scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4841-4859 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Space Time ◽  
Free Solution ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Lorentz Covariance ◽  
Brst Cohomology ◽  
Chern Simons

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM I: PAULI–FIERZ AND THREE-FORM

2008 ◽  
Vol 23 (29) ◽  
pp. 4721-4755 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Deformation Theory ◽  
Coupling Constant ◽  
Lorentz Covariance ◽  
Massless Spin ◽  
Brst Cohomology

Cross-couplings between a massless spin-two field (described in the free limit by the Pauli–Fierz action) and an Abelian three-form gauge field in D = 11 are investigated in the framework of the deformation theory based on local BRST cohomology. These consistent interactions are obtained on the grounds of smoothness in the coupling constant, locality, Lorentz covariance, Poincaré invariance, and the presence of at most two derivatives in the interacting Lagrangian. Our results confirm the uniqueness of the 11-dimensional interactions between a graviton and a three-form prescribed by general relativity.

scholarly journals BOSE–FERMI EQUIVALENCE IN THREE-DIMENSIONAL NONCOMMUTATIVE SPACETIME

2008 ◽  
Vol 23 (35) ◽  
pp. 3015-3022
Author(s):  
K. M. AJITH ◽  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Partition Function ◽  
Gauge Field ◽  
Three Dimensional ◽  
Coupling Constant ◽  
Spin Factor ◽  
Noncommutative Spacetime ◽  
Chern Simons

We study the fermionisation of Seiberg–Witten mapped action (to order θ) of the λϕ4 theory coupled minimally with U(1) gauge field governed by Chern–Simons action. Starting from the corresponding partition function we derive nonperturbatively (in coupling constant) the partition function of the spin-1/2 theory following Polyakov spin factor formalism. We find that the dual interacting fermionic theory is nonlocal. This feature also persists in the limit of vanishing self-coupling. In θ → 0 limit, the commutative result is obtained.

scholarly journals COUPLINGS BETWEEN A COLLECTION OF BF MODELS AND A SET OF THREE-FORM GAUGE FIELDS

2006 ◽  
Vol 21 (31) ◽  
pp. 6477-6490 ◽  
Author(s):  
CONSTANTIN BIZDADEA ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Gauge Theory ◽  
Master Equation ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Free Theory ◽  
Lagrangian Action ◽  
Deformation Procedure

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincaré invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.

scholarly journals PROBING THE FROISSART BOUND FOR MODELS WITH CHARGED VECTOR FIELDS IN D=3

1994 ◽  
Vol 09 (18) ◽  
pp. 1695-1700 ◽  
Author(s):  
O.M. DEL CIMA
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Amplitudes ◽  
Gauge Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tree Level ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Maxwell Fields ◽  
Chern Simons

One discusses the tree-level unitarity and presents asymptotic behavior of scattering amplitudes for three-dimensional gauge-invariant models where complex Chern- Simons-Maxwell fields (with and without a Proca-like mass) are coupled to an Abelian gauge field.

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.

VORTICES IN CURVED SPACE-TIME

1993 ◽  
Vol 08 (38) ◽  
pp. 3665-3672 ◽  
Author(s):  
J.D. EDELSTEIN ◽  
G. LOZANO ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Scalar Curvature ◽  
Gauge Field ◽  
Space Time ◽  
Higgs Model ◽  
Curved Space ◽  
Abelian Higgs Model ◽  
Vortex Solutions ◽  
Chern Simons ◽  
Higgs Scalar

We study an Abelian Higgs model coupled to a background metric. We find Bogomol’nyi equations when the coupling is achieved through an Rɸ2 term (R being the scalar curvature and ɸ the Higgs scalar). Remarkably, these equations coincide with those arising in models where the gauge field dynamics is governed by a Chern-Simons term so that vortex solutions in our system can be related to self-dual Chern-Simons vortices.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 2997-3012 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Lie Algebra ◽  
Space Time ◽  
Time Dependent ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Quadratic Action ◽  
Rigid Transformations

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.

scholarly journals WIGNER'S LITTLE GROUP AND BRST COHOMOLOGY FOR ONE-FORM ABELIAN GAUGE THEORY

2004 ◽  
Vol 19 (16) ◽  
pp. 2721-2737 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Decisive Role ◽  
Decomposition Theorem ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Brst Cohomology ◽  
The Relationship ◽  
Translation Subgroup

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of Wigner's little group for the free one-form Abelian gauge theory in four (3+1)-dimensions (4D) of space–time. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi–Rouet–Stora–Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.

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