Showing papers on "Topological string theory published in 1994"
TL;DR: In this paper, the authors developed techniques to compute higher loop string amplitudes for twisted N = 2 theories with ε = 3 (i.e. the critical case) by exploiting the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured by a master anomaly equation.
Abstract: We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the ‘number’ of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.
1,633 citations
TL;DR: In this article, it was shown that certain type II string amplitudes at genus g are given by the topological partition function Fg discussed recently by Bershadsky, Cecotti, Ooguri and Vafa.
443 citations
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TL;DR: In this article, the relationship between the classical description of the resolution of quotient singularities and the string picture is reviewed in the context of N=(2,2) superconformal field theories.
Abstract: In this paper the relationship between the classical description of the resolution of quotient singularities and the string picture is reviewed in the context of N=(2,2) superconformal field theories. A method for the analysis of quotients locally of the form C^d/G where G is abelian is presented. Methods derived from mirror symmetry are used to study the moduli space of the blowing-up process. The case C^2/Z_n is analyzed explicitly. This is largely a review paper to appear in "Essays on Mirror Manifolds, II".
122 citations
TL;DR: In this paper, it was shown that topological string theory is the derived functor of semi-relative cohomology, just as equivariant cohology is derived functor of basic cohology, and that homological algebra finds a place in the study of topologically string theory should not surprise the reader.
Abstract: The analogy between topological string theory and equivariant cohomology for differentiable actions of the circle group on manifolds has been widely remarked on. One of our aims in this paper is to make this analogy precise. We show that topological string theory is the “derived functor” of semi-relative cohomology, just as equivariant cohomology is the derived functor of basic cohomology. That homological algebra finds a place in the study of topological string theory should not surprise the reader, granted that topological string theory is the conformal field theorist's algebraic topology.
109 citations
TL;DR: In this paper, the authors prove local background independence of the complete quantum closed-string field theory using the recursion relations for string vertices and the existence of connections in CFT theory space.
90 citations
TL;DR: In this article, a topological Landau-Ginzburg model with superpotential W ( X ) = X −1 was studied and the role of gravitational descendants in this theory was examined.
62 citations
TL;DR: It is presented some evidence that topological minimal models associated with Lie algebras other than the A-D-E type do not have a consistent higher genus expansion beyond genus one.
Abstract: A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the free energy in the $A_1$ and $A_2$ models. We present some evidence that topological minimal models associated with Lie algebras other than the A-D-E type do not have a consistent higher genus expansion beyond genus one. We also present some new results on the $CP^1$ model at higher genera.
61 citations
TL;DR: In this article, the authors construct a topological Landau-Ginzburg formulation of the two-dimensional string at the self-dual radius and derive relations formally analogous to the string equation.
Abstract: We construct a topological Landau-Ginzburg formulation of the two-dimensional string at the self-dual radius. The model is an analytic continuation of the $A_{k+1}$ minimal model to $k=-3$. We compute the superpotential and calculate tachyon correlators in the Landau-Ginzburg framework. The results are in complete agreement with matrix model calculations. We identify the momentum one tachyon as the puncture operator, non-negative momentum tachyons as primary fields, and negative momentum ones as descendants. The model thus has an infinite number of primary fields, and the topological metric vanishes on the small phase space when restricted to these. We find a parity invariant multi-contact algebra with irreducible contact terms of arbitrarily large number of fields. The formulation of this Landau-Ginzburg description in terms of period integrals coincides with the genus zero $W_{1+\infty}$ identities of two-dimensional string theory. We study the underlying Toda lattice integrable hierarchy in the Lax formulation and find that the Landau-Ginzburg superpotential coincides with a derivative of the Baker-Akhiezer wave function in the dispersionless limit. This establishes a connection between the topological and integrable structures. Guided by this connection we derive relations formally analogous to the string equation.
54 citations
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TL;DR: In this paper, the Chern-Simons-Witten theory quantized on a torus as a free fermion system was reinterpreted as a classical string field theory.
