Quadratic Gauge Research Articles

Deconfinement to confinement by generalizing BRST symmetry on the sphere

Recently, it has been shown that the theory in the quadratic gauge on 4-sphere, [Formula: see text] consists of two phases namely, the confined and the deconfined phases. A suitable finite field-dependent Becchi–Rouet–Stora–Tyutin (FFBRST) transformation interrelates two different gauge fixed theories. In this paper, we use the FFBRST technique on the curved space for the first time and elaborate a novel application of it. We propose two different formulations of this technique that transform the deconfined phase action on sphere to the confined phase action on sphere inside the quadratic gauge. Both proposed passages change the phase with BRST invariance to the phase without BRST invariance unlike usual connections where the FFBRST operation leaves the BRST symmetry intact and there is a unique field theoretic essence of them, which makes them particularly important to study. Thus, the two different field redefinitions act as a new mechanism that execute phase transition between two real QCD phases on 4-sphere other than ghost condensation process.

BRST symmetry as a mechanism for confinement

The SU(N) QCD in a particular quadratic gauge is shown to contain two phases namely, the deconfined phase and the confined phase. A suitable field dependent parameter in the finite field dependent BRST (FFBRST) transformation interrelates the effective theories in two different gauges. In this paper, we propose a novel application and extension of the FFBRST technique that transforms the effective action in the deconfined phase to that in the confined phase within the quadratic gauge only. The proposed passage becomes interesting as it carries a unique field theoretic meaning and due to the fact that the technique changes the BRST invariant phase to BRST non invariant phase in an unconventional way unlike usual connections where both the theories, before and after application of FFBRST, are BRST invariant. We thus find a new process in field redefinition that executes deconfinement to confinement phase transition other than ghost condensation mechanism.

Compact space and infrared behavior of the effective QCD

We aim to investigate the infrared regime in the effective theory of the new quadratic gauge in the physical compact space by defining it on 4-sphere. Abelian dominance is characterized by off-diagonal gluons acquiring dynamical masses and it hints at existence of confinement. We do observe Abelian dominance in the ghost condensed vacuum of this theory on 4-sphere. Along with this observation, we find an unusual result that mass of an off-diagonal gluon on 4-sphere is position dependent in this theory as a consequence of the curved geometry. This suggests that the curvature of 4-sphere does not change the infrared behavior of present theory on 4-sphere from that of the theory with the same quadratic gauge in Euclidean spacetime as Abelian dominance is observed in Euclidean spacetime too while it has caused mass of an off-diagonal gluon on 4-sphere to be position dependent. The effective action in the confined phase on 4-sphere and that in the 4-dim Euclidean space are found to be identical in a profound outcome.

Study of Abelian dominance in Sp(N) QCD in the de Sitter background

We propose the effective theory based on the compact symplectic group Sp(N) in the new quadratic gauge on the 4-dimensional de Sitter spacetime (dS 4) with a view to investigate the infrared regime in it. Abelian dominance is characterized by off-diagonal gluons acquiring dynamical masses and it hints at existence of confinement. We do observe Abelian dominance in the ghost condensed vacuum of this theory in the de Sitter background. Along with this observation, we find an unusual result that the mass of an off-diagonal gluon on dS 4 is position dependent as a consequence of the curved geometry. In our previous papers, we have shown that Abelian dominance is strongly indicated in the Minkowski spacetime too. Therefore, the present observation suggests that the curvature of the dS 4 does not change the infrared behaviour of the present theory on dS 4 from that of the quadratic gauge fixed theory in Minkowski spacetime, but it causes the mass of an off-diagonal gluon on the dS 4 to be position dependent.

Superspace formulation in the absence of full anti-BRST symmetry

There are two known approaches to construct the six-dimensional superspace formulation of a gauge theory where the additional two dimensions are Grassmannian. One of the approaches (the second approach in this paper) requires both BRST and anti-BRST symmetries for the superspace formulation. In this paper, we consider an effective theory in a recently introduced quadratic gauge which has two pairs of ghosts. The theory does not have a full anti-BRST symmetry and only has full BRST symmetry. We show that it is possible to partially formulate this effective theory in the superspace using the second approach even in the absence of full anti-BRST symmetry due to the peculiar structure of the theory. We encounter a couple of technical difficulties which further brings useful insights.

Deconfinement to confinement as PT phase transition

We consider SU(N) QCD in a new quadratic gauge which highlights certain characteristic of the theory in the non-perturbative sector. By considering natural hermiticity property of the ghost fields we cast this model as non-Hermitian but symmetric under combined Parity (P) and Time reversal (T) transformations. We explicitly study the PT phase transition in this model. This is very first such study in the non-Hermitian gauge theory. The ghost fields condensate which give rise to spontaneous breaking of PT symmetry. This leads to realize the transition from deconfined phase to confined phase as a PT phase transition in this system. The hidden C-symmetry in this system is identified as inner automorphism in this theory. Explicit representation is constructed for the C-symmetry.

Superspace formulation with a new and extended BRST

Superspace formulation is an elegant proposal to deal with BRST symmetries and Ward identities of a gauge theory. A new effective SU(N) QCD in a novel quadratic gauge has recently been introduced which throws light on interesting non perturbative characteristics of QCD. The effective theory has an unusual feature of having two pairs of ghosts and thus has some unconventional BRST transformations. In this paper, we propose a formulation of this unique theory in a six-dimensional superspace in which additional two dimensions are Grassmannian. The process of stated formulation also brings to attention a novel result that not all sets of BRST transformations under which the theory is invariant lead to consistent superspace version. The work is also imperative in view of its implications on the ward identity in the superspace.

