Set Of Auxiliary Fields Research Articles

Democratic Lagrangians from topological bulk

Chiral form fields in d dimensions can be effectively described as edge modes of topological Chern-Simons theories in d+1 dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a d-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (d+1)-dimensional topological Lagrangian automatically leads to d-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity. Published by the American Physical Society 2024

BRST–BFV and BRST–BV descriptions for bosonic fields with continuous spin on R1,d−1

Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a [Formula: see text]-dimensional Minkowski space–time using a metric-like formulation are constructed on the basis of a constrained BRST–BFV approach we propose. The resulting BRST–BFV equations of motion for a scalar field augmented by ghost operators contain different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded constrained equations of motion with the initial irreducible Poincaré group conditions of a Bargmann–Wigner type, it is demonstrated that one should replace the field in these conditions by a class of gauge-equivalent configurations. Triplet-like, doublet-like constrained descriptions, as well as an unconstrained quartet-like non-Lagrangian and Lagrangian formulations, are derived using both Fronsdal-like and new tensor fields. In particular, the BRST–BV equations of motion and Lagrangian using an appropriate set of Lagrangian multipliers in the minimal sector of the respective field and antifield configurations are constructed in a manifest way.

Anisotropic singularities in chiral modified gravity

In four spacetime dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. All these theories describe just two propagating polarisations of the graviton. General relativity (GR) with an arbitrary cosmological constant is the only parity-invariant member of this family. We review how these modified gravity theories arise within the framework of pure-connection formulation. We introduce a new convenient parametrisation of this family of theories by using a certain set of auxiliary fields. Modifications of GR can be arranged so as to become important in regions with large Weyl curvature, while the behaviour is indistinguishable from GR where Weyl curvature is small. We show how the Kasner singularity of GR is resolved in a particular class of modified gravity theories of this type, leading to solutions in which the fundamental connection field is regular all through the spacetime. There arises a new asymptotically De Sitter region ‘behind’ the would-be singularity, the complete solution thus being of a bounce type.

Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background

We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.

BRST APPROACH TO LAGRANGIAN FORMULATION OF BOSONIC TOTALLY ANTISYMMETRIC TENSOR FIELDS IN CURVED SPACE

We apply the BRST approach, previously developed for higher spin field theories, to gauge-invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves as an additional demonstration of universality of the BRST approach for Lagrangian constructions in various field models.

BRST approach to Lagrangian construction for fermionic massless higher spin fields

We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any spin is given. It is shown that in fermionic case the higher spin field model is a reducible gauge theory and the order of reducibility grows with the value of spin. No off-shell constraints on the fields and the gauge parameters are used. We prove that in four dimensions after partial gauge fixing the Lagrangian obtained can be transformed to Fang–Fronsdal form however, in general case, it includes the auxiliary fields and possesses the more gauge symmetries in compare with Fang–Fronsdal Lagrangian. As an example of general procedure, we derive the new Lagrangian for spin 5 / 2 field containing all set of auxiliary fields and gauge symmetries of free fermionic higher spin field theory.

GREEN DYADIC AND DIPOLE RADIATION IN AN ELECTRICAL-MAGNETIC COUPLED COMPOSITE MATERIAL

A composite electrical-magnetic coupled metamaterial is proposed which consists of Ω-shaped and helix metal particles. Green dyadic and electromagnetic fields of a dipole radiator in such a composite metamaterial are presented by introducing a set of auxiliary fields. Right- and left-handed circularly polarized eigenwaves, which travel with different velocities and have exponentially-attenuated amplitudes, can be simultaneously excited.

Probabilistic reasoning in an augmented fact-proposition space and its applications

A simple and versatile probabilistic reasoning scheme is presented. Based on an augmentation of a multi-dimensional inference space indexed by a Cartesian product of the fact and proposition sets, the scheme simplifies the processes involved in the representation and computation of a probabilistic reasoning system. In the augmented space, a set of auxiliary fields is utilized in addition to the fact-proposition relations to manipulate the uncertainty and incompleteness of the information presented. The scheme enhances the functionality of a probabilistic reasoning and facilitates the building of practical reasoning systems. The utilization of the augmented space in reasoning is illustrated by two problems in computer-vision applications.

