that of Volkov and Soroka. We also show how a nilpotency constraint on a chiral curvature superfield emerges in this formulation.

New approach to curved projective superspace

We present a new formulation of curved projective superspace. The 4D N=2 supermanifold M^{4|8} (four bosonic and eight Grassmann coordinates) is extended by an auxiliary SU(2) manifold, which involves introducing a vielbein and related connections on the full M^{7|8} = M^{4|8} x SU(2). Constraints are chosen so that it is always possible to return to the central gauge where the auxiliary SU(2) manifold largely decouples from the curved manifold M^{4|8} describing 4D N=2 conformal supergravity. We introduce the relevant projective superspace action principle in the analytic subspace of M^{7|8} and construct its component reduction in terms of a five-form J living on M^4 x C, with C a contour in SU(2). This approach is inspired by and generalizes the original approach taken in arXiv:0805.4683 and related works, which can be identified with a complexified version of the central gauge of the formulation presented here.

Starobinsky inflation from new-minimal supergravity

In the new-minimal supergravity formulation we present the embedding of the R + R2 Starobinsky model of inflation. Starting from the superspace action we perform the projection to component fields and identify the Starobinsky model in the bosonic sector. Since there exist no other scalar fields, this is by construction a single field model. This higher curvature supergravity also gives rise to a propagating massive vector. Finally we comment on the issues of higher order corrections and initial conditions.

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.