Auxiliary Superfields Research Articles

Generating functional for Green's functions of fluid-loaded structures.

A key step in applying the auxiliary superfield method to complex systems is the representation of the Green's function of the system as derivatives of a generating functional. This representation is known to be valid for Hermitian systems, but this precludes the application of the method to systems with fluid loading or damping. Here, it is demonstrated that the known representation continues to be valid for fluid-loaded and damped systems. Thus, the auxiliary superfield method may be applied to such systems.

Auxiliary superfield method for statistical predictions of complex, structural acoustics systems: Saddle point approximation for the mean field.

The auxiliary superfield approach is proposed as a method to obtain statistical predictions of the acoustic response of complex elastic structures. The potential advantage of the method is the full retention of interference and resonance effects associated with the degrees of freedom being averaged over. It is not known whether this approach leads to tractable problems for structural acoustics systems, however. We have applied the method to the idealized case of an infinite, thin plate with attached oscillators to obtain the mean Green's function. The oscillators are assumed to have an uncorrelated, Gaussian distributed mass and stiffness distribution representing a simple form of complex internal structure. Using the auxiliary superfield approach, the mean Green's functions are expressed exactly as a functional integral. For relatively small disorder, the integral may be estimated by a saddle point approximation which leads to coupled integral equations for effective mass and stiffness matrices that can be solved numerically for a given spatial distribution of the disorder. With the solutions for these matrices, one obtains a self-consistently determined, generalized fuzzy structure model. We give analytical solutions for the simple case of a uniform spatial distribution. The results are promising for the application of the method to more challenging geometries.

Superspace first-order formalism for massless arbitrary superspin supermultiplets

A new description of free massless superfields of arbitrary superspin $Y$ ($Y>1/2$) is proposed. Following the first-order philosophy, we relax some of the properties (reality, gauge redundancy) of the unconstrained higher spin prepotentials and we construct first and half order invariants quantities. These are used to write trivially invariant actions. Additional auxiliary superfields that play the role of spin connections are used to enforce a new local symmetry that restores the degrees of freedom.

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.

Superspace formulation of massive half-integer superspin

An explicit form for the Lagrangian of a massive arbitrary half-integer super-spin Y = s + 1/2 supermultiplet is obtained in 4D, mathcal{N} = 1 superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary super- fields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is frac{8}{3} (s + 1)(4s2 + 11s + 3). For s = 1 our results are in agreement with those obtained in [1].

Self-dual $ \mathcal{N} $ = 2 Born-Infeld theory through auxiliary superfields

There is an evidence that the N=2 Born-Infeld theory with spontaneously broken N=4 supersymmetry exhibits self-duality. We perform a further check of this hypothesis by constructing a new representation for the N=2 Born-Infeld action through the auxiliary chiral superfield U. In such a formulation, self-duality is equivalent to U(1) invariance of the U interaction. We explicitly calculate the auxiliary interaction up to the 10th order and show its U(1) duality invariance, thus proving that the original action is self-dual to the same order. We also suggest a new method of recursive computation of the N=2 Born-Infeld action in the standard formulation, based solely on the nonlinear realization of the N=4 central charge on the N=2 superfield strengths W, \bar W.

A dynamical theory for linearized massive superspin 3/2

We present a new theory of free massive superspin Y = 3/2 irreducible representation of the 4D, $ \mathcal{N} $ = 1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y = 3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems.

N = 1 Gribov superfield extension

We propose a mechanism displaying confinement, as defined by the behavior of the propagators, for four-dimensional, N = 1 supersymmetric Yang–Mills theory in superfield formalism. In this work we intend to verify the possibility of extending the known Gribov problem of quantization of Yang–Mills theories and the implementation of a local action with auxiliary superfields, like the Gribov–Zwanziger approach, to this problem.

Auxiliary superfields in N=1 supersymmetric self-dual electrodynamics

We construct the general formulation ofN=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary superfields. Focusing on the U(1) case, we present the most general form of the U(1) invariant auxiliary interaction, consider a few instructive examples and show how to generate self-dual N=1 models with higher derivatives in this approach. PACS: 11.15.-q, 03.50.-z, 03.50.De

Auxiliary superfields in $ \mathcal{N} $ = 1 supersymmetric self-dual electrodynamics

We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary superfields. Focusing on the U(1) case, we present the most general form of the U(1) invariant auxiliary interaction, consider a few instructive examples and show how to generate self-dual N=1 models with higher derivatives in this approach.

Extended supersymmetric sigma models in AdS4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.

On superpotentials for nonlinear sigma-models with eight supercharges

Abstract Using projective superspace techniques, we consider 4D N = 2 and 5D N = 1 gauged supersymmetric nonlinear sigma-models for which the hyper-Kahler target space is (an open domain of the zero section of) the cotangent bundle of a real-analytic Kahler manifold. As in the 4D N = 1 case, one may gauge those holomorphic isometries of the base Kahler manifold (more precisely, their lifting to the cotangent bundle) which are generated by globally defined Killing potentials. In the U(1) case, by freezing the background vector (tropical) multiplet to a constant value of its gauge-invariant superfield strength, we demonstrate the generation of a chiral superpotential, upon elimination of the auxiliary superfields and dualisation of the complex linear multiplets into chiral ones. Our analysis uncovers a N = 2 superspace origin for the results recently obtained in [J. Bagger, C. Xiong, hep-th/0601165].

