BRST Invariant Action Research Articles

BRST and Anti-BRST Symmetry in Topological BF Theories

We realize the quantization of arbitrary-dimensional non-Abelian BF theories from the point of view of both the BRST symmetry and anti-BRST symmetry. The method relies on the possibility of enlarging the system of fields occurring in such theories by auxiliary fields introduced geometrically in terms of a superspace formalism. The off-shell nilpotency of the BRST and anti-BRST transformations of these fields is automatically guaranteed, thanks to the structure equations and the Bianchi identities. From this follows a direct construction of the BRST invariant full quantum action which leads, after the elimination of the auxiliary fields, to the same quantum action obtained in the context of the Batalin–Vilkovisky formalism. We also discuss how the constructed BRST invariant quantum action is anti-BRST invariant. In addition, we show that the non-Abelian BF theory in any space–time dimension possesses a vector supersymmetry of ghost number +1.

Dynamical non-Abelian two-form: BRST quantization

When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a $B\wedge F$ coupling and a kinetic term for $B$ is included, the gauge field develops an effective mass. The theory can be made invariant under a non-abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST-invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both abelian and non-abelian models of mass generation.

Worldsheets with extended supersymmetry

We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank ( N, N′), and their possible anomalies. Both classical and ghost conformally invariant multiplets of the left or right sector are assembled into the components of a single O(N)-superfield. The component with ghost number zero of this superfield is the N-supersymmetric generalization of the Beltrami differential. In a Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of Riemann surfaces coupled to local supersymmetry of rank N. It is also the source of all linear superconformal currents derived from ordinary operator product techniques. The interconnection between BRST invariant actions with different values of N ⩾ 3, and their possible link to topological 2D-gravity coupled to topological sigma models, are shown by straightforward algebraic considerations.

On the Gauge Invariant Lagrangian for Seiberg--Witten Topological Monopoles

A topological gauge invariant Lagrangian for Seiberg--Witten monopoleequations is constructed. The action is invariant under a huge classof gauge transformations which after BRST fixing leads to the BRSTinvariant action associated to Seiberg--Witten monopole topologicaltheory. The supersymmetric transformation of the fields involved inthe construction is obtained from the nilpotent BRST algebra.

Construction of the BRST-Invariant Action for a Gauged Self-Dual Theory by Making Use of the Batalin-Fradkin Algorithm11The project supported by the Grant LWTZ-1298 of the Chinese Academy of Sciences

The Batalin–Fradkin algorithm combined with the Batalin–Fradkin–Vilkovisky formalism is applied to a two-dimensional model of a self-dual field interacting chirally with a gauge field. A Becchi–Rouet–Stora–Tyutin gauge-fixing action is obtained with auxiliary fields introduced in the algorithm turning into a Wess–Zumino field. The chirality of the Wess-Zumino field appears in a natural way.

A NOVEL COVARIANT APPROACH TO THE QUANTIZATION OF INTERACTIVE CHIRAL BOSONS

A new covariant quantization of chiral bosons in the chiral Schwinger model with faddeevian regularization is carried out from Batalin-Fradkin (BF) algorithm. In order to turn the second class chiral constraint into first class constraints, infinitely many BF fields are first introduced. When combined with Batalin-Fradkin-Vilkovisky (BFV) formalism, two kinds of BRST-invariant actions have been derived. The first contains the Wess-Zumino action induced from the usual path-integral approach. But the second includes Wotzasek’s Wess-Zumino action coupled to the gauge fields.

Geometry and off-shell nilpotency for four-dimensional BF theories

We construct the off-shell nilpotent and metric independent BRST and anti-BRST operators for four-dimensional BF theories in terms of a superconnection formalism. The method is based on the natural introduction of auxiliary fields via a generalized supercurvature. We also discuss how to find the BRST and anti-BRST invariant gauge-fixed quantum action.

