Showing papers on "Topological string theory published in 1992"
01 Jan 1992
TL;DR: In this paper, the authors consider the application of large-N techniques in matrix models, that are used to simulate fluctuating triangulated surfaces, and make an effort to indicate some of the more startling interconnections.
Abstract: The last two years have seen the emergence of a beautiful new subject in mathematical physics. It manages to combine a most exotic range of disciplines: two-dimensional quantum field theory, intersection theory on the moduli space of Riemann surfaces, integrable hierarchies, matrix integrals, random surfaces, and many more. The common denominator of all these fields is two-dimensional quantum gravity or, more general, low-dimensional string theory. Here the application of large-N techniques in matrix models, that are used to simulate fluctuating triangulated surfaces [1]–[3], has led to complete solvability [4]–[8]. (See e.g. the review papers [9], and also the lectures of S. Shenker in this volume.) Shortly after the onset of the remarkable developments in matrix models, Edward Witten presented compelling evidence for a relationship between random surfaces and the algebraic topology of moduli space [10, 11]. This proposal involved a particular quantum field theory, known as topological gravity [12], whose properties were further established in [13, 14] and generalized to the so-called multi-matrix models in [15]–[19]. This subject can, among many other things, be considered as a fruitful application of quantum field theory techniques to a particular problem in pure mathematics, and as such is a prime example of a much bigger program, also largely due to Witten, that has been taking shape in recent years. It is impossible to do fully justice to this subject within the confines of these lecture notes. I will however make an effort to indicate some of the more startling interconnections.
141 citations
CERN1
TL;DR: In this paper, the exact underlying symmetry responsible for semiclassical duality is identified with the symmetry under affine Weyl transformations, which unifies the treatment of duality symmetries and shows that in the compact and unitary case, duality can survive as an exact symmetry.
Abstract: The duality symmetries of WZW and coset models are discussed. The exact underlying symmetry responsible for semiclassical duality is identified with the symmetry under affine Weyl transformations. This identification unifies the treatment of duality symmetries and shows that in the compact and unitary case they are exact symmetries of string theory to all orders in α' and in the string coupling constant. Non-compact WZW models and cosets are also discussed. A toy models is analyzed suggesting that duality can survive as an exact symmetry.
83 citations
TL;DR: In this paper, it was shown that N = 2 chiral (antichiral) multiplets lead to topological sigma models and N = two twisted chiral multiplets led to Landau-Ginzburg type topological quantum field theories.
81 citations
TL;DR: N=2 string amplitudes, when required to have the Lorentz covariance of the equivalent N=4 string, describe a self-dual form of N=3 super YangMills in 2+2 dimensions, a topological-like theory with vanishing loop corrections.
Abstract: N=2 string amplitudes, when required to have the Lorentz covariance of the equivalent N=4 string, describe a self-dual form of N=4 super YangMills in 2+2 dimensions. Spin-independent couplings and the ghost nature of SO(2,2) spacetime make it a topological-like theory with vanishing loop corrections.
70 citations
TL;DR: In this article, an effective target-space theory whose correlation functions are defined by the sum over connected Riemann surfaces of all genera is found to be itself topological, at least as long as the connectivity of the target space is kept fixed.
17 citations
Book•
01 Jan 1992
TL;DR: In this paper, the authors introduce topological and conformal field theory for string theory, and introduce a matrix model and a Liouville theory for topological string theory in 2 dimensions.
Abstract: Introduction to topological and conformal field theory, H.Verlinde introduction to matrix model and liouville theory, E.Martinec some properties of non-critical strings, D.Kutasov instantons and solitons in heterotic string theory, J.Harvey introduction to topological and conformal field theory, R.Dijkgraaf introduction to W Algebras, A.Bilal string theory in 2 dimensions, I.Klebanov instantons and solitons in heterotic string theory, C.Callan integrable models, L.D.Faddeev Liouville theory and its recent developments, L.Alvarez-Gaume target space duality symmetries and effective actions of string theory, D.Lust geometric structures in effective superstring lagrangians, P.Fre duality invariant effective action for supersymmetries, M.Porrati transition from critical to non-critical string at high temperatures, C.Kounnas correlation functions in compactified c=1 quantum gravity, I.Klebanov the origin of the string equation, C.Gomez quantization of Sl(2,R) Chern-Simons topological theory, C.Imbimbo string propagation in a black hole geometry, R.Dijkgraaf double scaling limit in the O(N) vector model, P.Di Vecchia singular vectors in virasoro representations, M.Bauer Schwinger-Dyson equations for 2-matrix model and Wa3 algebra, K.S.Narain O(N) vector model in the double scaling limit, J.Zinn-Justin.
