Sp(2) BRST invariant quantization of strings: The harmonic gauge

doi:10.1016/0550-3213(88)90204-0

Nuclear Physics B

Volume 297, Issue 1, 1 February 1988, Pages 171-182

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Abstract

We analyze the mixed algebra of local diffeomorphisms and Weyl transformations for bosonic strings. BRST and anti-BRST operators are then constructed keeping a manifest Sp(2) invariance. The harmonic gauge arises as a natural gauge choice. All this work is redone in the presence of a two-dimensional background metric. We manage to write down a simple action, to compute the stress tensor and to work out the critical dimensions.

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Cited by (6)

Quantum mechanics of a twisted superparticle
1990, Nuclear Physics, Section B
This paper is devoted to the quantization of the ten-dimensional superparticle in the formulation, due to Siegel, in which the local fermionic symmetry is implemented using explicit gauge fields and in which momentum coordinates conjugate to the fermionic superspace coordinates are introduced. Here, a truncation of the complete N = 1 superparticle is considered (the complete superparticle is analysed in a separate paper). This “truncated model” (which was the first modified superparticle considered by Siegel) is shown to be invariant under a “twisted” N = 2 space-time supersymmetry, and a light-cone gauge analysis shows that the physical spectrum is a representation of this algebra which includes negative norm states.
The Batalin-Vilkovisky method is used to covariantly quantize the system in two ways, one with an infinite number of ghost fields and one with only a finite number. In both cases, the BRST cohomology is analysed in detail.
Our results illustrate certain general features: (i) In a formulation with gauge fields for the fermionic symmetries the invariance can be fixed by imposing gauge conditions on the gauge fields. This results in a free quantum action, without the need for the problematic field redefinitions that arise in earlier formulations in which gauge conditions are imposed on the spinorial coordinates. (ii) There is an interesting pattern for the infinite number of ghost-for-ghosts, which naturally divide into two sets. The first is an infinite sequence of gauge fields while the second is a set of ghosts for the corresponding sequence of gauge invariances. (iii) The infinite set of quantum fields packages into simple infinite-dimensional spinor representations of the supergroup OSp(9, 1 | 2). The cohomology classes are particularly easy to describe in terms of OSp(9, 1 | 2) spinor notation.
Covariant quantum mechanics of the superstring
1989, Physics Letters B
Ten-dimensional superstring theory is covariantly quantized using the lagrangian BRST method of Batalin and Vilkovisky. In a conformal gauge the quantum action is given by a free-field action involving the classical fields and an infinite tower of ghosts. It is invariant under an infinite extension of the global supersymmetry of the classical action. A discussion is given of the cancellation of the conformal anomaly. The classical fields together with their ghosts fit into a vector and a metaplectic (spinor) representation of an OSp supergroup.
String world-sheet anomalies in non-conformal gauges
1989, Nuclear Physics, Section B
The Polyakov quantization of the bosonic string is treated in general homogeneous gauges where the world-sheet metric becomes a dynamical variable. We find that the gauge fixed action is governed by an effective, abelianized BRST (+anti-BRST) algebra which in addition to the ghost number charge contains a generator associated with the Langrange multiplier sector. Whereas in the conformal gauge the latter is trivial, in the general case it acquires an anomaly on a curved world-sheet. We calculate the various world-sheet anomalies in different gauges and finally prove that the conformal anomaly, which determines the critical dimension of the string, as well as the sum of the ghost number and Lagrange multiplier anomalies are gauge independent. Furthermore, we comment upon possible ghost number current anomalies from fixing the κ-symmetry in the covariant quantization of the Green-Schwarz superstring.
Global aspects of the harmonic gauge in bosonic string theory
1988, Nuclear Physics, Section B
The standard expression for the measure on Teichmüller space for the bosonic string on higher genus Riemann surfaces is transformed into a new expression which is exactly the ratio of determinants of the Faddeev-Popov method in the harmonic gauge. The new formula for the measure is checked by explicit computation for the sphere and torus. The measure can be expressed as a functional integral over ghosts and associated fields which incorporate the global geometry of the world-sheet. Measures for these fields are complete measures including zero modes, and the symmetry associated with the latter is gauge-fixed.
A summary is given of a recently completed mathematical proof that a version of the harmonic gauge determines a globally defined slice in the space of metrics on Riemann surfaces of genus greater than one. Some clarification is given of the peculiar conformal properties of the harmonic gauge, namely the nonvanishing of the stress tensor component $T_{zZ}$ . As a pedagogical matter, the difference between the change of variables method conventionally used to obtain the string measure and the Faddeev-Popov method is clarified.
A local fermionic ghost number anomaly for the Kallosh quantization of the heterotic string
1988, Physics Letters B
We observe that the action for the Green-Schwarz heterotic string in the form given by Kallosh and Morozov has a local fermionic symmetry ghost number anomaly which does not appear in Carlip's form of the action. However, we point out, by analogy with the harmonic gauge bosonic string, that the gauge-independent total number anomaly associated with ghosts and gauge fixing is zero, so the anomaly is innocuous.
OSp(2,24) for open-string fields
1988, Physical Review D

^☆: This work is supported in part by funds provided by the US Department of Energy (DOE) under contract #DE-AC02-76ER03069.

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Sp(2) BRST invariant quantization of strings: The harmonic gauge☆

Abstract

Nucl. Phys.

Phys. Lett.

Nucl. Phys.

Nucl. Phys.

Phys. Lett.