Chiral Scalar Superfield Research Articles

A large-N tensor model with four supercharges

We study a supersymmetric tensor model with four supercharges and O(N)3 global symmetry. The model is based on a chiral scalar superfield with three indices and quartic tetrahedral interaction in the superpotential, which is relevant below three dimensions. In the large-N limit the model is dominated by melonic diagrams. We solve the Dyson-Schwinger equations in superspace for generic d and extract the dimension of the chiral field and the dimensions of bilinear operators transforming in various representations of O(N)3. We find that all operator dimensions are real and above the unitarity bound for 1 < d < 3. Our results also agree with perturbative results in 3 − ε expansion. Finally, we extract the large spin behaviour of bilinear operators and discuss the connection with lightcone bootstrap.

Higher spin supercurrents in anti-de Sitter space

We propose higher spin supercurrent multiplets for mathcal{N}=1 supersymmetric field theories in four-dimensional anti-de Sitter space (AdS). Their explicit realisations are derived for various supersymmetric theories, including a model of N massive chiral scalar superfields with an arbitrary mass matrix. We also present new off-shell gauge formulations for the massless mathcal{N}=1 supersymmetric multiplet of integer superspin s in AdS, where s = 2, 3, . . . , as well as for the massless gravitino multiplet (superspin s = 1) which requires special consideration.

Non-conformal higher spin supercurrents

In four spacetime dimensions there exist two off-shell formulations for the massless multiplet of superspin (s+12), where s=2,3,…. These supersymmetric higher spin gauge theories, known as longitudinal and transverse, are dual to each other and describe two massless fields of spin (s+12) and (s+1) upon elimination of the auxiliary fields. They respectively reduce, in the limiting case of s=1, to the linearised actions for the old minimal and the n=−1 non-minimal N=1 supergravity theories. Associated with these gauge massless theories are non-conformal higher spin supercurrent multiplets which we describe. We demonstrate that the longitudinal higher spin supercurrents are realised in the model for a massive chiral scalar superfield only if s is odd, s=2n+1, with n=1,2,….

$ \mathcal{N} $ = 4 supersymmetric Yang-Mills theories in AdS3

For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4 vector multiplets, we provide complete N=4 SYM actions in (2,0) AdS superspace for all types of N=4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting N=2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS_3 and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the N=4 Cotton superfield. Thus our results explain the mysterious structure of N=4 supersymmetric Yang-Mills theories on S^3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.

The Volkov–Akulov–Starobinsky supergravity

We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield X, which is subject however to the constraint X2=0 so that it describes only a Volkov–Akulov goldstino and an auxiliary field. We also construct the dual higher-derivative model, which rests on a chiral scalar curvature superfield R subject to the constraint R2=0, where the goldstino dual arises from the gauge-invariant gravitino field strength as γmnDmψn. The final bosonic action is an R+R2 theory involving an axial vector Am that only propagates a physical pseudoscalar mode.

On the supersymmetrization of inflation in f (R) gravity

An N=1 Poincare supergravity action, suitable for describing the Starobinsky inflation, is proposed. It extends f(R) gravity to supergravity in its old-minimal version. The action is parametrized by a single holomorphic potential and a single non-holomorphic potential, and can be dualized into the standard matter-coupled supergravity action, with the "matter" given by two chiral superfields. The action extends the earlier proposals for embedding the Starobinsky inflation into supergravity, and can be further generalized to include quantum corrections to the inflation. Our approach assumes the gravitational origin of inflaton and quintessence in the context of supergravity, by using a single chiral scalar curvature superfield.

Nonlinear sigma models with AdS supersymmetry in three dimensions

In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative integers p>=q such that p+q=N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear sigma-models. We classify all possible types of hyperkahler target spaces for the cases N=3 and N=4 by making use of two different realizations for the most general (p,q) supersymmetric sigma-models: (i) off-shell formulations in terms of N=3 and N=4 projective supermultiplets; and (ii) on-shell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N=3,4 AdS supersymmetry, nonlinear sigma-models can support one of the following target space geometries: (i) hyperkahler cones; (ii) non-compact hyperkahler manifolds with a U(1) isometry group which acts non-trivially on the two-sphere of complex structures; (iii) arbitrary hyperkahler manifolds including compact ones. The option (iii) is realized only in the case of critical (4,0) AdS supersymmetry. As an application of the (4,0) AdS techniques developed, we also construct the most general nonlinear sigma-model in Minkowski space with a non-centrally extended N=4 Poincare supersymmetry. Its target space is a hyperkahler cone (which is characteristic of N=4 superconformal sigma-models), but the sigma-model is massive. The Lagrangian includes a positive potential constructed in terms of the homothetic conformal Killing vector the target space is endowed with. This mechanism of mass generation differs from the standard one which corresponds to a sigma-model with the ordinary N=4 Poincare supersymmetry and which makes use of a tri-holomorphic Killing vector.

