Covariant Superfield Research Articles

Hidden Supersymmetry as a Key to Constructing Low-Energy Superfield Effective Actions

In this review paper, we outline and exemplify the general method of constructing the supefield low-energy quantum effective action of supersymmetric Yang-Mills (SYM) theories with extended supersymmetry in the Coulomb phase, grounded upon the requirement of invariance under the non-manifest (hidden) part of the underlying supersymmetry. In this way we restore the ${\cal N}=4$ supersymmetric effective actions in $4D, {\cal N}=4$ SYM, ${\cal N}=2$ supersymmetric effective actions in $5D, {\cal N}=2$ SYM and ${\cal N}=(1,1)$ supersymmetric effective actions in $6D, {\cal N}=(1,1)$ SYM theories. The manifest off-shell fractions of the full supersymmetry are, respectively, $4D, {\cal N}=2$, $5D, {\cal N}=1$ and $6D, {\cal N}=(1,0)$ supersymmetries. In all cases the effective actions depend on the corresponding covariant superfield SYM strengths and the hypermultiplet superfields. The whole construction essentially exploits a power of the harmonic superspace formalism.

Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

Deformed mathcal{N}=8 mechanics of (8, 8, 0) multiplets

We construct new models of “curved” SU(4|1) supersymmetric mechanics based on two versions of the off-shell multiplet (8, 8, 0) which are “mirror” to each other. The worldline realizations of the supergroup SU(4|1) are treated as a deformation of flat mathcal{N}=8 , d = 1 supersymmetry. Using SU(4|1) chiral superfields, we derive invariant actions for the first-type (8, 8, 0) multiplet, which parametrizes special Kähler manifolds. Since we are not aware of a manifestly SU(4|1) covariant superfield formalism for the second-type (8, 8, 0) multiplet, we perform a general construction of SU(4|1) invariant actions for both multiplet types in terms of SU(2|1) superfields. An important class of such actions enjoys superconformal OSp(8|2) invariance. We also build off-shell actions for the SU(4|1) multiplets (6, 8, 2) and (7, 8, 1) through appropriate substitutions for the component fields in the (8, 8, 0) actions. The (6, 8, 2) actions are shown to respect superconformal SU(4|1, 1) invariance.

Chern-Simons actions and their gaugings in 4D, N =1 superspace

We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.

Light-cone analysis of the pure spinor formalism for the superstring

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2\pi i}\oint\lambda^{\alpha}d_{\alpha}$. In this paper, a similarity transformation is found which simplifies the form of $Q$ and maps the light-cone description of the superstring vertices into DDF-like operators in the cohomology of $Q$.

Higher spins from non-linear realizations of [formula omitted

We exhibit surprising relations between higher spin theory and non-linear realizations of the supergroup OSp(1|8), a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. We construct a realization of OSp(1|8) on the coset supermanifold OSp(1|8)/SL(4,R) which involves the tensorial superspace R(10|4) and Goldstone superfields given on it. The covariant superfield equation encompassing the component ones for all integer and half-integer massless higher spins amounts to the vanishing of covariant spinor derivatives of the suitable Goldstone superfields, and, via Maurer–Cartan equations, to the vanishing of SL(4,R) supercurvature in odd directions of R(10|4). Aiming at higher spin extension of the Ogievetsky–Sokatchev formulation of N=1 supergravity, we generalize the notion of N=1 chirality and construct first examples of invariant superfield actions involving a non-trivial interaction. Some other potential implications of OSp(1|8) in the proposed setting are briefly outlined.

Non-anticommutative chiral singlet deformation of [formula omitted] gauge theory

We study the SO ( 4 ) × SU ( 2 ) invariant Q-deformation of Euclidean N = ( 1 , 1 ) gauge theories in the harmonic superspace formulation. This deformation preserves chirality and Grassmann harmonic analyticity but breaks N = ( 1 , 1 ) to N = ( 1 , 0 ) supersymmetry. The action of the deformed gauge theory is an integral over the chiral superspace, and only the purely chiral part of the covariant superfield strength contributes to it. We give the component form of the N = ( 1 , 0 ) supersymmetric action for the gauge groups U(1) and U ( n > 1 ) . In the U(1) and U(2) cases, we find the explicit nonlinear field redefinition (Seiberg–Witten map) relating the deformed N = ( 1 , 1 ) gauge multiplet to the undeformed one. This map exists in the general U ( n ) case as well, and we use this fact to argue that the deformed U ( n ) gauge theory can be nonlinearly reduced to a theory with the gauge group SU ( n ) .

