Closed String Field Theory Research Articles

A note on gauge transformations in Batalin-Vilkovisky theory

We give a generally covariant description, in the sense of symplectic geometry, of gauge transformations in Batalin-Vilkovisky quantization. Gauge transformations exist not only at the classical level, but also at the quantum level, where they leave the action-weighted measure dμ s≡ dμ exp (2S/ ) ̵ invariant. The quantum gauge transformations and their Lie algebra are - ̵ deformations of the classical gauge transformation and their Lie algebra. The corresponding Lie brackets [ , ] q, and [ , ] c, are constructed in terms of the symplectic structure and the measure d μ s . We discuss closed string field theory as an application.

Batalin-Vilkoviski master equation and absence of anomakies in string field theory

We study the Batalin-Vilkovisky master equation for both open and closed string field theory with special attention to anomalies. Open string field theory is anomaly free once the minimal coupling to closed strings induced by loop amplitudes is considered. In closed string field theory the full-fledged master equation has to be solved order by order in perturbation theory. The existence of a solution implies the absence of anomalies. We briefly discuss the relation of the iterative process of solution to methods used in the first quantized formalism and comment on some possible nonperturbative corrections.

Manifestly covariant, gauge-invariant interacting closed-string field theory

We argue that Witten's covariant open-string field theory already implies its covariant closed-string field theory analog. The respective analog closedstring field theory is explicitly exhibited.

On string field theory and effective actions

A truncation of string field theory is compared with the duality invariant effective action of $D=4, N=4$ heterotic strings to cubic order. The three string vertex must satisfy a set of compatibility conditions. Any cyclic three string vertex is compatible with the $D=4, N=4$ effective field theory. The effective actions may be useful in understanding the non--polynomial structure and the underlying symmetry of covariant closed string field theory, and in addressing issues of background independence. We also discuss the effective action and string field theory of the $N=2$ string.

A star product in lattice gauge theory

We consider a variant of the cup product of simplicial cochains and its applications in discrete formulations of non-abelian gauge theory. The standard geometrical ingredients in the continuum theory all have natural analogues on a simplicial complex when this star product is used to translate the wedge product of differential forms. Although the star product is non-associative, it is graded-commutative, and the coboundary operator acts as a deviation on the star algebra. As such, it is reminiscent of the star product considered in some approaches to closed string field theory, and we discuss applications to the three dimensional non-abelian Chern-Simons theory.

On background-independent open-string field theory.

A framework for background independent open-string field theory is proposed. The approach involves using the BV formalism -- in a way suggested by recent developments in closed-string field theory -- to implicitly define a gauge invariant Lagrangian in a hypothetical ``space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are BRST invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator.

Dilaton Condensation in the Covariantized Light-Cone Closed String Field Theory

We analyze dilaton condensation in the covariantized light·cone closed string field theory. We show by explicit calculation that an infinitesimal condensation of the dilaton field gives rise to the shift of the string coupling constant 9 by an amount (Jg= -(Cd -2)/2)g, where d is the space-time dimension. This agrees with Yoneya's result obtained in the light-cone gauge string field theory. We also show that the direct effect of the dilaton condensation is interpreted as the Weyl-scaling of the full OSP(d -1,112) metric including the ghost direction also.

The finite gauge transformations in closed string field theory

The finite gauge transformations for the classical nonpolynomial closed string field theory are constructed by iteration of infinitesimal transformations. A simple rule for the determination of the coefficients of the arising series is found.

Soft Dilaton Theorem in String Field Theory

The soft dilaton theorem is derived in covariant and light-cone gauge closed string field theories. We have to take special care of the singularity of the diagrams where the zero-momentum dilaton is attached to one of the external on-shell lines

Dilaton Condensation in the Covariantized Light-Cone Closed String Field Theory

Dilaton Condensation in the Covariantized Light-Cone Closed String Field Theory

Introduction to SH Lie algebras for physicists

Closed string field theory leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures. It also appeared in work on higher spin particles \cite{BBvD}. Representation theoretic analogs arose in the mathematical analysis of the Batalin-Fradkin-Vilkovisky approach to constrained Hamiltonians. A major goal of this paper is to see the relevant formulas, especially in closed string field theory, as a generalization of those for a differential graded Lie algebra, hopefully describing the mathematical essentials in terms accessible to {\it physicists}.

Gauge and general coordinate invariance in non-polynomial closed string field theory

An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low-energy effective field theory. A set of string field theoretic symmetries that act on the fields in low-energy effective field theory as general coordinate transformation and antisymmetric tensor gauge transformation is identified. The analysis is carried out to first order in the fields; thus the symmetry transformations in string field theory reproduce the linear and the first non-linear terms in the gauge transformations in the low-energy effective field theory.

ACTION PRINCIPLE, VIRASORO STRUCTURE AND ANALYTICITY IN NONPERTURBATIVE TWO-DIMENSIONAL GRAVITY

The consequences of symmetry properties of a previously proposed action principle which describes the theory space of two-dimensional gravity are investigated. The string equation corresponding to the double scaling limit of the one-matrix model with general polynomial potential is expressed as a bilinear equation for the τ function of the KP hierarchy. The Virasoro condition for the τ function is then shown to be a Ward-like identity derived from the string equation corresponding to a conformal symmetry of the action principle. The possibility of a Ginzburg-Landau type integral representation of the τ function as a version of noncritical closed string field theory in less-than-one-dimensional space-time is discussed. Finally, the role of analyticity with respect to the eigenvalue of the puncture operator in interpreting the action principle is emphasized.

The polyakov path integral over bordered surfaces

The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework

A criterion for flatness in minimal area metrics that define string diagrams

It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2π. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yieds a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set,U if there is a unique closed curve of length 2π through every point inU and all of these closed curves are in the same free homotopy class.

Space-time versus world-sheet renormalization group equation in string theory

We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string.

Jacobi Identity Anomaly in Closed String Field Theory

Jacobi Identity Anomaly in Closed String Field Theory

Jacobi Identity Anomaly in Closed String Field Theory

The Jacobi identity, which is an indispensable property for gauge invariant closed string field theory, is apparently broken in cases where one of the four legs of the identity has vanishing string-length. This phenomenon contradicts the general proof of the identity valid at the critical dimension. We examine the general proof and clarify the mechanism of this Jacobi identity anomaly

Minimal area problems and quantum open strings

We discuss minimal area problems for surfaces with boundaries and both open and closed string punctures. We define open-closed string diagrams to be surfaces with metrics of minimal area under the condition that any nontrivial Jordan open curve be longer or equal to π and any nontrivial Jordan closed curve be longer or equal to 2π. It is proven that the double of an open-closed string diagram is a closed string diagram of covariant closed string field theory.

General covariance in pre-geometrical string field theory

We study the general coordinate transformation invariance of pre-geometrical string field theory (PGSFT), a closed string field theory described by a purely cubic action. General covariance is necessary if PGSFT is to be a formulation of string theory independent of the space-time background. The transformation of only the X μ (σ) coordinate cannot be a symmetry and we propose an improved transformation changing also the FP-ghost coordinate. We find that PGSFT has general covariance at least for (infinitesimal) coordinate change δ× μ = Ξ μ ( x) which is a polynomial in x μ .