Local duality, chiral supersymmetry and fermion-like formulation of non-Abelian pure gauge fields (original) (raw)
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A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality
The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is a dual potential, but it is a 2-indexed tensor T µν of the Freedman-Townsend type. Though not itself functioning as such, T µν gives rise to a dual parallel transport,à µ , for the phase of the wave function of the colour magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard colour (electric) charge itself is found to be a monopole ofà µ . At the same time, the gauge symmetry is found doubled from say SU (N ) to SU (N ) × SU (N ). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a 'universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of .
Non-Abelian Yang-Mills analogue of classical electromagnetic duality
Physical Review D, 1995
The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is a dual potential, but it is a 2-indexed tensor T µν of the Freedman-Townsend type. Though not itself functioning as such, T µν gives rise to a dual parallel transport,à µ , for the phase of the wave function of the colour magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard colour (electric) charge itself is found to be a monopole ofà µ . At the same time, the gauge symmetry is found doubled from say SU (N ) to SU (N ) × SU (N ). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a 'universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of .
Generalized dual symmetry for non-Abelian Yang-Mills fields
Physical Review D, 1996
It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport tildeAmu(x)\tilde{A}_\mu(x)tildeAmu(x) constructed earlier for monopoles is seen to function also as a potential in giving full description of the gauge field, playing thus an entirely dual symmetric role to the usual potential Amu(x)A_\mu(x)Amu(x). Sources of AAA are monopoles of tildeA\tilde{A}tildeA and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equations for respectively the classical and Dirac point charge; this applies whether the charge is electric or magnetic, the two cases being related just by a dual transform. The dual transformation itself is explicit, though somewhat complicated, being given in terms of loop space variables of the Polyakov type.
Canonical non-Abelian dual transformations in supersymmetric field theories
Physical Review D, 1995
A generating functional FFF is found for a canonical nonabelian dual transformation which maps the supersymmetric chiral O(4) sigma\sigmasigma-model to an equivalent supersymmetric extension of the dual sigma\sigmasigma-model. This FFF produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {\em symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional TTT which relates wavefunctions in the two quantum theories is argued to be {\em exactly} given by T=exp(iF)T=\exp(iF)T=exp(iF).
Non-Abelian tensor gauge fields and extended current algebra. Generalization of Yang-Mills theory
We suggest an infinite-dimensional extension of the gauge transformations which includes non-Abelian tensor gauge fields. Extended gauge transformations of non-Abelian tensor gauge fields form a new large group which has natural geometrical interpretation it terms of extended current algebra associated with compact Lie group. We shall demonstrate that one can construct two infinite series of gauge invariant quadratic forms, so that a linear combination of them comprises the general Lagrangian. The general Lagrangian exhibits enhanced local gauge invariants with double number of gauge parameters and allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field. Therefore it describes two polarizations of helicity-two and helicity-zero massless charged tensor gauge bosons.
Spinorial Reduction of the Superdimensional Dual-covariant Field Theory
2015
In this paper we produce further specification of the geometric and algebraic properties of the earlier introduced superdimensional dual-covariant field theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field theory (UFT). Considerations in the present paper are directed by a requirement of transformational invariance of connections of derivatives of dual state vector (DSV) and unified gauge field (UGF matrices) to these objects themselves established by mean of N split metric matrices of a rank {\mu} (SM, an extended analog of Dirac matrices) in frame of the related Euler-Lagrange equations for DSV, UGF and SM derived in [1]. This requirement is posed on SFT as one of the aspects of the general demand of irreducibility claimed to UFT; it leads to rotational invariance of SM and grand metric tensor (GM) as being structured on SM. Study in this work has led to explication of geometrical nature of SM and DSV as spin-affinors (variable in space of the unified man...
Electric/magnetic duality for chiral gauge theories with anomaly cancellation
Journal of High Energy Physics, 2008
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes previous work on the symplectically covariant formulation of anomaly-free gauge theories as they typically occur in extended supergravity, and now also includes general theories with (pseudo-)anomalous gauge interactions as they may occur in global or local N = 1 supersymmetry. This generalization is achieved by relaxing the linear constraint on the embedding tensor so as to allow for a symmetric 3-tensor related to electric and/or magnetic quantum anomalies in these theories. Apart from electric and magnetic gauge fields, the resulting Lagrangians also feature two-form fields and can accommodate various unusual duality frames as they often appear, e.g., in string compactifications with background fluxes.
On duality in supersymmetric Yang-Mills theory
Physics Letters B, 1995
arXiv:hep-th/9505004v1 1 May 1995 WIS/4/95 We discuss non-abelian SU (N c ) gauge theory coupled to an adjoint chiral superfield X, and a number of fundamental chiral superfields Q i . Using duality, we show that turning on a superpotential W (X) = Tr k l=1 g l X l+1 leads to non-trivial long distance dynamics, a large number of multicritical IR fixed points and vacua, connected to each other by varying the coefficients g l .
International Journal of Modern Physics A, 2019
We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary [Formula: see text]-dimensional interacting non-Abelian 1-form gauge theory where there is an [Formula: see text] gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our [Formula: see text]-dimensiona...