Towards a consistent noncommutative supersymmetric Yang-Mills theory: Superfield covariant analysis

Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for ${\mathcal N} = 1, 2$, and finite for ${\mathcal N} = 4$. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the ${\cal N} = 1, 2, 4$ noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield $V$. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the $V$ superfield exhibits UV divergences. They are found to cancel, in the Feynman gauge, for the maximally extended ${\cal N} = 4$ supersymmetric theory. This gives support to the belief that the ${\cal N} = 4$ NCSYM theory is UV finite.

Superfield covariant analysis of the divergence structure of noncommutative supersymmetricQED4

Commutative supersymmetric Yang-Mills is known to be renormalizable for ${\cal N} = 1, 2$, while finite for ${\cal N} = 4$. However, in the noncommutative version of the model (NCSQED$_4$) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED$_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for ${\cal N} = 1$ that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.

On the finiteness of noncommutative supersymmetric QED3 in the covariant superfield formulation

The three-dimensional noncommutative supersymmetric QED is investigated within the superfield approach. We prove the absence of UV/IR mixing in the theory at any loop order and demonstrate its one-loop finiteness.

Modifications of Sp(2) covariant superfield quantization

We propose a modification of the Sp(2) covariant superfield quantization to realize a superalgebra of generating operators isomorphic to the massless limit of the corresponding superalgebra of the osp(1,2) covariant formalism. The modified scheme ensures the compatibility of the superalgebra of generating operators with extended BRST symmetry without imposing restrictions eliminating superfield components from the quantum action. The formalism coincides with the Sp(2) covariant superfield scheme and with the massless limit of the osp(1,2) covariant quantization in particular cases of gauge-fixing and solutions of the quantum master equations.

Background harmonic superfields inN=2 supergravity

A modification of the harmonic superfield formalism in $D=4, N=2$ supergravity using a subsidiary condition of covariance under the background supersymmetry with a central charge ($B$-covariance) is considered. Conservation of analyticity together with the $B$-covariance leads to the appearance of linear gravitational superfields. Analytic prepotentials arise in a decomposition of the background linear superfields in terms of spinor coordinates and transform in a nonstandard way under the background supersymmetry. The linear gravitational superfields can be written via spinor derivatives of nonanalytic spinor prepotentials. The perturbative expansion of the extended supergravity action in terms of the $B$-covariant superfields and the corresponding version of the differential-geometric formalism are considered. We discuss the dual harmonic representation of the linearized extended supergravity, which corresponds to the dynamical condition of Grassmann analyticity.

The reduction of N = 1 supersymmetric Yang-Mills theory to the light-cone gauge

We describe in detail how the non-polynomial N = 1 super Yang-Mills lagrangian in superfield form can be reduced to the light-cone gauge with only propagating modes. This is achieved by integrating out the inappropriate light-cone projections of the superspace Grasmann variables, leaving a light-cone superspace lagrangian agreeing with that obtained earlier by one of us. The implications of this for the construction of a covariant superfield version of N = 4 SYM are discussed briefly.

Superfield formulation of OSp(1,4) supersymmetry

A self-contained superfield approach to global supersymmetry in anti-de Sitter space (OSp(1,4)) is developed. General transformation laws for OSp(1,4) superfields are established, and all basic elements of the OSp(1,4)-covariant formalism, such as covariant superfield derivatives, invariant integration measures over the superspace OSp(1,4)/O(1,3) in both the real and shifted bases, relations between different parametrisations of superspace, etc., are given explicitly. The reducibility questions are analysed, focusing in particular on the structure of chiral representations of OSp(1,4). The simplest linear OSp(1,4)-invariant models are constructed: the OSp(1,4) analogue of the Wess-Zumino model and OSp(1,4) extension of the Yang-Mills theory. The first model, together with the spontaneous breaking of OSp(1,4), exhibits an effect of the spontaneous violation of P and CP parties with the strength related to the anti-de Sitter radius. The relation of the proposed approach to supergravity is discussed.