In this paper we analyse the structure of the BRST charge of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
We propose the superconnection formalism to construct the off-shell BRST-VSUSY superalgebra for D=4 BF theories. The method is based on the natural introduction of physical fields as well as auxiliary fields via superconnections and their associated supercurvatures defined on a superspace. We also give a prescription to build the off-shell BRST-VSUSY exact quantum action.
Algebra of the constraints of twistor-like p-branes restoring 3/4 fraction of the spontaneously broken D=4 N=1 supersymmetry is studied using the conversion method. Classical and quantum realizations of the BRST charge, unified superalgebra of the global generalized superconformal OSp(1|8) and Virasoro and Weyl symmetries are constructed. It is shown that the quantum Hermitian BRST charge is nilpotent and the quantized OSp(1|8) superalgebra is closed.
We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a unique superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A set of discrete symmetry transformation for a set of GL_{qp} (1|1) covariant superalgebras turns out to be the analogue of the Hodge duality * operation of different…
Given a matrix Lie algebra one can construct the 3-Lie algebra by means of the trace of a matrix. In the present paper we show that this approach can be extended to the infinite-dimensional Lie algebra of vector fields on a manifold if instead of the trace of a matrix we consider a differential 1-form which satisfies certain conditions. Then we show that the same approach can be extended to matrix Lie superalgebras if instead of the trace of a matrix we make use of the super trace of a matrix. It is proved that a graded triple commutator of matrices constructed with the help of the graded comm…
A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper solutions of the quantum master equations in the osp(1,2)-covariant formalism are realized in that superspace as invariance under translations combined with mass-dependent special conformal transformations. The Sp(2) symmetry -…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincaré superalgebras with brane charges and study its representations. The existence of new supermultiplets in different dimensions including an ultra short supermultiplet in D=11 different from the supergravity multiplet is shown. Generalizations of superalgebras containing brane charges, including those in D$>$11 are considered. The realization of these algebras at the level of relativistic particle models and, upon quantization, at the l…
The exceptional superalgebra $\D21a$ has been classified as a candidate conformal supersymmetry algera in two dimensions. We propose an alternative interpretation of it as an extended BFV-BRST quantisation superalgebra in 2D ($D(2,1;1) \simeq osp(2,2|2)$). A superfield realization is presented wherein the standard extended phase space coordinates can be identified. The physical states are studied via the cohomology of the BRST operator. Finally we reverse engineer a classical action corresponding to the algebraic model we have constructed, and identify the Lagrangian equations of motion.
The exceptional superalgebra $D(2,1;α)$ has been classified as a candidate conformal supersymmetry algebra in two dimensions. We propose an alternative interpretation of it as extended BFV-BRST quantisation superalgebras in 2D ($D(2,1;1) \simeq osp(2,2|2)$). A superfield realization is presented wherein the standard extended phase space coordinates can be identified. The physical states are studied via the cohomology of the BRST operator. It is conjectured that the underlying model giving rise to this `quantisation' is that of a scalar relativistic particle in 1+1 dimensions, for which the lig…
We replace our earlier condition that physical states of the superstring have non-negative grading by the requirement that they are analytic in a new real commuting constant t which we associate with the central charge of the underlying Kac-Moody superalgebra. The analogy with the twisted N=2 SYM theory suggests that our covariant superstring is a twisted version of another formulation with an equivariant cohomology. We prove that our vertex operators correspond in one-to-one fashion to the vertex operators in Berkovits' approach based on pure spinors. Also the zero-momentum cohomology is equa…
We give an explicit formula for the Becchi-Rouet-Stora-Tyutin (BRST) charge associated with Poisson superalgebras. To this end, we split the master equation for the BRST charge into a pair of equations such that one of them is equivalent to the original one. We find the general solution to this equation. The solution possesses a graphical representation in terms of diagrams.
We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
In this paper we analyse the ABJM theory in ${\cal N}=1$ superspace. Firstly we study the linear and non-linear BRST transformations for the ABJM theory. Then we derive the finite field dependent version of these BRST (FFBRST) transformations. Further we show that such FFBRST transformations relate the generating functional in linear gauge to the generating functional in the non-linear gauge of ABJM theory.
We introduce, within the Refined-Gribov-Zwanziger setup, a composite BRST invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behaviour of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.
The new extensions of the Poincaré superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent representations of the superalgebra. The parametrization of the coset space $G/H$, with $G$ a given extended supergroup and $H$ the Lorentz subgroup, that corresponds to the linear transformations is presented.
The local BRST cohomology of the gauged non-linear sigma model on a group manifold is worked out for any Lie group G. We consider both, the case where the gauge field is dynamical and the case where it has no kinetic term (G/G topological theory). Our results shed a novel light on the problem of gauging the WZW term as well as on the nature of the topological terms introduced a few years ago by De Wit, Hull and Rocek. We also consider the BRST cohomology of the rigid symmetries of the ungauged model and recover the results of D'Hoker and Weinberg on the most general effective actions compatibl…
In this Letter, we propose a model which is equivalent to the Yang-Mills theory at long distances but for which all symmetries are realized linearly. On top of the gauge and Fadeev-Popov ghosts fields, the model presents several massive fields, all of which can be merged in a unique vector field with support in a curved superspace. The equivalence of this model with the gauge-fixed Yang-Mills theory is shown to result from the decoupling of these extra massive modes at small momenta. Most of the symmetries of Yang-Mills theory, including the famous BRST symmetry, can be interpreted in this way…
The renormalization group flow in the theory space of a BRST invariant string $σ$-model is investigated. For the open bosonic string the non-perturbative off-shell effective action and its gauge symmetry properties are determined from $β$-functions defined by the local Weyl anomaly. The interactions are shown to explicitly break the free theory BRST invariance generating new non-linear gauge symmetries of the type present in Witten's string field theory. In the Feynman-Siegel gauge the $σ$-model is shown to generate Witten's structure of vertex couplings.
