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We construct a toy model of Witten's open string field theory by truncating the Virasoro group to its SU(1,1) subgroup. The string field is given in terms of finite-dimensional matrices, which satisfy a non-trivial BRST cohomology. The string gauge group is found to be SO(3). Finally, we perform the gauge fixing of the action, finding an explicit formula for calculating the partition function.  相似文献   

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A unitary field transformation useful for examination of the BRST-symmetries in free bosonic open-string field theory is introduced. It is similar to Siegel and Zwiebach's transformation, but leads to a hermitian BRST-charge in contrast to theirs. The transformed BRST-transformation factorizes into two parts, making the gauge-unfixing procedure rather trivial. Both the minimal-type gauge-invariant action and Witten's action are dealt with.  相似文献   

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《Nuclear Physics B》1986,276(2):325-338
We discuss the gauge-fixing procedure of the covariant formulation of the open bosonic string recently proposed by Neveu, Nicolai and West (the so-called finite set). We show that this theory has new symmetries. However, it does not seem possible to recover the correct number of physical degrees of freedom.  相似文献   

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A differential-geometric approach to the closed Bose-string field theory is developed in a framework where the Lorentz and reparametrisation invariances are manifest. The Virasoro anomaly in the quantum theory is cancelled by the minimal introduction of the conformal mode, extending the usual string functionals defined on the space of embeddings. An action is written down, and this approach to strings is compared with the second-quantised formalism for the single particle.  相似文献   

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《Nuclear Physics B》1988,296(1):220-252
The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, Kn symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the Kn symmetries which are local in spacetime, are presented.  相似文献   

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Using conformal mapping techniques, we obtain a new BRST invariant operator ϒ encoding in closed form transition amplitudes between open strings and closed strings. The residues of the closed string poles in the non-planar one-loop two-point diagram of Witten's string field theory are finite sums of products of these amplitudes.  相似文献   

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《Nuclear Physics B》1988,303(2):305-328
Conformal field theory techniques are used to analyze a recently proposed transformation of Witten's interaction vertex from center-of-mass to mid-point variables. As presented in the literature the transformed vertex has the surprising property of being non-local in the mid-point coordinates unless an additional non-unitary transformation is performed. This renders the kinetic term non-local and poses additional problems. Here we show that, besides being non-local, the transformed vertex does not satisfy the overlap equations and fails to be BRST invariant. These bad properties are the result of an associativity anomaly of the type considered by Horowitz and Strominger. However, this anomaly is “almost trivial” in the sense that most of its bad effects can be avoided by choosing a proper regularization.  相似文献   

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《Physics letters. [Part B]》1987,195(4):541-546
Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.  相似文献   

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《Nuclear Physics B》1986,278(1):91-120
The covariant perturbation theory rules that should arise from any gauge invariant string field theory, such as those proposed on the basis of BRST formalism, are set forth. The resulting path integral expressions naturally produce coordinate invariant densities on the moduli space of Riemann surfaces; these include the Koba-Nielsen amplitudes. The connection between string field theory and modular invariance is discussed, and it is proposed that future explorations in string field theory focus on coordinate invariant quantities on moduli space.  相似文献   

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A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.  相似文献   

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《Nuclear Physics B》1986,268(2):253-294
An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action, whose linearized approximation reproduces the conventional Veneziano spectrum. A derivation of conventional Veneziano model amplitudes from this gauge invariant action is sketched. Some brief comments are made about attempts to extend these results to open superstrings and to closed strings.  相似文献   

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The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a gauge-invariant string field action around non-conformal backgrounds. The construction makes no reference to any conformal theory. Its two-dimensional field-theoretic aspect is based on a generalized BRST operator satisfying a set of Weyl descent equations. Its geometric aspect uses a complex of moduli spaces of two-dimensional Riemannian manifolds having ordinary punctures, and organized by the number of special punctures which goes from zero to infinity. In this complex there is a Batalin-Vilkovisky algebra that includes naturally the operator which adds one special puncture. We obtain a classical field equation that appears to relax the condition of conformal invariance usually taken to define classical string backgrounds.  相似文献   

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