scholarly journals Modified 2D Proca Theory: Revisited under BRST and (Anti-)chiral Superfield Formalisms

2020 ◽  
Vol 2020 ◽  
pp. 1-38 ◽  
Author(s):  
B. Chauhan ◽  
S. Kumar ◽  
A. Tripathi ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Decisive Role ◽  
Present Theory ◽  
Kinetic Term ◽  
Conserved Charges ◽  
Form Theory ◽  
Lagrangian Densities ◽  
Chiral Superfield ◽  
Matter Fields

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e., off-shell nilpotent) (anti-)BRST, (anti-)co-BRST, and some discrete dual symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e., a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present Stückelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF) condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions and (ii) the physics behind the negative kinetic term associated with the pseudoscalar field of our present theory.

scholarly journals Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D Non-Abelian 1-Form Gauge Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
S. Kumar ◽  
B. Chauhan ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Theoretical Strength ◽  
Conserved Charges ◽  
Lagrangian Densities ◽  
Matter Fields ◽  
Chiral Superfields

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives, and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formalism, where only the (anti)chiral superfields are used.

scholarly journals A NOTE ON THE (ANTI-)BRST INVARIANT LAGRANGIAN DENSITIES FOR THE FREE ABELIAN 2-FORM GAUGE THEORY

2010 ◽  
Vol 25 (28) ◽  
pp. 2457-2467
Author(s):  
SAURABH GUPTA ◽  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Lagrange Multiplier ◽  
Field Condition ◽  
Equations Of Motion ◽  
Present Theory ◽  
Lagrange Equations ◽  
Symmetry Transformations ◽  
The Absolute ◽  
Lagrangian Densities

We show that the previously known off-shell nilpotent [Formula: see text] and absolutely anticommuting (sb sab + sab sb = 0) Becchi–Rouet–Stora–Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci–Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler–Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.

scholarly journals Nilpotent (anti-)BRST and (anti-)co-BRST symmetries in 2D non-Abelian gauge theory: Some novel observations

2021 ◽  
Author(s):  
S. Kumar ◽  
B. K. Kureel ◽  
R. P. Malik
Keyword(s):  
Differential Geometry ◽  
Gauge Theory ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Conserved Charges ◽  
Symmetry Operators ◽  
Symmetry Transformations ◽  
Continuous Symmetries ◽  
Lagrangian Densities

We discuss the nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In the literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci–Ferrari (CF)-type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel.

scholarly journals SUPERFIELD APPROACH TO A NOVEL SYMMETRY FOR NON-ABELIAN GAUGE THEORY

2002 ◽  
Vol 17 (03) ◽  
pp. 185-196 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Geometrical Interpretation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Conserved Charges ◽  
Continuous Symmetries ◽  
Matter Fields

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two (1+1)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four (2+2)-dimensional compact supermanifold.

scholarly journals Some novel features in 2D non-Abelian theory: BRST approach

2017 ◽  
Vol 32 (22) ◽  
pp. 1750136 ◽  
Author(s):  
N. Srinivas ◽  
S. Kumar ◽  
B. K. Kureel ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Lagrange Multipliers ◽  
Brst Symmetry ◽  
Abelian Theory ◽  
Symmetry Transformations ◽  
Lagrangian Densities ◽  
Matter Fields

Within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism, we discuss some novel features of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci–Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.

scholarly journals Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

2017 ◽  
Vol 32 (33) ◽  
pp. 1750193 ◽  
Author(s):  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
The Self ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Theory ◽  
Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

scholarly journals HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

2007 ◽  
Vol 22 (28) ◽  
pp. 5155-5172 ◽  
Author(s):  
R. B. MANN ◽  
E. M. POPESCU
Keyword(s):  
Gauge Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Present Context ◽  
Dimensional Gravity ◽  
Wide Perspective ◽  
Higher Gauge Theory ◽  
Matter Fields ◽  
New Framework

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

scholarly journals DUALITY IN SUPERSYMMETRIC YANG–MILLS AND THE QUANTUM HALL EFFECT

2006 ◽  
Vol 21 (20) ◽  
pp. 1567-1585
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Experimental Evidence ◽  
Quantum Hall Effect ◽  
Modular Group ◽  
Quantum Hall ◽  
Low Energy ◽  
Kinetic Term ◽  
Yang Mills ◽  
Topological Parameter

The evidence for the parallel rôles played by the modular group in [Formula: see text] supersymmetric Yang–Mills in (3+1) dimensions and the quantum Hall effect in (2+1) dimensions is reviewed. In both cases a subgroup of the full modular group acts as a map between different low energy phases of the theory, parametrised by a complex parameter in the upper-half-complex plane whose real part is a topological parameter and whose imaginary part is the coupling associated the kinetic term of the effective U(1) gauge theory. In the case of the quantum Hall effect experimental evidence in favour of the modular action is also reviewed.

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