Showing papers on "Topological string theory published in 1990"
01 Nov 1990
TL;DR: In this article, a review of topological string theory is given, where the authors describe the symmetries and properties of the physical amplitudes of the topological field theory and derive the Schwinger-Dyson equations in recursion relations between world-sheet correlation functions at different genera.
Abstract: In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera. ∗Based on lectures presented at the Spring School on Strings and Quantum Gravity, Trieste, April 24 – May 2, 1990 and the Cargése Workshop on Random Surfaces, Quantum Gravity and Strings, May 28 – June 1, 1990.
202 citations
TL;DR: One-loop corrections to topological field theory in three and four dimensions are presented in this article, where the authors compute the effective action and β-function in four-dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved.
103 citations
01 Jun 1990
TL;DR: In this paper, a simple non-abelian C-S theory of spin is described and its canonical quantization on nontrivial Riemann surfaces leads to a system with finite number of degrees of freedom.
Abstract: The outline of this review is as follows. In Section II a simple non-abelian C-S theory is described. It is the quantum mechanical theory of spin and it serves as an illustrative example for quantization of systems with finite phase space. In Section III general non-abelian Chern-Simons theories are discussed. It is shown how their canonical quantization on nontrivial Riemann surfaces leads to a system with finite number of degrees of freedom. The connection with conformal field theory is then explained using the abelian example. Implications to knot theory and quantum gravity are then discussed in Section IV. (orig.).
45 citations
37 citations
Journal Article•
TL;DR: In this paper, the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory is explained. But the main aim is to clearly explain how this Hamiltonian arises from the formulation of Morse theory as applied by Floer to the inifinite dimensional space of gauge connections.
Abstract: In these lecture notes we give a «historical» introduction to topological gauge theories. Our main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. We show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the inifinite dimensional space of gauge connections, with the Chern-Simons functional as the appropriate Morse function(al)
19 citations
TL;DR: In this paper, the authors examined two methods of fixing the gauge symmetry in Witten's topological Yang-Mills theory and found that both procedures produce the same nontrivial correlation functions.
Abstract: We examine two methods of fixing the gauge symmetry in Witten’s topological Yang-Mills theory. We find that both procedures produce the same nontrivial correlation functions. Our results also apply to other topological field theories, such as topological gravity.
16 citations
TL;DR: It is shown how to construct a topological quantum field theory which corresponds to a given moduli space and its relations with the Chern-Simons theory and conformal field theory are discussed.
Abstract: We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. Geometrical properties are invoked to prove that the observables of those theories are not trivial. The case of the SO(2,1) group is separately discussed. A topological field theory is linked to the moduli space of self-dual'' connections over Riemann surfaces. Another relation between the Chern-Simons theory and topological quantum field theory in three dimensions is established. We present the theory which corresponds to three-dimensional gravity. Expressions for the Casson invariants are given. Possible generalizations are briefly discussed.
15 citations
TL;DR: In this article, a topological invariant version of two-dimensional Landau-Ginzburg field theory is constructed, which turns out to describe the topological phase of N = 2 superconformal field theory.
10 citations
TL;DR: In this article, a field theoretical discussion of the complex constructed by Floer in order to prove the Arnold conjecture concerning a Morse theory for the fixed point set of diffeomorphisms of a symplectic manifold is offered.
9 citations
01 Jan 1990
TL;DR: The Atiyah-Singer index theorem has an extremely simple rewriting in terms of quantum mechanics language as discussed by the authors, which leads naturally to extensions of this theorem to infinite dimensional spaces, namely the space of loops of any given compact closed manifold.
