Showing papers on "Topological string theory published in 1991"
19 Dec 1991
TL;DR: In this article, the mirror manifold problem is explained from the point of view of topological field theory, which can be naturally understood from the perspective of the mirror map between mirror moduli spaces.
Abstract: These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.
687 citations
TL;DR: In this article, it was shown that a natural representation of the string field theory is that of free, two-dimensional Dirac fermions, and the higher-order contributions to the correlation functions of the observables arise from translationally non-invariant corrections to the fermion kinetic energy.
119 citations
TL;DR: In this article, the authors calculate spherical N point correlation functions in string theories with c⩽1, where the amplitudes are given by two dimensional integrals, which are computed in their domain of convergence in momentum space.
109 citations
TL;DR: In this article, an operator formulation of the string field theory proposed by E. Witten using half-string oscillator modes is presented, where the physical string states are identified as infinite matrices and interactions at the level of vertices can be calculated in terms of products and traces of these matrices without relying on ill-defined manipulations of functional integrals.
50 citations
TL;DR: In this article, it was shown that Mumford invariants of moduli spaces of curves are obtainable from a gauge fixed action of a topological quantum field theory in two dimensions.
Abstract: We show that invariants of Mumford for moduli spaces of curves are obtainable from a gauge fixed action of a topological quantum field theory in two dimensions. The method is completely analogous to the relation of Donaldson invariants with the topological quantum field theory for gauge theories in four dimensions.
45 citations
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TL;DR: In this paper, the importance of loop spaces for a deeper understanding of the geometrical origin of duality in string theory is discussed, and mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: topological sigma models and topological Landau-Ginzburg models.
Abstract: Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: Topological sigma models and topological Landau-Ginzburg models. Some suggestions are made for generalization of the notion of mirror symmetry.
40 citations
TL;DR: In this paper, the status of the program to reformulate string theory as a theory of topological fields and gravity in 3D space is discussed, and the authors discuss the current status of their work.
Abstract: We discuss the status of the program to reformulate string theory as a theory of topological fields and gravity in 3 dimensions.
24 citations
TL;DR: It is shown that the theory of Witten's string field theory is shown to coincide with the one which is expected in the formal Lagrangian path-integral quantization that has been conventionally used.
Abstract: We quantize Witten's string field theory by regarding the light-cone component of the midpoint of the string as time. In this formalism, the string interaction is represented as a local interaction, and one can apply the canonical quantization procedure. The kinetic term of the string field theory does not have the divergent coefficient which appeared in previous works. A path integral with respect to canonical momenta in phase space can be performed. The theory is shown to coincide with the one which is expected in the formal Lagrangian path-integral quantization that has been conventionally used
17 citations
TL;DR: It is shown that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in terms of three-dimensional physics.
Abstract: It is known that much of the structure of string theory can be derived from three-dimensional topological field theory and gravity. We show here that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in terms of three-dimensional physics.
TL;DR: In this paper, the Nambu-Goto theory in D = 2 dimensions is canonically transformed to study topological aspects of the theory using the Batalin-Fradkin-Vilkovisky formalism, and it is shown that the transformed theory is related to various topological theories in two dimensions including topological gravity.
TL;DR: In this paper, a three-dimensional topological field theory of the Witten type is constructed, which consists of an SU (2) gauge field and a Higgs field giving rise to monopole sectors.
CERN1
TL;DR: In this paper, a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group is defined in terms of intersection theory on the moduli space of flat connections on a 2-dimensional surface.
TL;DR: In this paper, it was shown that Donaldson polynomials are nonzero only when supersymmetry is unbroken and their nontriviality is due to the anomaly of charge U.
TL;DR: In this article, the classical theory of a topological model which is constructed by setting the kinetic term of a (one-dimensional) sigma model at the classical level equal to zero is examined.
Abstract: The classical theory of a topological model which is constructed by setting the kinetic term of a (one-dimensional) sigma model at the classical level equal to zero is examined. The constraints and the geometry of the phase space of the supersymmetric extensions of the topological theory are studied. The rigid symmetries of a (supersymmetric) sigma model and its corresponding topological theory are gauged. Finally, the author examines the quantum theory of the one-dimensional sigma model in the limit where its kinetic term is set equal to zero and compare it with the quantum theory of the corresponding topological model.
TL;DR: In this paper, a recursion relation of the S -matrix for the open bosonic string was derived from a constraint equation analogous to the Virasoro constraints of the τ-function in the matrix model or topological gravity.
TL;DR: In this article, the authors examined the quantization of a topological sigma model in 2D superspace with a 2D flat target manifold and showed that the topological supergravity is obtained as the quantum theory by taking the superdiffeomorphism invariance into account.
Abstract: We examined the quantization of a topological sigma model in 2D superspace with a 2D flat target manifold It is shown that the topological supergravity is obtained as the quantum theory by taking the superdiffeomorphism invariance into account We also discuss the global (twisted) supersymmetries realized in the quantum theory
TL;DR: In this paper, the one-loop β-function is computed for topological sigma models, and the theory is finite with vanishing β function for supersymmetric quantum mechanics.
Abstract: The one-loop β-function is computed for topological sigma models. By gauge fixing the topological shift symmetry in the delta-function gauge, we find that the theory is finite with vanishing β-function. A similar result is shown to hold for supersymmetric quantum mechanics.
TL;DR: In this article, the BRST quantization of zero-dimensional string theory was studied by using Singer's observation of a SL(2, R ) gauge symmetry, and it was shown that the partition function does not reduce to a product of ratios of determinants for n>2.
TL;DR: In this paper, it is shown that 2D topological models can be interpreted as non-critical strings with some unusual BRST structure, and a possible correspondence with the series of multi-critical points of the one-matrix model.
TL;DR: In this article, the general coordinate transformation invariance of pre-geometrical string field theory (PGSFT) was studied and an improved FP-ghost coordinate transformation was proposed.
01 Jan 1991
TL;DR: Based on the target space modular invariance of the nonperturbative superpotential of the four-dimensional N=1 supersymmetric string vacua, topologically stable stringy domain walls are found.
Abstract: We point out that the moduli sector of the $(2,2)$ string compactification with its nonperturbatively preserved non-compact symmetries is a fertile framework to study global topological defects, thus providing a natural source for the large scale structure formation. Based on the target space modular invariance of the nonperturbative superpotential of the four-dimensional N=1 supersymmetric string vacua, topologically stable stringy domain walls are found. They are supersymmetric solutions, thus saturating the Bogomolnyi bound. It is also shown that there are moduli sectors that allow for the global monopole-type and texture-type configurations whose radial stability is ensured by higher derivative terms.