scholarly journals DOUBLET GROUPS, EXTENDED LIE ALGEBRAS, AND WELL DEFINED GAUGE THEORIES FOR THE TWO-FORM FIELD

2005 ◽  
Vol 20 (12) ◽  
pp. 2673-2685 ◽  
Author(s):  
MARCELO BOTTA CANTCHEFF
Keyword(s):  
Lie Algebras ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Yang Mills ◽  
Nonassociative Algebras ◽  
Form Field ◽  
Tensor Current ◽  
Chern Simons ◽  
Matter Fields ◽  
General Connection

We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also shown that nonassociative algebras naturally appear in this formalism, which are briefly discussed. Afterwards, a general connection which includes a two-form field is settled-down, solving the problem of setting a gauge theory for the Kalb–Ramond field for generical groups. Topological Chern–Simons theories can also be defined in four dimensions, and this approach clarifies their relation to the so-called B ∧ F theories. We also revise some standard aspects of Kalb–Ramond theories in view of these new perspectives. Since this gauge connection is built upon a pair of fields consisting of a one-form and a two-form, one may define Yang–Mills theories as usually and, remarkably, also minimal coupling with bosonic matter, where the Kalb–Ramond field appears naturally as mediator; so, a new associated conserved charge can be defined. For the Abelian case, we explicitly construct the minimal interaction between B-field and matter following a "gauge principle" and find a novel conserved tensor current. This is our most significative result from the physical viewpoint. This framework is also generalized in such a way that any p-rank tensor may be formulated as a gauge field.

CONFORMALLY COVARIANT DRESSING TRANSFORMATIONS FOR SUPER SELF-DUALITY EQUATIONS IN D=4

1989 ◽  
Vol 04 (10) ◽  
pp. 971-982
Author(s):  
J. AVAN
Keyword(s):  
Linear System ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Yang Mills ◽  
Self Duality ◽  
Loop Algebras ◽  
Field Dependent

A set of conformally covariant dressing transformations is constructed for the supersym-metric N=3 self-duality equations in four dimensions, using the associated covariant linear system. They form a closed, 5+6-index algebra, up to field-dependent gauge transformations, containing the previously known loop algebras as a particular subset. This construction generalizes the formerly built set of conformally covariant DT for ordinary self-dual Yang-Mills.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

scholarly journals CHAPLINE–MANTON INTERACTION VERTICES AND HAMILTONIAN BRST COHOMOLOGY

2000 ◽  
Vol 15 (06) ◽  
pp. 893-903 ◽  
Author(s):  
C. BIZDADEA ◽  
L. SALIU ◽  
S. O. SALIU
Keyword(s):  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Interaction Term ◽  
Chern Simons

Consistent interactions between Yang–Mills gauge fields and an Abelian two-form are investigated by using a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and the BRST-invariant Hamiltonian of the uncoupled model generates the Yang–Mills Chern–Simons interaction term. The resulting interactions deform both the gauge transformations and their algebra, but not the reducibility relations.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

1992 ◽  
Vol 07 (02) ◽  
pp. 235-256 ◽  
Author(s):  
MANUEL ASOREY ◽  
FERNANDO FALCETO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Condition ◽  
Simons Theory ◽  
Coupling Constant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
The One ◽  
Chern Simons ◽  
Three Dimensional Space

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

N=2 SUPERSTRING THEORY GENERATES SUPERSYMMETRIC CHERN-SIMONS THEORIES

1994 ◽  
Vol 09 (35) ◽  
pp. 3255-3266 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Integrable Models ◽  
Three Dimensions ◽  
Superstring Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Fundamental Significance ◽  
Background Fields ◽  
Chern Simons

We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.

scholarly journals Slavnov–Taylor Identities from the Causal Point of View

1997 ◽  
Vol 12 (18) ◽  
pp. 3205-3248 ◽  
Author(s):  
Michael Dütsch
Keyword(s):  
Perturbation Theory ◽  
Gauge Invariance ◽  
Point Of View ◽  
Green Functions ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Free Fields ◽  
Matter Fields ◽  
Slavnov Taylor Identities

