We review the detailed structure of the large N = 4 superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing N = 4 strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical N = 4 string theories. e-mail address: [email protected] e-mail address: [email protected], ohta@...

The problem of describing the singular vectors of W 3 and W (2) 3 Verma modules is addressed, viewing these algebras as BRST quantized Drinfeld-Sokolov (DS) reductions of A (1) 2. Singular vectors of an A (1) 2 Verma module are mapped into W algebra singular vectors and are shown to differ from the latter by terms trivial in the BRST cohomology. These maps are realized by quantum versions of th...

We study the spectra of G/G coset models by computing BRST cohomology of affine Lie algebras with coefficients in tensor product of two modules. One-to-one correspondence between the spectra of A1/A 1 1 and that of the minimal matter coupled to gravity (including boundary states of the Kac table) is observed. This phenomena is discussed from the point of hamiltonian reduction of BRST complexes ...

Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be ...

We summarize some recent results on the BRST analysis of physical states of 2D gravity coupled to c ≤ 1 conformal matter and the supersymmetric generalization. CERN-TH.6279/91 BRX TH-326 USC-91/34 October 1991 ∗ To appear in the proceedings of the 1991 Cargèse Summer School on “New Symmetry Principles in Quantum Field Theory,” Cargèse, July 15-27, 1991. BRST ANALYSIS OF PHYSICAL STATES FOR 2D (...

This paper is devoted to the quantization of the second-ilk superparticle using the Batalin-Vilkovisky method. We show the full structure of the master action. By imposing gauge conditions on the gauge fields rather than on coordinates we find a gauge-fixed quantum action which is free. The structure of the BRST charge is exhibited, and the BRST cohomology yields the same physical spectrum as t...

We introduce an operator version of the BRST-BFV effective action for arbitrary systems with first-class constraints. Using the Schwinger action principle we calculate the propagators corresponding to: (i) the parametrized non-relativistic free particle, (ii) the relativistic free particle and (iii) the spining relativistic free particle. Our calculation correctly imposes the BRST-invariance at...

It is shown how the BRST quantization can be applied to a gauge invariant sector of theories with anomalously broken symmetries. This result is used to show that shifting the anomalies to a classically trivial sector of fields (Wess-Zumino mechanism) makes it possible to quantize the physical sector using a standard BRST procedure, as for a non anomalous theory. The trivial sector plays the rol...

We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. The WZNW action reduces to our earlier free-field quantum action after a field redefinition, and to the GreenSchwarz classical action after constraining the current in Berkovits’ BRST charge to vanish. Physical states form the cohomology of a BRST ch...

We consider the M(2, 3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We construct an algebra of operators acting on the BRST cohom...