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.

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.

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 a supersymmetric completion of theR4term in IIB supergravity

We analyze the possibility of constructing a supersymmetric invariant that contains the ${R}^{4}$ term among its components as a superpotential term in type IIB on-shell superspace. We consider a scalar superpotential, i.e. an arbitrary holomorphic function of a chiral scalar superfield. In general, type IIB superspace does not allow for the existence of chiral superfields, but the obstruction vanishes for a specific superfield, the dilaton superfield. This superfield contains all fields of type IIB supergravity among its components, and its existence is implied by the solution of the Bianchi identities. The construction requires the existence of an appropriate chiral measure, and we find an obstruction to the existence of such a measure. The obstruction is closely related to the obstruction for the existence of chiral superfields and is non-linear in the fields. These results imply that the type IIB superinvariant related to the ${R}^{4}$ term is not associated with a scalar chiral superpotential.

Dynamical superfield theory of free massive superspin-1 multiplet

We construct an N=1 supersymmetric Lagrangian model for the massive superspin-1 superfield. The model is described by a dynamical spinor superfield and an auxiliary chiral scalar superfield. On-shell this model leads to a spin-12, spin-32 and two spin-1 propagating component fields. The superfield action is given and its structure in the fermionic component sector is presented. We prove that the most general theory is characterized by a one parameter family of actions. The massless limit is shown to correspond to the dynamics of both the gravitino and superhelicity-12 multiplets.

Bogomol’nyi-Prasad-Sommerfield walls and junctions in supersymmetric nonlinear sigma models

BPS walls and junctions are studied in ${\cal N}=1$ SUSY nonlinear sigma models in four spacetime dimensions. New BPS junction solutions connecting N discrete vacua are found for nonlinear sigma models with several chiral scalar superfields. A nonlinear sigma model with a single chiral scalar superfield is also found which has a moduli space of the topology of $S^1$ and admits BPS walls and junctions connecting arbitrary points in moduli space. SUSY condition in nonlinear sigma models are classified either as stationary points of superpotential or singularities of the K\"ahler metric in field space. The total number of SUSY vacua is invariant under holomorphic field redefinitions if we count ``runaway vacua'' also.

Cosmic string configuration in the supersymmetric CSKR theory

We study a cosmic string solution of an ( N=1)-supersymmetric version of the Cremmer–Scherk–Kalb–Ramond (CSKR) model coupled to scalars and fermions. The 2-form gauge potential is proposed to couple non-minimally to matter, here described by a chiral scalar superfield. The important outcome is that supersymmetry is kept exact in the core and it may also hold in the exterior region of the string. We contemplate the configurations of the bosonic sector and we check that the solutions saturate the Bogomol'nyi bound. A glimpse on the fermionic zero modes is also given.

Structure of the chiral scalar superfield in ten dimensions

We describe the tensors and spinor-tensors included in the θ-expansion of the ten-dimensional chiral scalar superfield. The product decompositions of all the irreducible structures with θ and the θ2 tensor are provided as a first step toward the obtention of a full tensor calculus for the superfield.

PREPOTENTIALS FOR (2, 2) SUPERGRAVITY

We present a complete solution to the constraints for two-dimensional N = 2 supergravity in N = 2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield Hm and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield ϕ.

An intermediate scale induced by F-typeK SUSY breaking in [formula omitted] SUGRA

In the framework of SU(n,1) SU(n) × U(1) supergravity theory, the F-type SUSY breaking mass splitting for a gauge non-singlet chiral scalar superfield is shown to radiatively induce both the intermediate symmetry breaking and electroweak symmetry breaking with the breaking scales M INT(≈10 11–12 GeV) and 〈 h〉≈O(10 2 GeV) being heirarchically separated. this hierarchy is due to a mechanism that there exists a non-renormalizable superpotential term which gives rise to a (Higgs field) 6 term in the scalar potential for the intermediate symmetry breaking Higgses but there appears no such term for the electroweak symmetry breaking Higgs. In case of the SU(4)×SU(2) L × SU(2) R string model, this mechanism explains the reason why SU(2)R breaks down earlier (i.e., at a bigger scale) than SU(2)L.

Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence

The theories of a chiral spinor and real scalar superfield (scalar multiplet) in an external field of simple supergravity are considered. Both theories are gauge theories with linearly dependent generators. The prescription for quantization is given, the quantum effective actions are constructed and quantum equivalence of the above-mentioned theories to the theory of a nonconformal chiral scalar superfield is proved.