Extended from method of antifield-BRST formalism for topological quantum field theories

The author presents a concise method to construct a BRST-invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution to the master equation is directly obtained by means of the extended forms that involve all the required ghosts and antifields. The BV actions for the non-Abelian BF theories (in four and higher dimensions) and for the Chern-Simons theory are constructed by means of the extended form method. An extension of the BF theory in four dimensions to include a 'cosmological term' is also examined and the close connection with the topological Yang-Mills theory is indicated.

BRST analysis of 2+1 gravity.

The classical formulation and the canonical and path-integral quantization of triad Einstein gravity in 2+1 dimensions is discussed using the Hamiltonian Becchi-Rouet-Stora-Tyutin (BRST) approach. We construct the BRST charge and demonstrate explicitly the BRST symmetry of the theory. We show explicitly that for this particular system, where both approaches can be carried up to their last consequences, the canonical BRST quantization coincides exactly with Dirac quantization. We also show how to construct from the BRST-invariant action the gauge-fixed action used by Witten to calculate topology-changing amplitudes.

THE QUANTUM MECHANICS OF AN N=1 SUPERPARTICLE IN AN EXTENDED SUPERSPACE

A new ten-dimensional superparticle action with local symmetries implemented via gauge fields is formulated in a superspace with an extra anticommuting space-time spinor coordinate. Light-cone quantization gives the spectrum of N=1 super-Yang-Mills. Covariant gauge choices in which the gauge fields are set to constants lead to free BRST-invariant quantum actions. Possible ghost systems include one with only a finite number of ghosts and several with an infinite number. In each case, the BRST cohomology class of zero ghost number gives the spectrum of N=1 super-Yang-Mills.

On the covariant quantization of a first-class superparticle

The Batalin–Vilkovisky formalism is used to quantize covariantly a formulation of the superparticle with only first-class constraints. Towers of ghosts are found that split into ghosts-for-ghosts and ghost gauge fields. Subsolutions to the master equation with spinor and bispinor ghosts contain terms cubic in antifields and lead to free gauge-fixed BRST-invariant actions. The final formulation with multispinor ghosts is nilpotent only on the classical shell.

Bosonic string theory in covariant gauge

We discuss path integral formulations of the first quantization of open and closed bosonic strings in the proper-time gauges which ensure manifest covariance. The string propagators given by path integrals à la Polyakov are evaluated. The evaluated propagators uniquely determine the actions for the free string fields in the second quantized theories. The BRST invariant actions for free bosonic string fields proposed by Siegel are shown to emerge naturally. A geometrical explanation for the proper-time gauge conditions as appropriate gauge fixing conditions is presented. We also evaluate the BRST invariant one loop string path integral.

Perturbation theory for quantized string fields

We discuss the problem of gauge fixing in string field theory. We show that BRST invariance requires the gauge-fixed action to contain terms cubic in the ghost…of ghost of ghost fields. The final BRST invariant gauge-fixed action for the gauge b 0 A=0 is extremely simple: with the proper interpretation (as given in this article), it is essentially the one anticipated earlier in the work of Giddings, Martinec, and Witten in their analysis of the BRST invariant world-sheet approach to string theory. We derive the Feynman rules from this action and explain in detail how the sum over surfaces of the BRST first-quantized string is reproduced. This result depends crucially on the correct assignment for the Grassmann character of the string field and its ghost…of ghost of ghost string fields. If all these fields are unified in in a single string field Φ containing all ghost numbers, the requirement is that Φ be uniformly Grassmann odd. Finally, we do some sample calculations which provide some simple checks on our general results.

BRST INVARIANCE WITH BACKGROUND FIELDS

We apply the horizontality method for obtaining BRST transformations and invariant actions to cases where background fields are present. We consider Yang-Mills and pure gravity and in superspace N=1 super Yang-Mills, chiral matter and the free gravitino multiplet. In the super Yang-Mills case we see a simple example of a recent observation that the Nielsen-Kallosh ghosts of a theory are the BRST auxiliary fields.