BRST STRUCTURE AND AUXILIARY FIELDS OF SIMPLE SUPERGRAVITY

A generalized Lagrangian BRST formalism is used to study the quantum structure of the simple supergravity, whose classical gauge algebra is not closed. It is shown that in this approach one can naturally introduce a set of auxiliary fields as certain combinations of ghosts and antifields, so that the resulting theory has the closed classical gauge algebra.

SUSY AUXILIARY FIELDS FROM BRST ANALYSIS

A generalized Lagrangian BRST formalism is used to study globally supersymmetric systems with open classical gauge algebra. It is shown that in this approach one can naturally introduce a set of auxiliary fields, so that new form of the original theory has closed classical algebra.

BRS symmetry of supergravity in superspace and its projection to component formalism

The BRS symmetry of supergravity theories is geometrically constructed in superspace. The construction is formally identical to the one which holds for gauge theories coupled to gravity. If the classical superspace constraints associated to a given set of auxiliary fields are known it is possible to obtain by projection the whole set of BRS transformation laws in component formalism. We illustrate the method with various representations of N = 1, D = 4 Poincaré supergravity. In particular we consider couplings of Chern-Simons forms. Our analysis proves the absence of U(1) anomaly in the new minimal supergravity for any coupling of matter fields.

ON THE AUXILIARY FIELDS OF SUPERGRAVITY THEORIES

An algorithm to obtain a minimal set of auxiliary fields for the fermionic sector of supergravity theories is presented. Explicit examples are given as illustrations and the N=1, D=10 case is studied in detail.

On the reducibility of the new non-minimal sets of auxiliary fields for N=1 supergravity

If a new criterion of reducibility for auxiliary field sets is employed, the authors show that the two new non-minimal sets for N=1 supergravity are reducible.

Conformal and poincaré tensor calculi in N=1 supergravity

We present the superconformal tensor calculus for N=1 supergravity in a complete form; irreducible multiplets, their multiplication and embedding formulae and invariant action formulae. It is further clarified in detail how the various versions of N=1 Poincaré supergravity (i.e. with different sets of auxiliary fields) are reproduced from the unique superconformal theory. The tensor calculi for all the known versions of Poincaré supergravity are derived explicitly.

A new group theoretical technique for the analysis of Bianchi identities and its application to the auxiliary field problem of D = 5 supergravity

For any (super)group and hence for any geometrical (super)theory Bianchi identities imply that certain 3-forms vanish. In order to perform a systematic analysis of their implications in the presence of constraints one needs a complete basis of independent 3-forms spanning the 3-form linear space. In this paper we discuss a general procedure for the derivation of such a basis in the case of supersymmetric theories involving commuting spinor 1-forms. Our technique is based on the decomposition of the product of group representations into irreducible components and replaces all Fierz rearrangements. We give as examples the cases of N = 1, d = 4, N = 2, d = 4 and N = 2, d = 5 supergravity. Then applying our algebraic techniques to the last of these three models, the only other known example, besides N = 1, d = 4 supergravity, of a pure geometrical theory, we derive its off-shell structure containing 48 bosons and 48 fermions. The torsion-like constraints which we implement in the Bianchis in order to obtain our set of auxiliary fields are a subset of the complete set of variational equations of the theory so that we derive our off-shell multiplet without any reference to an embedding conformal symmetry. The point with which we still need to use ingenuity is the selection of those equations which are to be kept and those which are to be thrown out.

The density multiplet in superspace

We calculate the components of the density multipletE inN=1 superspace and the last component of the chiral density multiplet ℰ inSU(2) extended superspace with a minimal set of auxiliary fields.

Superplane integrability and three dimensional supergravity

The requirement of integrability in all light-like superplanes yields the proper kinematical constraints for the three-dimensional supergravity theory formulated in superspace. The theory with the Breitenlohner set of auxiliary fields is obtained.

Supergravity with and without superspace

We show that the superspace formalism follows from the component formalism. After constructing the supervielbeins and superconnections off-shell in second-order formalism with the minimal set of auxiliary fields, we show that the resulting supertorsions satisfy the constraints of the various equivalent superspace approaches.