Superfield approach to a novel symmetry for non-Abelian gauge theory

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 supermanifold.Comment: LaTeX, 12 pages, equations (4.2)--(4.6) correcte

Topological aspects in non-Abelian gauge theory

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two dimensional free non-Abelian gauge theory having no interaction with matter fields. The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two dimensional manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST- and co-BRST invariants.Comment: (1+11) pages, LaTeX, no figure

Superfield Approach To Nilpotent Symmetries For QED From A Single Restriction: An Alternative To The Horizontality Condition

We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A_\mu), the (anti-)ghost fields ((\bar C)C) and the Dirac fields (\psi, \bar\psi) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting a single restriction on the six (4, 2)-dimensional supermanifold. A set of four even spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and two odd Grassmannian variables \theta and \bar\theta parametrize this six dimensional supermanifold. The new gauge invariant restriction on the above supermanifold owes its origin to the (super) covariant derivatives and their intimate relations with the (super) 2-form curvatures (\tilde F^{(2)})F^{(2)} constructed with the help of (super) 1-form gauge connections (\tilde A^{(1)})A^{(1)} and (super) exterior derivatives (\tilde d)d. The results obtained separately by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, are shown to be a simple consequence of this new single restriction on the above supermanifold. Thus, our present endeavour provides an alternative to (and, in some sense, generalization of) the horizontality condition of the usual superfield formalism applied to the derivation of BRST symmetries.Comment: LaTeX file, 15 pages, journal-versio

Two loop effective potential for < A^2_\mu > in the Landau gauge in quantum chromodynamics

We construct the effective potential for the dimension two composite operator 1/2 A^{a 2}_\mu in QCD with massless quarks in the Landau gauge for an arbitrary colour group at two loops. For SU(3) we show that an estimate for the effective gluon mass decreases as N_f increases.Comment: 17 latex page

Abelian 3-form gauge theory: superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow Region, Russi

Field dependent nilpotent symmetry for gauge theories

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.Comment: 25 pages, No figures, Revte

The Volume Source Technique for flavor singlets: a second look

We reconsider the Volume Source Technique (VST) for the determination of flavor singlet quantities on the lattice. We point out a difficulty arising in the case of fermions in real representations of the gauge group and propose an improved version of the method (IVST) based on random gauge transformations of the background configuration. We compare the performance of IVST with the method based on stochastic estimators (SET). We consider the case of the N=1 Supersymmetric Yang-Mills Theory (SYM), where just one fermionic flavor is present, the gluino in the adjoint representation, and only flavor singlet states are possible. The work is part of an inclusive analysis of the spectrum of the lightest particles of the theory, based on the simulation of the model on a $16^3\cdot32$ lattice with dynamical gluinos in the Wilson scheme.Comment: 11 pages, 6 figures, some formulations change

Comments on the Equivalence between Chern-Simons Theory and Topological Massive Yang-Mills Theory in 3D

The classical formal equivalence upon a redefinition of the gauge connection between Chern-Simons theory and topological massive Yang-Mills theory in three-dimensional Euclidean space-time is analyzed at the quantum level within the BRST formulation of the Equivalence Theorem. The parameter controlling the change in the gauge connection is the inverse $\lambda$ of the topological mass. The BRST differential associated with the gauge connection redefinition is derived and the corresponding Slavnov-Taylor (ST) identities are proven to be anomaly-free. The Green functions of local operators constructed only from the ($\lambda$-dependent) transformed gauge connection, as well as those of BRST invariant operators, are shown to be independent of the parameter $\lambda$, as a consequence of the validity of the ST identities. The relevance of the antighost-ghost fields, needed to take into account at the quantum level the Jacobian of the change in the gauge connection, is analyzed. Their role in the identification of the physical states of the model within conventional perturbative gauge theory is discussed.Comment: 19 pages, LATEX, to appear in Journal of High Energy Physic

Testing the self-duality of topological lumps in SU(3) lattice gauge theory

We discuss a simple formula which connects the field-strength tensor to a spectral sum over certain quadratic forms of the eigenvectors of the lattice Dirac operator. We analyze these terms for the near zero-modes and find that they give rise to contributions which are essentially either self-dual or anti self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more dominated by quantum fluctuations and are less (anti) self-dual. In the high temperature phase of QCD we find considerably reduced (anti) self-duality for the modes near the edge of the spectral gap.Comment: Remarks added, to appear in Phys. Rev. Let

Notoph Gauge Theory: Superfield Formalism

We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticommutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.Comment: LaTeX file, 12 pages, Talk delivered at SQS'09 (BLTP, JINR, Dubna