We review the construction of gauge field theories from BRST first-quantized systems and its relation to the unfolded formalism. In particular, the BRST extension of the non linear unfolded formalism is discussed in some details.
In this paper we will analyse a noncommutative deformation of the ABJM theory in N=1 superspace formalism. We will then analyse the BRST and the anti-BRST symmetries for this deformed ABJM theory, in linear as well as non-linear gauges. We will show that the sum of gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and non-linear gauges. We will show that in Landau and Curci-Ferrari gauges this deformed ABJM theory is invariant under a additional set of symmetry transformations. We …
We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints. Such a polynomial is characterized by the coefficients forming a set of higher order structure constraints. Assuming the set of constraints to be linearly independent, we find the restrictions on the structure constraints when the nilpotent BRST charge can be written in a simple and universal form. In the case of quadratically nonlinear algebras we find the expression for…
In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of group-theoretical techniques and then we give a possible way to solve the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST symmetry. In the final part we present a study of the Batalin-Vilkovisky quantisation method for non-linear gauges in non-Abelian gauge theories.
Boundary interactions of closed-string with open-strings are examined intended to provide a constructive formulation of boundary string field theory. As an illustration, we consider the BPS $D$-brane of the type II superstring in a constant NS-NS two-form background, and study the boundary interaction with arbitrary configurations of gauge field on the brane. The boundary interaction is presented, within the world-sheet cut-off theories, as an off-shell boundary state in the closed-string Hilbert space. It is regarded as a closed-string theoretical counterpart of the Wilson loop in the world-v…
A linear odd Poisson bracket realized solely in terms of Grassmann variables is suggested. It is revealed that with the bracket, corresponding to a semi-simple Lie group, both a Grassmann-odd Casimir function and invariant (with respect to this group) nilpotent differential operators of the first, second and third orders are naturally related and enter into a finite-dimensional Lie superalgebra. A connection of the quantities, forming this Lie superalgebra, with the BRST charge, $Δ$-operator and ghost number operator is indicated.
We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger--Lambert--Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and non-linear gauges. Remarkably, for Delbourgo-Jarvis-Baulieu-Thierry-Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost-anti-ghost condensation. Further, we discuss the ghost-anti-ghost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.
We show that the Hilbert space of the standard linear harmonic oscillator is a complete orbit of the osp(2,1;2) spectrum-generating superalgebra, and that this is the smallest such algebraic structure. The ubiquitous appearance of the linear harmonic oscillator in virtually all domains of theoretical physics guarantees a corresponding ubiquity of appropriate generalizations of this spectrum-generating superalgebra.
In this proceeding, $SU(N)$ Yang-Mills theory is quantized in the linear covariant gauges, while taking into account the issue of Gribov copies and we construct the one-loop effective potential for a set of mass dimension 2 condensates, including the Gribov parameter, that refines the infrared region of the Gribov-Zwanziger theory, whilst respecting renormalization group invariance and BRST symmetry.
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies à la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. An example of a Hamiltonian possessing such a hidden algebra is analyzed.
We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan procedure for a quadratic superalgebra and whose elements are realized as a formal power series with respect to non-commuting elements. To this end, we propose an algebraic procedure of Verma module construction and its realization in terms of non-commuting creation and annihilation operators of a given Heisenberg--Weyl superalgebra. In doing so, we set up a proble…
In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it tu…
We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analysed in Batalin-Vilkovisky (BV) formulatio…
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is motivated by previous work on N=(4,4) supersymmetric non-linear sigma models on K3 surfaces and on a vertex operator superalgebra with Conway group symmetry. Here we present an example of the correspondence for N=(4,4) supersymmetric non-linear sigma models on four-tori, and compare it to the K3 case.
The study of quantum Lie algebras motivates a use of non-canonical ghosts and anti-ghosts for non-linear algebras, like W-algebras. This leads, for the W_3 and W_3^(2) algebras, to the BRST operator having the conventional cubic form.
In [Z.Tsuboi, Nucl. Phys. B 826 (2010) 399 [arXiv:0906.2039]], we proposed Wronskian-like solutions of the T-system for [M,N]-hook of the general linear superalgebra gl(M|N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1,N1]-hook and [M2,N2]-hook (M=M1+M1, N=N1+N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl(M|N). Our solutions also include a Wronskian-like solution discussed in [N.Gromov, V.Kazakov, S.Leurent, Z.Tsuboi, JHEP 1101 (2011) 155 [arXiv:1010.2720…
We analyse the Abelian $N=1$ super-Chern-Simons model coupled to parity-preserving matter in linear and non-linear gauges with exact BRST invariance. Then we analyse the theory in field/antifield formulation to discuss the model at quantum level. Furthermore, we implement the field/antifield dependent transformation parameter to generalize the BRST symmetry of the theory. The novelty of field/antifield dependent BRST transformation is that under change of variable the Jacobian of the functional integral extends the quantum action from linear gauge to non-linear gauge. The results are establish…
Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra generators are written down.
A description of the quantum superalgebra $U_q[sl(n+1|m)]$ and in particular of the special linear superalgebra $sl(n+1|m)$ via creation and annihilation generators (CAGs) is given. It provides an alternative to the canonical description of $U_q[sl(n+1|m)]$ in terms of Chevalley generators. A conjecture that the Fock representations of the CAGs provide microscopic realizations of exclusion statistics is formulated.