Superfield formalism for the one loop effective action and CP(N) model in three dimensions

To obtain the one loop effective action for a given superfield theory, one encounters the notion such as the `supertrace' of a differential operator on superspace. We develop, in a systematic way for the superspace of arbitrary dimension, a method to determine the supertrace precisely. We present a formula to express the supertrace explicitly as the superspace integral, which enables us to write the one loop effective action within the superfield formalism and still maintain the manifest supersymmetry. In the second part of the paper, we apply the result to a three dimensional N=1 supersymmetric CP(N) model in the auxiliary superfield formalism. The model contains a novel topological interaction term. We show in the large N limit the one loop effective action is given by the supersymmetric Maxwell-Chern-Simons theory.

New 4D, N=1 superfield theory: model of free massive superspin- [formula omitted] multiplet

We present a Lagrangian formulation for the free superspin- 3 2 massive 4D, N=1 superfield. The model is described by a dynamical real vector superfield and an auxiliary real scalar superfield. The corresponding multiplet contains spin-1, spin-2 and two spin- 3 2 propagating component fields on-shell. The auxiliary superfield is needed to ensure that the on-shell vector superfield carries only the irreducible representation of the Poincaré supergroup with a given mass and the fixed superspin of 3 2 . The bosonic sector of the component level of the model is also presented.

CNM models, holomorphic functions and projective superspace c-maps

Continuing the investigation of CNM (chiral-non-minimal) hypermultiplet non-linear σ-models, we propose extensions of the concept of the c-map which relate holomorphic functions to hyper-Kähler geometrics. In particular, we show that a whole series of hyper-Kähler potentials can be derived by replacing the role of the 4D, N = 1 tensor multiplet in the original c-map by 4D, N = 1 non-minimal multiplets and auxiliary superfields. The resulting N = 2 models appear to have interesting connections to Calabi-Yau manifolds and algebraic varieties. These models also emphasize the fact that special hyper-Kähler manifolds (the analogs of special Kähler manifolds) without isometries exist.

Supersymmetry breaking in the Nambu-Jona-Lasinio approach

Gaugino condensation in the hidden sector of supergravity models is described within a Nambu-Jona-Lasinio type of approach by minimization of a one-loop potential. The essential ingredients of the mechanism are auxiliary superfields whose v.e.v. generate gaugino condensation and supersymmetry breaking, introduced through Lagrange multipliers. For phenomenologically acceptable values of the gauge couplings, gaugino condensation is disfavoured in this approach. For completeness, it is shown that supersymmetry breaking would occur for a stronger coupling, but at a scale inconsistent with the expectations.

GRADED GL(1|1) BRST SYMMETRY IN COVARIANT QUANTIZATION OF SUPERSYMMETRIC CHIRAL BOSONS AND HETEROTIC STRINGS

We present a covariant path integral quantization of supersymmetric chiral bosons (leftons and rightons). An infinite set of auxiliary scalar superfields are introduced to convert the second-class chiral constraint into first-class ones. Our gauge-fixed action has an extended BRST symmetry described by the graded algebra GL(1|1). A regularization respecting this symmetry is proposed to deal with the contributions of the infinite towers of auxiliary fields and associated ghosts and is verified to lead to the desired partition function. We apply our formulation to give a covariant quantization of the heterotic-type NSR strings, and show that (super)conformal anomalies from all unphysical degrees of freedom are cancelled, even in noncritical dimensions. Our treatment does not suffer from Siegel gauge anomaly, because of the use of linear chiral constraints.

AN ACTION FOR SUPER-W3-GRAVITY

A superspace action for non-chiral super-W3-gravity is constructed. It generalizes the chiral result of Hull, and like him we assume a stronger condition on the dijk tensors than in W3-gravity. By introducing auxiliary superfields in rigid superspace, we are able to reduce the problem to the gauging in each chiral sector separately.

General NSR string reggeon vertices from a dual ramond vertex

We introduce a new vertex in the Ramond sector of the NSR string which generalizes the fermionic version of an old construction due to Sciuto and to Della Selva and Saito, the fermionic emission vertex of Corrigan and Olive. The new vertex makes use of an NS auxiliary superfield and describes the emission of two fermionic reggeons associated with one and the same Hilbert space. It is written entirely in terms of world sheet superfields and if restricted to its bosonic part it is dual to the OPE of two ordinary bosonic Sciuto-Della Selva-Saito vertices. The formalism based on this new “dual Ramual vertex” is completely general and we demonstrate explicitly how to obtain the known results for Coulomb scattering and for the matter sector of the four-fermion amplitude. Finally, the correlation corresponding to the N-boson 2 M-fermion reggeon vertex is given.

The confrontation of no-scale supergravity with cosmology

We present a number of exact cosmological solutions in the SU(1, 1)/U(1) “no-scale” theory of supergravity. We show that the auxiliary superfield acts as a negative stress and this permits the existence of a wide class of solutions which avoid the singularities that appear in the cosmological models of general relativity. However, by way of compensation, the dilation field always evolves so as to alter the sign of the coupling of matter to gravity in the vicinity of any expansion minimum or singularity. Moreover, the coupling of the dilation to any conventional matter sources present in the universe which is imposed by the theory does not appear to permit either power-law or exponential inflation to take place. The evolution of the mean expansion scale-factor is controlled by the auxiliary field density rather than by any conventional matter or inflaton fields present in the universe. These results indicate that classical “no-scale” supergravity theory (or at least its SU(1,1)/U(1) bosonic incarnation) may not provide acceptable models of the early universe.