Auxiliary Scalar Field Research Articles

Self-dual tensors and gravitational anomalies in 4 n + 2 dimensions

Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4 n + 2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two-dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two-dimensional complex Weyl fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method.

Duality of self-dual actions

Using examples of a D = 2 chiral scalar and a duality-symmetric formulation of D = 4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D = 4 case, upon performing a duality transformation of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this new covariant action and discuss its coupling to external dyonic sources. We also demonstrate that the formulations considered are self-dual with respect to a dualization of the field strengths of the chiral fields.

Discrete symmetry breaking and restoration at finite temperature in 3D Gross-Neveu model

Dynamical spontaneous breaking of some discrete symmetries including special parities and time reversal and their restoration at finite temperature T are researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the real-time thermal field theory in the fermion bubble diagram approximation. When the momentum cut-off Λ is large enough, the equation of critical chemical potential μ c and critical temperature T c will be Λ-independent and identical to the one obtained by auxiliary scalar field approach. The dynamical fermion mass m≡ m( T, μ), as the order parameter of symmetry breaking, has the same ( T c − T) 1/2 behavior at T≲ T c as one in 4D NJL-model and this shows the second-order phase transition feature of the symmetry restoration at T> T c . It is also proven that no scalar bound state could exist in this model.

Lorentz-invariant actions for chiralp-forms

We demonstrate how a Lorentz-covariant formulation of the chiral $p$-form model in $D=2(p+1)$ containing infinitely many auxiliary fields is related to a Lorentz-covariant formulation with only one auxiliary scalar field entering a chiral $p$-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all first class. In contrast with the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines the energy of a single chiral $p$-form. In the case of $D=2$ chiral scalars the constraint can be improved by use of a ``twisting'' procedure (without the loss of the property to be first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to the possible absence of an anomaly in an appropriate quantum version of the model.

Graphical evolution of spin network states

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.

Covariant action for a D = 11 five-brane with the chiral field

We propose a complete Born-Infeld-like action for a bosonic 5-brane with a worldvolume chiral field in a background of gravitational and antisymmetric gauge fields of D = 11 supergravity. When the five-brane couples to a three-rank antisymmetric gauge field, local symmetries of the five-brane require the addition to the action of an appropriate Wess-Zumino term. To preseve general coordinate and Lorentz invariance of the model we introduce a single auxiliary scalar field. The auxiliary field can be eliminated by gauge fixing a corresponding local symmetry at the price of the loss of manifest d = 6 worldvolume covariance. The double dimensional reduction of the five-brane model results in the Born-Infeld action with the Wess-Zumino term for a D = 10 four-D-brane.

Spontaneous Symmetry Breaking in Discretized Light-Cone Quantization

Spontaneous symmetry breaking of the light-front Gross-Neveu model is studied in the framework of the discretized light-cone quantization. Introducing a scalar auxiliary field and adding its kinetic term, we obtain a constraint on the longitudinal zero mode of the scalar field. This zero-mode constraint is solved by using the $1/N$ expansion. In the leading order, we find a nontrivial solution which gives the fermion nonzero mass and thus breaks the discrete symmetry of the model. It is essential for obtaining the nontrivial solution to treat adequately an infrared divergence which appears in the continuum limit. We also discuss the constituent picture of the model. The Fock vacuum is trivial and an eigenstate of the light-cone Hamiltonian. In the large $N$ limit, the Hamiltonian consists of the kinetic term of the fermion with dressed mass and the interaction term of these fermions.

Canonical reduction of two-dimensional gravity for particle dynamics

We develop the formalism for canonical reduction of (1 + 1)-dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the (3 + 1)-dimensional case; however in (1 + 1) dimensions an auxiliary scalar field is shown to have an important role. The reduced Hamiltonian is expressed as a form of spatial integral of the second derivative of the scalar field. Since in (1 + 1) dimensions there exists no dynamical degree of freedom of the gravitational field (i.e. the transverse-traceless part of the metric tensor is zero), the reduced Hamiltonian is completely determined in terms of the particles' canonical variables (coordinates and momenta). The explicit form of the Hamiltonian is calculated both in post-linear and post-Newtonian approximations.

