ANOMALOUS GAUSS LAW ALGEBRAS

Supplementing the Gauss law operator of an anomalous gauge theory with a certain set of functionals of the gauge potentials, one obtains a closed algebra. The algebras obtained in this way are Abelian extensions of the Lie algebra of the group of gauge transformations, and are natural generalizations of Kac-Moody algebras, both in two and four dimensions.

Download Full-text

AdS superprojectors

Journal of High Energy Physics ◽

10.1007/jhep04(2021)074 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

E. I. Buchbinder ◽

D. Hutchings ◽

S. M. Kuzenko ◽

M. Ponds

Keyword(s):

Shell Model ◽

Differential Operators ◽

Second Order ◽

Projection Operators ◽

De Sitter ◽

Gauge Invariant ◽

Gauge Transformations ◽

Four Dimensions ◽

Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

Download Full-text

The phase structure of SU(2) lattice gauge theory with an action including larger interaction loops in four dimensions

Physics Letters B ◽

10.1016/0370-2693(83)91041-9 ◽

1983 ◽

Vol 130 (3-4) ◽

pp. 194-198

Author(s):

T. Niuya ◽

K. Odaka

Keyword(s):

Gauge Theory ◽

Phase Structure ◽

Lattice Gauge Theory ◽

Four Dimensions ◽

Lattice Gauge

Download Full-text

Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

Canadian Journal of Physics ◽

10.1139/cjp-2013-0457 ◽

2014 ◽

Vol 92 (9) ◽

pp. 1033-1042 ◽

Cited By ~ 4

Author(s):

S. Gupta ◽

R. Kumar ◽

R.P. Malik

Keyword(s):

Gauge Theory ◽

Brst Symmetry ◽

Point Of View ◽

Abelian Gauge ◽

Gauge Invariant ◽

Abelian Gauge Theory ◽

Gauge Transformations ◽

Yang Mills ◽

Symmetry Transformations ◽

Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

Download Full-text

Local existence of N=1 supersymmetric gauge theory in four Dimensions

10.1063/1.4917120 ◽

2015 ◽

Author(s):

Fiki T. Akbar ◽

Bobby E. Gunara ◽

Freddy P. Zen ◽

Triyanta

Keyword(s):

Supersymmetric Gauge Theory ◽

Gauge Theory ◽

Local Existence ◽

Four Dimensions ◽

Supersymmetric Gauge

Download Full-text

Numerical studies of Wilson loops in SU(3) gauge theory in four dimensions

Physical Review D ◽

10.1103/physrevd.26.2166 ◽

1982 ◽

Vol 26 (8) ◽

pp. 2166-2168 ◽

Cited By ~ 35

Author(s):

Michael Creutz ◽

K. J. M. Moriarty

Keyword(s):

Gauge Theory ◽

Wilson Loops ◽

Four Dimensions ◽

Numerical Studies

Download Full-text

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

Modern Physics Letters A ◽

10.1142/s0217732389001143 ◽

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.

Download Full-text

General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory

Axioms ◽

10.3390/axioms8010024 ◽

2019 ◽

Vol 8 (1) ◽

pp. 24

Author(s):

Marta Dudek ◽

Janusz Garecki

Keyword(s):

General Relativity ◽

Gauge Theory ◽

Cosmological Constant ◽

Gauge Field ◽

Geometrical Interpretation ◽

Positive Cosmological Constant ◽

Four Dimensions ◽

Action Integral ◽

Fields Equations

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

Download Full-text

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

International Journal of Modern Physics A ◽

10.1142/s0217751x06034331 ◽

2006 ◽

Vol 21 (31) ◽

pp. 6477-6490 ◽

Cited By ~ 3

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.

Download Full-text