We continue the investigation of quantized Yang–Mills theories coupled to matter fields in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S matrix and the corresponding gauge transformations are simple transformations of the free fields only. In spite of this simplicity, gauge invariance implies the usual Slavnov–Taylor identities. The main purpose of this paper is to prove the latter statement. Since the Slavnov–Taylor identities are formulated in terms of Green functions, we investigate the agreement of two perturbative definitions of Green functions, namely Epstein and Glaser's definition with the Gell-Mann–Low series.

scholarly journals Surface charges toolkit for gravity

2020 ◽  
Vol 29 (06) ◽  
pp. 2050040
Author(s):  
Ernesto Frodden ◽  
Diego Hidalgo
Keyword(s):  
Surface Charge ◽  
Gauge Theories ◽  
Differential Forms ◽  
Gravity Theory ◽  
Surface Charges ◽  
Local Surface ◽  
Yang Mills ◽  
Gravity Theories ◽  
Chern Simons ◽  
Matter Fields

These notes provide a detailed catalog of surface charge formulas for different classes of gravity theories. The present catalog reviews and extends the existing literature on the topic. Part of the focus is on reviewing the method to compute quasi-local surface charges for gauge theories in order to clarify conceptual issues and their range of applicability. Many surface charge formulas for gravity theories are expressed in metric, tetrads-connection, Chern–Simons connection, and even BF variables. For most of them, the language of differential forms is exploited and contrasted with the more popular metric components language. The gravity theory is coupled with matter fields as scalar, Maxwell, Skyrme, Yang–Mills, and spinors. Furthermore, three examples with ready-to-download notebook codes, show the method in full action. Several new results are highlighted through the notes.

DYNAMICS OF MAGNETIC FIELDS IN MAXWELL, YANG–MILLS AND CHERN–SIMONS THEORIES ON THE TORUS

1993 ◽  
Vol 08 (15) ◽  
pp. 2623-2682 ◽  
Author(s):  
MARK BURGESS ◽  
ALAN McLACHLAN ◽  
DAVID J. TOMS
Keyword(s):  
Magnetic Fields ◽  
Dynamical Symmetry ◽  
Simons Theory ◽  
Radiative Corrections ◽  
Four Dimensions ◽  
Yang Mills ◽  
Consistency Requirement ◽  
Condensate Formation ◽  
Abelian Fields ◽  
Chern Simons

We reconsider the problem of uniform magnetic fields passing perpendicularly through a two-torus. We focus on dynamical effects from nonintegrable phases on the torus at nonzero B and from magnetic fields themselves in the vacuum. The spectrum is computed and is shown to be always independent of the nonintegrable phases on the torus. It is concluded that a Chern–Simons term will always be induced by radiative corrections to fermions on the torus when B ≠ 0. The special case of an electromagnetically uncharged anyon gas is noted and shown to be a system whose spectrum can depend on the nonintegrable phases in the two torus directions, subject to a consistency requirement. In three and four dimensions dynamical symmetry breaking of non-Abelian fields and associated condensate formation is possible by radiative corrections. The classification of non-Abelian magnetic fields in terms of "flux integers" is discussed, and a method for obtaining such integers for an arbitrary gauge algebra is presented which provides a rigorous generalization of 't Hooft's su(2) classification. Finally, we remark on the off-shell effective action in Chern–Simons theory.

scholarly journals An improved holographic nodal line semimetal

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Yan Liu ◽  
Xin-Meng Wu
Keyword(s):  
Mass Term ◽  
Nodal Line ◽  
Duality Relation ◽  
Strongly Coupled ◽  
Nodal Lines ◽  
Form Field ◽  
Improved Model ◽  
Fermionic Spectrum ◽  
Chern Simons ◽  
Tensor Operators

Abstract We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $$ \overline{\psi}{\gamma}^{\mu v}\psi $$ ψ ¯ γ μv ψ and $$ \overline{\psi}{\gamma}^{\mu v}{\gamma}^5\psi $$ ψ ¯ γ μv γ 5 ψ . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

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