N = 2 supersymmetric Calabi-Yau hypersurface sigma-models on curved two-dimensions

We consider the effect of curved two-dimensional space-time on Witten's N = 2 supersymmetric sigma models interpolating Calabi-Yau hypersurfaces to Landau-Ginzburg models. In order for the former models to have significant connection to superstring theory, only the N = (1, 1) or N = (1, 0) part of the total N = (2, 2) world-sheet supersymmetry is made local. With the N = (1, 0) local supersymmetry, the nice feature of the hypersurface sigma-model with global supersymmetry interpolating the Calabi-Yau and Landau-Ginzburg models is maintained. In the case of the N = (1, 1) local supersymmetry, the elimination of a scalar auxiliary field for supergravity deletes the kinetic term of a vector in the vector multiplet, invalidating extrapolations between the two models. We overcome this problem by adding an extra U(1) vector multiplet. Our results indicate that the correspondence between the Calabi-Yau and Landau-Ginzburg models on curved two-dimensions is valid both for N = (1, 0) and N = (1, 1) local supersymmetries. The coupling of N = (2, 2) vector multiplets to other multiplets with N = (1, 1) local supersymmetry is also developed.

Massive renormalizable Abelian gauge theory in 2+1 dimensions.

The standard formulation of a massive Abelian vector field in $2+1$ dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to super renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self energy is computed using operator regularization, a technique which respects the three dimensional character of the antisymmetric tensor $\epsilon_{\alpha\beta\gamma}$. This method is used to evaluate the vector self energy to two-loop order; it is found to vanish showing that the beta function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.

An unconstrained Hamiltonian formulation for incompressible fluid flow

The equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical Hamiltonian system. The incompressibility of the flow is consequent upon certain first integrals of the motion. The variable conjugate to the configuration field is not the usual linear momentum, but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure. The definition of the Hamiltonian involves a minimization with respect to this auxiliary field. The method of derivation may be generally applied to obtain unconstrained Hamiltonian descriptions of Lagrangian field equations subject to pointwise constraints.

THREE-DIMENSIONAL $\left( {\bar \psi \psi } \right)^2 $ MODEL AND OPTIMIZED EXPANSION

An alternative way to study the (2+1)-dimensional four-fermion model using the method of optimized expansions has been proposed. Contrary to Ref. 5 we use the technique of auxiliary scalar fields. In this the interpolation Lagrangian becomes nonlinear over the parameter ε. The effective potential has been constructed with the help of the canonical optimized procedure. A similar phase structure, as in the 1/N expansion, has been predicted. The β-function of the theory has been calculated in the framework of the optimized expansion method.

Sl(2, R) Currents in 2D-Gravity Are Generators of Improper Gauge Transformation

The concept of improper gauge transformation, introduced originally by Regge and Teitelboim, is used to analyse the constraint structure of induced 2D-gravity, specifically in order to reveal the sl(2, R)) invariance. A local form of the induced action is taken by introducing an auxiliary scalar field. The sl(2, R)) symmetry is shown to exist in a gauge invariant way. It is shown how one can gauge fix the system to obtain the quantum sl(2, R)) currents in the light cone gauge. Interesting connections between our local formulation with geometric quantization results are mentioned briefly. Some recent canonical formulations of 2D-gravity have also been examined.

Nonlinear optimized expansions and the Gross-Neuveu model

An alternative approach to the investigations of the phase structure of the Gross-Neveu model by the optimized expansion method is proposed. Contrary to [6], in order to conserve the Lorentz invariance, the auxiliary scalar fields technique is used. As a result, the interpolation Lagrangian becomes nonlinear in the artificial parameter e. The effective potential is constructed by the canonical optimization procedure. The predictions for the phase structure of the model are as in the 1/N expansion method.

A ten-dimensional super-Yang-Mills action with off-shell supersymmetry

After adding seven auxiliary scalar fields, the action for ten-dimensional super-Yang-Mills contains an equal number of bosonic and fermionic non-gauge fields. Besides being manifestly Lorentz and gauge-invariant, this action contains nine spacetime supersymmetries whose algebra closes off-shell. Octonions provide a convenient notation for displaying these symmetries.

SLAVNOV-TAYLOR IDENTITIES FOR YANG-MILLS THEORY IN CONFORMAL GAUGE

Yang-Mills theory in conformal (essentially nonlocal) gauge is considered. This gauge is expressed in a local form by means of two auxiliary scalar fields. By the use of the BRST symmetry, the Slavnov-Taylor identities are obtained. These identities are applied to prove the renormalizability of the theory as well as to investigate the structure of the radiative corrections to the two-point vertex functions. It is shown that here a new class of conformal anomalies arises, connected with the absence of radiative corrections to the propagators including auxiliary fields.