16 citations
TL;DR: In this paper, the authors analyze topological string theory on a two-dimensional torus, focusing on symmetries in the matter sector, and find a nilpotent charge which behaves like a spacetime topological BRST operator.
14 citations
TL;DR: In this article, it was shown that critical and subcritical N = 2 string theory gives a realization of a superfield extension of the topological conformal algebra, and that the vanishing of the background ghost charge can be explained.
13 citations
TL;DR: In this paper, a topological Chern-Simons theory is considered as a specific model of a more general theory describing the quantum kinematics of coloured framed Plek ton s in R2.
Abstract: Chern-Simons theory is formulated quantum field theoretically in terms of string operators, which are localized on finite non-selfintersecting paths in the zero-time plane R2. It is shown how the Weyl algebra approach to the abelian Chern-Simons theory leads to a bundle theoretic construction of these ‘Chern-Simons string operators’. To proceed to the non-abelian case topological Chern-Simons theory is considered as a specific model of a more general theory describing the quantum kinematics of coloured framed Plek ton s inR2. This theory allows the construction of string operators as pair-creation operators, mapping n-Plekton states into (n+2)-Plekton states. Link invariants are obtained as vacuum correlation functions of string operators and obey a natural version of reflection positivity. The vacuum sector of such a purely kinematical Plekton theory may be recovered from the link invariants by Osterwalder-Schrader reconstruction. To make the theory work one needs the structures of a ribbon graph category, for which the representations of a quasi-triangular quasi-Hopf algebra may serve as a specific realization.
12 citations
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TL;DR: In this paper, the authors discuss the non-perturbative formulation for string theory and present a field theory-like formulation of topological and non-topological models, which explicitly obeys the duality of these theories.
Abstract: We discuss the non--perturbative formulation for $c \leq 1$ string theory. The field theory like formulation of topological and non--topological models is presented. The integral representation for arbitrary $(p,q)$ solutions is derived which explicitly obeys $p-q$ duality of these theories. The exact solutions to string equation and various examples are also discussed.
TL;DR: In this paper, the authors analyze topological string theory on a two-dimensional torus, focusing on symmetries in the matter sector, and find a nilpotent charge which behaves like a spacetime topological BRST operator.
Abstract: We analyze topological string theory on a two dimensional torus, focusing on symmetries in the matter sector. Even before coupling to gravity, the topological torus has an infinite number of point-like physical observables, which give rise via the BRST descent equations to an infinite symmetry algebra of the model. The point-like observables of ghost number zero form a topological ground ring, whose generators span a spacetime manifold; the symmetry algebra represents all (ground ring valued) diffeomorphisms of the spacetime. At nonzero ghost numbers, the topological ground ring is extended to a superring, the spacetime manifold becomes a supermanifold, and the symmetry algebra preserves a symplectic form on it. In a decompactified limit of cylindrical target topology, we find a nilpotent charge which behaves like a spacetime topological BRST operator. After coupling to topological gravity, this model might represent a topological phase of $c=1$ string theory. We also point out some analogies to two dimensional superstrings with the chiral GSO projection, and to string theory with $c=-2$.
TL;DR: In this article, the string model is formulated in terms of two-dimensional differential forms of arbitrary rank and the local supersymmetric string action with local conformal and Lorentz symmetries is constructed.
Abstract: The string model is formulated in terms of two-dimensional differential forms of arbitrary rank The local supersymmetric string action with local conformal and Lorentz symmetries is constructed The connection with topological quantum field theory is discussed Covariant quantization of the model is investigated The critical space-time dimension is found to bed=4
TL;DR: In this article, a symmetry principle based on a local version of topological BRST invariance was proposed to select gauge conditions appropriate for topological quantum field theories in supersymmetric quantum mechanics.
TL;DR: In this article, a formal relationship between scattering amplitudes in critical bosonic string theory and correlation functions of operators in topological string theory is found, and the relationship between the two types of properties is analyzed.
TL;DR: In this article, a topological field theory is constructed by twisting the N = 3 superconformal field theory, and the algebraic structure of the theory can be identified as that of an n = 3 topological superconforming theory.
