Dual-BRST symmetry: 6D Abelian 3-form gauge theory

Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the offshell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.

Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

“…For instance, such theories are Abelian p-form (p = 1, 2, 3) gauge theories which have been shown to be the field theoretic models for the Hodge theory in D = 2p dimensions of spacetime (see, e.g. [12][13][14][15][16]). These theories respect six continuous symmetries that lead to the derivation of canonical basic brackets amongst the creation and annihilation operators.…”

“…We have proposed many models for the Hodge theory which are from the domains of p-form (p = 1, 2, 3) gauge theories [12][13][14][15][16] and N = 2 SUSY quantum mechanics [17][18][19]. One of the decisive features of the models for the Hodge theories, connected with the p-form gauge theories, is that these theories are always endowed with six continuous symmetries within the framework of BRST formalism.…”

𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta

“…We have proven that the 1D model of a rigid rotor [17], N = 2 SUSY quantum mechanical model with any arbitrary superpotential [16], N = 2 SUSY model for the motion of a charged particle under influence of a magnetic field [18], free 4D Abelian 2-form and 6D Abelian 3-form gauge theories [19][20][21], etc., are models for the Hodge theory. For all these models, we can perform the canonical quantization without taking recourse to the mathematical definition of the canonical conjugate momenta.…”

A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

“…In the main paper, the dual operators acting on the field space have been introduced in a general context. For a practical description in the context of field-spaces, see [19]. There, the author starts from a field theory with physical terms and identifies the discrete symmetry as the one induced by the Hodge- * operator in the physical context.…”

“…For an example of how the Hodge star induces a discrete symmetry I follow [19,24,25]. The main idea there was to represent the Hodge decomposition operators (d, δ, ∆) as some symmetries of a given BRST-invariant Lagrangean of a gauge theory.…”