Lorentz-covariant quantization of the heterotic superstring (original) (raw)

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Construction of the covariantly quantized heterotic superstring

Nuclear Physics B, 1990

We give a detailed discussion of the construction of the Batalin-Vilkovisky BRST charge for the heterotic superstring. In particular, we completely solve the higher-ghost sector using a recursion relation. The gauge choice W+ 0 = 0, which we previously proposed for the superparticle, leads to a free quantum action.

Improved covariant quantization of the heterotic superstring

Nuclear Physics B, 1991

A generalized lagrangian BRST formalism is developed and used to study the covariant quantization of the heterotic superstring. The quantum action is by construction invariant under the off-shell nilpotent BRST transformations, which is achieved by introducing a minimal set of auxiliary variables with nonzero ghost number. The method relies on the classical gauge structure, and represents a natural lagrangian extension of the ideas existing in the hamiltonian BRST approach.

Covariant Quantization of Superstrings Without Pure Spinor Constraints

Journal of High Energy Physics, 2002

We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST charge, is treated as a new generator with a new b − c system. We construct a nilpotent BRST current, an anomalous ghost current and an anomaly-free energy-momentum tensor. For open superstrings, we find the correct massless spectrum. In addition, we construct a Lorentz invariant B-field to be used for the computation of the integrated vertex operators and amplitudes.

Manifestly superPoincaré-covariant quantization of the Green-Schwarz superstring

Physics Letters B - PHYS LETT B, 1988

The Green-Schwarz (GS) superstring is reformulated in a physically equivalent way by embedding it into a larger system containing additional fermionic string-as well as bosonic harmonic variables and possessing additional gauge invariances. The main feature of the new GS superstring system is that it contains covariant and functionally independent first-class constraints only. This allows straightforward application of the BFV-BRST formalism for a manifestly superPoincaré-covariant canonical quantization. The corresponding BRST charge turns out to be of second rank and, therefore, the BFV-BRST action contains fourth-order ghost terms.

An introduction to the covariant quantization of superstrings

Classical and Quantum Gravity, 2003

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green-Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.

The covariant quantum superstring and superparticle from their classical actions

Physics Letters B, 2003

We develop an approach based on the Noether method to construct nilpotent BRST charges and BRST-invariant actions. We apply this approach first to the holomorphic part of the flat-space covariant superstring, and we find that the ghosts b, c z which we introduced by hand in our earlier work, are needed to fix gauge symmetries of the ghost action. Then we apply this technique to the superparticle and determine its cohomology. Finally, we extend our results to the combined left-and right-moving sectors of the superstring.

Quantum geometry of the covariant superstring with N = 1 global supersymmetry

Physics Letters B, 1986

The quantization of the superstring with N = 1 global supersymmetry is considered in the functional integral formalism. The term in the effective action defined by the conformal anomaly is calculated. It is shown that the effective action is determined not only by the intrinsic properties of the surface (i.e. by the metric h~3) but depends also on the way the surface is embedded in D-dimensional space (i.e. on the second quadratic form of the surface). The selfduality ofN = 1 superstring theory with a Wess-Zumino term is pointed out.

κ-Anomalies and space-time supersymmetry in the Green-Schwarz heterotic superstring

Nuclear Physics B, 1995

The computation of κ-anomalies in the Green-Schwarz heterotic superstring sigmamodel and the corresponding Wess-Zumino consistency condition constitute a powerful alternative approach for the derivation of manifestly supersymmetric string effective actions. With respect to the beta-function approach this technique presents the advantage that a result which is obtained with the computation of beta-functions at n loops can be obtained through the calculation of κ-anomalies at n − 1 loops. In this paper we derive by a direct one-loop perturbative computation the κ-anomaly associated to the Yang-Mills Chern-Simons threeform and, for the first time, the one associated to the Lorentz Chern-Simons threeform. In the calculation we shall use a convenient set of constraints for the pure N = 1, D = 10 supergravity theory which is algebraically identical to the standard set of constraints for the pure N = 1, D = 10 super Yang-Mills theory. Contrary to what is often stated in the literature we show that the Lorentz κ-anomaly gets contributions from the integration over both the fermionic and bosonic degrees of freedom of the string. A careful analysis of the absolute coefficients of all these anomalies reveals that they can be absorbed by setting dH = α ′ 4 (tr F 2 − tr R 2), where α ′ is the string tension, the expected result. We show that this relation ensures also the absence of gauge and Lorentz anomalies in the sigma-model effective action. Moreover, the consistency condition of the κ-anomalies ensures the closure of the SUSY algebra in the Bianchi identities. We evidenciate the 1 Supported in part by M.P.I. This work is carried out in the framework of the European Community Programme "Gauge Theories, Applied Supersymmetry and Quantum Gravity" with a financial contribution under contract SC1-CT92-D789. presence of infrared divergences in the heterotic string sigma model, which are due to the presence of the d = 2 scalar massless fields of the string, and present a conjecture for their cancellation which is intimately related to the locality and Wess-Zumino consistency of the κ-anomalies.

The Canonical Structure of the Superstring Action

Canadian Journal of Physics, 2016

We consider the canonical structure of the Green–Schwarz superstring in 9 + 1 dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in 2 + 1 and 3 + 1 dimensions. A key feature of this structure is that the primary fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac bracket then the second group of primary fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary fermionic first-class constraints can be used to find the generator of a local fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space–time to see if the fermionic gauge symmetry can be made simpler than it is in 2 + 1, 3 + 1, and 9 + 1 dimensions. With a 3 + 3 dimensional target space, we find that such a simplification occurs. We finally show ...