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TL;DR: In this article, a brief overview of strings propagating on non-compact coset spaces G/H is presented in terms of WZW models, and the role played by isometries in the existence of target space duality and by fixed points of the gauge transformations in the presence of singularities and horizons is emphasized.
Abstract: A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauge transformations in the existence of singularities and horizons, is emphasized. A general classification of the spaces with a single time-like coordinate is presented. The spacetime geometry of a class of models, existing for every dimension and having cosmological and black hole-like interpretations, is discussed.
TL;DR: In this article, a homomorphism exists between the constraint algebras of TQFT and those of canonical gravity for 2+1 and 1+1 dimensional hypersurfaces.
Abstract: The constraints of $BF$ topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of Topological Quantum Field Theories (TQFT's). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for 2+1 and 1+1 dimensional space-times foliated as $M=\Sigma\times\IR$, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.
TL;DR: In this paper, the twisted version of the Wess-Zumino-Witten model was studied and the fixed points under BRST transformation were reduced to a simple topological field theory.
Abstract: We study the twisted version of the supersymmetric $G/T=SU(n)/U(1)^{\otimes(n-1)} gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological field theory, that is, the topological matter system in the K.Li's theory of 2 dimensional gravity for the case of $n=2$, and its generalization for $n \geq 3$.
TL;DR: In this article, it was shown that the generating function for self-avoiding paths is formally obtainable from a Witten topological field theory, even if the physical quantities for polymers are not the physical quantity in the BRST approach.
Abstract: We show that the generating function for self-avoiding paths is formally obtainable from a Witten topological field theory, even if the physical quantities for polymers are not the physical quantities in the BRST approach. We argue that in the dense phase the BRST invariance should generally be broken at the quantum level.
TL;DR: In this paper, a topological gauge theory in two dimensions with symmetry groups ISO(2, 1), SO( 2, 1) and SO(1, 2) is presented.
TL;DR: In this article, the duality symmetries of topological backgrounds with N = 2 backgrounds were shown to be symmetric with topological conformal field theories, and the topological string background is obtained from a "twisting" of an n = 2 superconformal field theory describing an ordinary background of the superstring.
Abstract: Target-space properties of string backgrounds corresponding to topological conformal field theories are discussed. The topological string background is obtained from a "twisting" of an N = 2 superconformal field theory describing an ordinary background of the superstring. Thus, we are able to relate the duality symmetries of topological backgrounds with N = 2 backgrounds.
TL;DR: In this article, an extended version of the topological Yang-Mills theory (ETYMT) is introduced and the properties of the ETYMT are discussed from standpoint of the covariant canonical quantization.
Abstract: Introducing infinite number of fields, we construct an extended version of the topological Yang-Mills theory. The properties of the extended topological Yang-Mills theory (ETYMT) are discussed from standpoint of the covariant canonical quantization. It is shown that the ETYMT becomes a cohomological topological field theory or a theory equivalent to a quantum Yang-Mills theory with anti-self-dual constraint according to subsidiary conditions imposed on state-vector space. On the basis of the ETYMT, we may understand a transition from an unbroken phase to a physical phase (broken phase)
TL;DR: In this article, the perturbative renormalizability of a previously proposed topological Lagrangian a la Witten and Fujikawa describing polymers was shown within the quantum action principle framework.
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TL;DR: In this article, a double-step picture changing operator for the non-critical NSR string is constructed and string amplitudes for D = 2 have poles corresponding to the n-level NS excitations with discrete momenta.
Abstract: String field theory for the non-critical NSR string is described. In particular it gives string field theory for the 2D super-gravity coupled to a $\hat{c}=1$ matter field. For this purpose double-step pictures changing operators for the non-critical NSR string are constructed. Analogues of the critical supersymmetry transformations are written for $D<10$, they form a closed on-shell algebra, however their action on vertices is defined only for discrete value of the Liouville momentum. For D=2 this means that spinor massless field has its superpartner in the NS sector only if its momentum is fixed.
Starting from string field theory we calculate string amplitudes. These amplitudes for D=2 have poles which are related with discrete set of primary fields, namely 2R$\to$2R amplitude has poles corresponding to the n-level NS excitations with discrete momenta $p_1=n,~~p_2=-1\pm (n+1)$.
TL;DR: In this article, the authors introduced an infinite number of fields which form a half-infinite chain representation of the BRST algebra and constructed an extended topological Yang-Mills theory.