Abstract: These lectures are concerned with index theorems as seen from the point of view of field theory: not with the various uses of index theorems in field and string theory —like the study of anomalies—, but merely with the use of supersymmetric quantum field theory to prove (or maybe more accurately to derive) index theorems. Of course we are eventually more interested by the physical consequences of the theorems than by their proofs, but I would like to convince you that in the process of understanding the structure of physical theories —in this case field and string theories— one often recovers deep mathematical results and sometimes discovers exciting new ones. As we will see it is quite remarkable that one of the most profound result of the last twenty years in mathematics, the Atiyah-Singer index theorem [1][2], has an extremely simple rewriting in terms of quantum mechanics language. But perhaps the most surprising fact is that the field theoretical approach leads naturally to extensions of this theorem to infinite dimensional spaces, namely the space of loops of any given compact closed manifold. In fact the story I will try to present has three very different versions and I am going to concentrate mainly on one of them which stems from the study of the Dirac-Ramond operator introduced long time ago in the study of string theory (see for example [3]). This operator is the generalization to loop space of the Dirac operator and we are going to compute its index just as easily as one computes the index of the Dirac operator [4,5,6,7,8,9]. The second version of the story, due to Schellekens and Warner [10][11], came independently from the study of a generating function for all the field theory anomalies coming from string theory.
7 citations
TL;DR: In this article, a two-dimensional topological field theory for non-abelian Higgs vortices was constructed and discussed relevant features of the resulting BRST quantized theory and also discussed topological invariants.
TL;DR: In this article, the β-function in Witten's 4-dimensional topological Yang-Mills theory was calculated using the heat kernel method, and the β function was shown to be the same as that of Witten.
Abstract: We calculate the β-function in Witten's 4-dimensional topological Yang-Mills theory, using the heat kernel method.
01 Jan 1990
TL;DR: In this paper, the relationship between path integrals, geometric quantization and representation theory for a simple quantum theory whose Hilbert space is a group representation is discussed, and the relation to recent work of Witten on Chern-Simons gauge theory is also discussed.
Abstract: We discuss the relationship between path integrals, geometric quantization and representation theory for a simple quantum theory whose Hilbert space is a group representation. The path integrals involved have interesting cohomological significance and can be evaluated in terms of fixed point formulas to give the Kirillov and Weyl character formulas. The relation to recent work of Witten on Chern-Simons gauge theory is also discussed.
TL;DR: In this article, the authors investigated 2D quantum gravity in the conventional formalism of conformal field theory (CFT) and showed that the value c=−2 seems distinguished in such a continual theory, just as it does in the lattice and topological approaches to 2D gravity.
TL;DR: In this paper, the possible existence of a stable nontopological string configuration and its gravitational field is discussed in the weak-field limit, and a simple-model topological string case is considered.
Abstract: Gravitational fields of string configurations are discussed in the weak-field limit. After reviewing the simple-model topological string case, the electric-current-carrying string case is considered. The possible existence of a stable nontopological string configuration and its gravitational field is also discussed.
TL;DR: It is shown that loop wave equations in non-Abelian Chern-Simons gauge theory are exactly solved by a conformally invariant topological fermionic string theory.
Abstract: We show that loop wave equations in non-Abelian Chern-Simons gauge theory are exactly solved by a conformally invariant topological fermionic string theory.
TL;DR: In this article, the authors carried out canonical quantization of Witten's string field theory in the mid-point time formalism, where a divergence which arises in kinetic term can be regularized by discretizing the string.
01 Jan 1990
TL;DR: In this paper, the authors discuss topological quantum field theories related to the Donaldson theory of four manifolds through dimensional reduction, which leads to theories of instantons, magnetic monopoles, vortices as well as other theories.
Abstract: We discuss Topological Quantum Field Theories related to the Donaldson theory of four manifolds through dimensional reduction. This leads to theories of instantons, magnetic monopoles, vortices as well as other theories. Stochastic quantization offers a unifying picture of relating theories differing in one dimension. We show how the different topological field theories offer different perspectives on knot theory. Finally, a four-dimenensional picture of surfaces in four dimensions is proposed as a four manifold viewpoint on knot theory.
TL;DR: In this paper, the consequences of local supersymmetry in topological field theories are investigated, and it is shown how the Q - symmetry is naturally realized in superspace, and the geometrical nature of topological gravities is revealed.
TL;DR: In this article, the number of the topological degrees of freedom is calculated by using the world sheet instanton action, and it is shown that the topology quantum field may be the unbroken phase of string theory.
Abstract: The number of the topological degrees of freedom is calculated by using the world sheet instanton action. The result has shown that the topology quantum field may be the unbroken phase of string theory.
TL;DR: In this paper, the authors show that the scale invariance is equivalent to the condition of Weyl invariance for two-dimensional string field equations with a gauge symmetry, which is an extension of Wilson's renormalization group equation.