Abstract: We reinterpret U(N) Chern-Simons-Witten theory quantized on a torus as a free fermion system Its Hilbert space and some observables are simply related to those of group quantum mechanics, even at finite N and k Its large N limit can be described using techniques developed for matrix quantum mechanics and two-dimensional Yang-Mills theory We discuss the bosonization of this theory, which for YM_2 gave a precise interpretation of Wilson loop operators in terms of string creation and annihilation operators, and examine its consequences for a string interpretation here The formalism seems entirely adequate for the leading large N results and in a sense can be thought of as a `classical string field theory' In considering subleading orders in 1/N, we identify some major differences between CSW and YM_2, which must be dealt with to find a CSW gauge string interpretation Although these particular differences are probably not relevant for `QCD string,' they do illustrate some of the issues there, and we comment on this We also propose an approach to dealing with large N transitions
48 citations
TL;DR: In this paper, the dependence of the gauge couplings on the dilation field in string effective theories at the one-loop level was investigated and it was shown that the analogue lagrangian with the dilaton in a linear multiplet naturally gives the correct answer.
43 citations
TL;DR: In this article, a generalization of topological sigma models suitable for coupling to topological open strings is presented, where the targets are Kahler manifolds with a real structure, compatible with the Kahler metric.
TL;DR: In this article, the algebraic BRS renormalization of Witten's topological Yang-Mills field theory was revisited by making use of a vector supersymmetry Ward identity which improves the finiteness properties of the model.
TL;DR: The N = 2 holomorphic Yang-Mills theory on compact Kahler manifolds has been studied in this article, where it is shown that intersection parings on the moduli space of Einstein-hermitianconnections can be determined by examining the small-coupling behavior of the N =2 holomorphic YMM theory.
TL;DR: In this article, the moduli space of N = 2 superconformal field theories is reviewed and a review of recent work which has significantly honed the geometric understanding and interpretation of the modulus space of certain N=2 superconforming field theories are presented.
Abstract: Recent work which has significantly honed the geometric understanding and interpretation of the moduli space of certain N=2 superconformal field theories is reviewed. This has resolved some important issues in mirror symmetry and has also established that string theory admits physically smooth processes which can result in a change in topology of the spatial universe. Recent work which illuminates some properties of physically related theories associated with singular spaces such as orbifolds is described.
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TL;DR: In this article, string backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory.
Abstract: String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and topological gravity are studied. For each field theory, an algebraic counterpart, the (homotopy) algebra satisfied by the tree level correlators, is constructed.
TL;DR: In this article, it was shown that if the momenta belong to an integral lattice, then every physical state of string theory leads to a symmetry of the scattering amplitudes.
Abstract: It is shown that if the momenta belong to an integral lattice, then every physical state of string theory leads to a symmetry of the scattering amplitudes. We discuss the role of this symmetry when the momenta are those provided by the usual D.D.F construction and show that the string compactified on the torus associated with the self-dual Lorentzian lattice, $\Pi^{25,1}$ possess the Fake Monster Lie algebra as a symmetry.
TL;DR: In this article, the B-twisted topological sigma model is represented as a particle theory, obtained by reducing the Sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity.
Abstract: The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a PARTICLE theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on ANY Kahler manifold--it does not require the Calabi-Yau condition--so it may provide a more generalized setting for the B model than the topological sigma model. The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, and agrees with that of the original B model. After showing how to deform the Kahler and complex structures in the particle, we prove the independence of this partition function on the Kahler structure, and investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories.
TL;DR: In this paper, a topological theory which contains explicitly Kodaira-Spencer deformation theory was proposed, and it was shown that three-point correlation functions give the Yakawa couplings for a generic point in the moduli space of complex structures.
TL;DR: In this article, new relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space; and they are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations.
Abstract: New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined with the dilaton equation and the ghost number conservation, the equation for the first chern class of the target space gives a constraint on the topological sum (over genera and (multi-)degrees) of partition functions. For the $\CP^1$ model, it coincides with the dilatation constraint which is derivable in the matrix model recently introduced by Eguchi and Yang.
