Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0706.4168

Symmetry invariance, anticommutativity and nilpotency in BRST approach to QED: superfield formalism

R. P. Malik
View original source ↗Read source document ↗Export metadata ↓

Abstract

We provide the geometrical interpretation for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) interacting U(1) gauge theory within the framework of superfield approach to BRST formalism. This interacting theory, where there is an explicit coupling between the U(1) gauge field and matter (Dirac) fields, is considered on a (4, 2)-dimensional supermanifold parametrized by the four spacetime variables x^μ(μ= 0, 1, 2, 3) and a pair of Grassmannian variables θand \barθ(with θ^2 = \bar θ^2 = 0, θ\barθ+ \bar θθ= 0$). We express the Lagrangian density and (anti-)BRST charges in the language of the superfields and show that (i) the (anti-)BRST invariance of the 4D Lagrangian density is equivalent to the translation of the super Lagrangian density along the Grassmannian direction(s) (θand/or \barθ) of the (4, 2)-dimensional supermanifold such that the outcome of the above translation(s) is zero, and (ii) the anticommutativity and nilpotency of the (anti-)BRST charges are the automatic consequences of our superfield formulation.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. P. Malik. 2011-11-17. Symmetry invariance, anticommutativity and nilpotency in BRST approach to QED: superfield formalism. https://arxiv.org/abs/0706.4168

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A GLSM realization of derived equivalence in $U(1) \times U(2)$ models

This paper studies the derived equivalence between Calabi--Yau mixed branches using the B-brane hemisphere partition function in anomalous gauged linear sigma models (GLSMs). For a family of anomalous $U(2)$ GLSMs, we study the infrared behavior of B-branes under RG flow and the variation of FI parameters in the quantum Kähler moduli space. As characterized by the big and small window categories of the GLSM, the RG flow effect is analyzed according to the properties of their B-brane central charges as hemisphere partition functions. The result generalizes the band restriction rules in anomalous abelian GLSMs (Clingempeel--Floch--Romo) to some $U(2)$ models. As an application, we study a family of $U(1)\times U(k)$ models for $k=1,2$, which realize a Fano UV sigma model and two IR phases as mixed branches accompanied by local Calabi--Yau Higgs components. By applying the restriction rules, we establish new derived equivalences between Calabi--Yau varieties from these anomalous models.

hep-th↗
arXiv2026

Inner Horizon Saddles and a Spectral KSW Criterion

The Bekenstein-Hawking entropy formula $ρ= e^{A/4G}$ receives significant corrections for charged black holes near extremality. Using standard results in JT gravity, the correction term can semiclassically be expressed as minus the exponential of the inner horizon area, $e^{A_{\text{inner}}/4G}$, and the cancellation between these two exponentials enforces a vanishing density of states towards extremality, when the two horizons collide. Building on arXiv:2402.10162, we argue that the correction term corresponds to a complex saddle geometry of the bulk gravitational path integral. The proposed geometry has a negative boundary length and caps off at the inner horizon; we refer to it as the inner horizon saddle. We discuss how the saddle, and its accompanying minus sign, contribute to the density of states through a Picard-Lefschetz analysis of the inverse Laplace contour, together with a stability analysis of the saddle. We also address the inner horizon saddle's violation of the Kontsevich-Segal-Witten (KSW) allowability criterion for the inclusion of complex metrics. Despite this violation, which is believed to cause unphysical divergences in path integral computations, one can describe one-loop effects on the inner horizon saddle by carefully treating wrong-sign modes. Motivated by this observation, we propose a weaker version of the KSW criterion, which we call the spectral KSW criterion. Its purpose is to characterize when one-loop corrections around complex gravitational saddles are well defined.

hep-th↗
arXiv2026

Collision Dynamics of False-Vacuum Oscillons

We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a negative quartic term. We construct small-amplitude oscillon solutions around the false vacuum using the Fodor {\emph{et al.}} expansion, and show that the force between oscillons decays exponentially at large separation, with a strength modulated by their relative phase. Numerical simulations of two-oscillon collisions exhibit reflection, crossing, and formation of excited oscillons. Resonance windows occur, similar to those found in kink-antikink collisions. In the normal theory, if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair, initiating a phase transition to the true vacuum. We also simulate the collision of oscillons evolved from a slightly perturbed sphaleron.

hep-th↗