On lattice chiral gauge theories

We consider the Smit-Swift-Aoki formulation of a lattice chiral gauge theory, in which the Wilson and other non-invariant terms in the action are made gauge-invariant by the coupling with a non-linear auxiliary scalar field, Ω. We show that Ω decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, barring unforeseen cancellations, explicit ghost fields are necessary to ensure decoupling. Thus, for these theories to give rise to the correct continuum limit, the requirements discussed in our previous work have to be satisfied. Similar considerations apply to schemes with mirror fermions. Finally, we discuss simpler cases with a global chiral symmetry and show that the theory becomes free at decoupling. Recent numerical simulations agree with our considerations.

NON-PERTURBATTVE VACUUM FOR SUPERSTRING FIELD THEORY AND SUPERSYMMETRY BREAKING

We analyze possible ground states for the covariant string field theory action of the open NSR-superstring. A remarkable feature of this action is that it possesses a rich set of the auxiliary local fields. We found that some of low-lying scalar auxiliary fields acquire non-zero vacuum expectation values providing a new mechanism for supersymmetry breaking. The gauge vector field become massive while the physical spinor remains massless, thus the supersymmetry is broken in the non-perturbative vacuum.

HIGHER SPIN ALGEBRAS AND QUANTIZATION ON THE SPHERE AND HYPERBOLOID

The oscillator-type realization is proposed for the continuous set of infinite-dimensional algebras of quantum operators on the two-dimensional sphere and hyperboloid. This realization is typical for infinite-dimensional higher spin algebras related to higher spin gauge theories. It involves the Klein-type operator that emerges nontrivially in the Heisenberg-type commutation relations for the oscillators. The invariant trace and bilinear form are constructed. The latter is shown to degenerate for all odd-integer values of the continuous parameter ν, which parametrizes the class of algebras under investigation. The degeneration points are shown to correspond to ordinary finite-dimensional matrix algebras and superalgebras. Possible applications of these results to higher spin gauge theories are discussed. In particular, it is noted that the deformation parameter ν can be interpreted as a vacuum value of some auxiliary scalar field in an appropriate higher spin gauge theory.

SUPERSPACE CONSTRAINTS AND CHERN-SIMONS COHOMOLOGY IN D=4 SUPERSTRING EFFECTIVE THEORIES

The linear multiplet, composed of the dilaton ϕ, of an antisymmetric gauge field Bμν and of a spinor χ is always present in any superstring induced N=1D=4 supergravity model. We consider its coupling to supergravity using only superspace Bianchi identities and the rheonomy approach. In this way, our results are fully general and independent from the choice of any Lagrangian, a concept which is never mentioned in this paper. We consider two situations corresponding to two different free differential algebras: (1) the case where there are no Chern-Simons terms in the Bμν field strength Hμνρ and (2) the case where such terms are included in Hμνρ. Case (2) is obviously the one chosen by string theory on the ground of anomaly cancellation. In both cases, we must solve the H-Bianchi identity using a solution of the super Poincare’ Bianchi identities as a background. Such a solution, besides the physical fields displays a certain number of auxiliary fields. The most general solution of the super Poincare’ Bianchis we have to consider corresponds to 16⊕16 off-shell multiplet which, by suitable choices can be reduced either to the so-called old minimal or to the new minimal 12⊕12 multiplet. We give the general solution of the H-Bianchi within the 16⊕16 formulation both with and without Chern-Simons terms. This is done through the D=4 analogue of Bonora-Pasti-Tonin theorem of the 10D anomaly free supergravity. By specializing our parameters, we obtain the form of the coupling in the new minimal model retrieving in this case the results of Cecotti, Ferrara and Villasante. In addition we clarify the geometrical meaning of R-symmetry showing that in the absence of Chern-Simons forms, the condition for the embedding of the linear multiplet into the Kaehler manifold [Formula: see text] spanned by the chiral multiplets (existence on [Formula: see text] of a U(1) Killing vector) is the same condition which guarantees the existence of a local Weyl transformation by means of which the 16⊕16 curvatures can be reduced to the new minimal form and the scalar complex scalar auxiliary field S can be set to zero. Finally, we discuss the arbitrariness contained in the solution of the H-Bianchi identities at the level of the (0, 3) superspace sector. We derive the D=4 analogue of the superspace cocycle which is responsible for the Grisaru-Zanon R4-terms in the D=10 case.