Search for Abelian dominance in the effective SO(N) theory

Recently a new quadratic gauge has been introduced in the SU(N) QCD in which interesting non perturbative characteristics of QCD has been brought to light. One of the characteristics is Abelian dominance, which is one of the signatures of color confinement in a dual superconductor picture. The SO(N) QCD has been used quite often for various studies. In this paper, we extend the application of the quadratic gauge to SO(N) QCD and probe different vacua of the effective theory in which ghosts condense to search existence of Abelian dominance. We begin with the vacuum whose SU(N) group version leads us to find the evidence of Abelian dominance in SU(N) QCD. Contrary to expectation, we do not observe Abelian dominance in such vacuum here. Taking hint from this consequence, another vacuum is then examined in which existence of Abelian dominance is strongly indicated. The geometric explanation for the results in both the vacua has been provided.

Non-perturbative to perturbative QCD via the FFBRST

Recently a new type of quadratic gauge was introduced in QCD in which the degrees of freedom are suggestive of a phase of abelian dominance. In its simplest form it is also free of Gribov ambiguity. However this gauge is not suitable for usual perturbation theory. The finite field dependent BRST (FFBRST) transformation is a method established to interrelate generating functionals for different effective versions of gauge fixed field theories. In this paper we propose a FFBRST transformation suitable for transforming the theory in the new quadratic gauge into the standard Lorenz gauge Faddeev–Popov version of the effective lagrangian. The task is made interesting by the fact that the effective lagrangian is invariant under two different BRST transformations which leads to suitable extension of the previous procedures to accomplish the required result. We are thus able to identify a field redefinition to go from a non-perturbative phase of QCD to perturbative QCD.

Supersymmetric extended string field theory in NSn sector and NSn − 1–R sector

We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu–Schwarz (NS) sectors with or without one Ramond (R) sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [1]. The theory for NSn sector and NSn−1–R sector contains general n-th rank tensor fields and (n−1)-th rank spinor–tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor–tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.

Absence of the Gribov ambiguity in a quadratic gauge

The Gribov ambiguity exists in various gauges except algebraic gauges. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold $\mathbb{S}^3$, when a proper boundary condition on the gauge configuration is taken into account. Thus, providing one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the \tmem{BRST} invariance is preserved in this gauge.

Absence of the Gribov ambiguity in a special algebraic gauge

The Gribov ambiguity exists in various gauges except algebraic gauges. However in general, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We show that nontrivial copies can not occur in this gauge. We then provide an example of spherically symmetric gauge field configuration and prove that with a proper boundary condition on the configuration, this gauge removes the ambiguity on a compact manifold .

Beyond Einstein–Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms

Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein–Cartan(–Sciama–Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero–Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh–Yan form, can be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al and Baekler et al, emerges also in the framework of Diakonov et al. We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann–Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) In a Riemann–Cartan spacetime, that is, in a spacetime with torsion, parity-violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann–Cartan spacetime is a natural habitat for chiral fermionic matter fields.

Stringy instanton corrections to $ \mathcal{N} = 2 $ gauge couplings

We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localization properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. In the heteoric side the corrections to the quadratic gauge couplings are provided by a 1-loop threshold computation and, under the duality map, match precisely the first few stringy instanton effects in the type I' setup. This agreement represents a very non-trivial test of our approach to the exotic instanton calculus.

Yang-Mills Gravity and Gravitational Radiation

A new translation gauge theory of gravity in flat space-time with a new Yang-Mills action involves quadratic gauge curvature and fermions. The theory shows that the presence of an “effective Riemannian metric tensor” for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space-time. In the post-Newtonian approximation of the tensor gauge field produced by the energymomentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

YANG–MILLS GRAVITY IN FLAT SPACE–TIME I: CLASSICAL GRAVITY WITH TRANSLATION GAUGE SYMMETRY

We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space–time with a new Yang–Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space–time. In the post-Newtonian approximation of the tensor gauge field produced by the energy–momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

General quadratic gauge theory: constraint structure, symmetries and physical functions

How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure with the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether can we identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present article is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfill such a program, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyze a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analyzing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.

Rotating frames and gauge invariance in two-dimensional many-body quantum systems

We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge-invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases we discuss their Gribov ambiguities and commutator algebra. We construct the momentum operators, inner product and Hamiltonian in both types of gauges, for systems with and without translation invariance. The analogy with the quantization of QED in non-covariant gauges is emphasized. Our results are applied to quasi-rigid systems in the Eckart frame.

Quadratic s-form field actions with semi-bounded energy

Abstract We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s -form fields. This provides a starting point to study the uniqueness of the Yang–Mills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gravity in four space–time dimensions even in the presence of a Minkowskian metric background.

COVARIANT QUANTIZATION OF SPINNING SUPERPARTICLES

We have applied the method of Batalin and Vilkovisky to obtain covariant quantization of massless spinning superparticles in D dimensions with M rigid target space and N local worldline supersymmetries. Appropriate gauge fixing has been introduced to obtain a quadratic gauge fixed action.