TL;DR: In this article, the authors analyzed the spacetime symmetries of topological string theory on a two-dimensional torus, and pointed out that the topological BRST geometry of the model is that of the Batalin-Vilkovisky formalism.
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TL;DR: In this article, the authors studied the $c=1$ string theory from the point of view of topological field theories, and a change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed matrix model.
Abstract: In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed matrix model. It is proposed that the deformed matrix model is related to a D-series Landau-Ginzburg superpotential.
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TL;DR: Some aspects of mirror symmetry are reviewed in this paper, with an emphasis on more recent results extending mirror transform to higher genus Riemann surfaces and its relation to the Kodaira-Spencer theory of gravity.
Abstract: Some aspects of Mirror symmetry are reviewed, with an emphasis on more recent results extending mirror transform to higher genus Riemann surfaces and its relation to the Kodaira-Spencer theory of gravity (talk given in the Geometry and Topology Conference, April 93, Harvard, in honor of Raoul Bott)
TL;DR: In this article, the relation between topological string theory and singularity theory using the partition function of the AN−1 topology string defined by a matrix integral of Kontsevich type is studied.
01 Jan 1994
TL;DR: In this article, the authors give a review of the application of perturbative techniques to topologi-cal quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations.
Abstract: We give a review of the application of perturbative techniques to topologi-cal quantum eld theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
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TL;DR: The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet as discussed by the authors, and it is shown that independence of a metric in quantum mechanical amplitudes implies that the dependence on such vector density zeroes is purely topological.
Abstract: The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization allows for the definition of several, possibly inequivalent quantum theories. String amplitudes are constructed from vector densities with zeroes for each in- or out-going string. It is shown that independence of a metric in quantum mechanical amplitudes implies that the dependence on such vector density zeroes is purely topological. For example, there is no need for integration over their world-sheet positions.
TL;DR: In this paper, the moduli space constraint is introduced as a gauge fixing in the N = 2 Liouville model of constrained topological gravity, which is a generalization of the BRST algebra.
TL;DR: In this paper, the authors consider the continuum string theory corresponding to the Marinari-Parisi supersymmetric matrix model and argue that the world-sheet physics is exotic, and different from any known supersymetric string theory.
Abstract: We consider the continuum string theory corresponding to the Marinari-Parisi supersymmetric matrix model. We argue that the world-sheet physics is exotic, and different from any known supersymmetric string theory. The embedding superspace coordinates become disordered on the world-sheet, but because of the noncompactness of the embedding time the disorder becomes complete only at asymptotic world-sheet scales.
01 Aug 1994
TL;DR: In this article, the exact results for two-dimensional N=2 Supersymmetric Theories are given, and a string project in multicolour QCD is described. But the results are limited to a single dimension.
Abstract: Exact Results for Two-Dimensional N=2 Supersymmetric Theories, S. Cecotti Developments in 2D String Theory, A. Jevicki A String Project in Multicolour QCD, V. Kazakov Matrix Models and String Theory, I. Klebanov Black Hole Evaporation and Quantum Gravity, H. Verlinde Barriers in Quantum Gravity, J. Ambjorn Two-Dimensional Black Hole and Nonperturbative String Theory, A. Dhar U(N) Gauge Theory and Lattice Strings, I. Kostov Applications of 0(d,d) Transformations to Generate New Geometries, J. Maharana Quantization of Mirror Symmetry, H. Ooguri W-Strings 93, C. Pope and other papers.
01 Jan 1994
TL;DR: In this article, the exact results for two-dimensional N=2 Supersymmetric Theories are given, and a string project in multicolour QCD is described. But the results are limited to a single dimension.
Abstract: Exact Results for Two-Dimensional N=2 Supersymmetric Theories, S. Cecotti Developments in 2D String Theory, A. Jevicki A String Project in Multicolour QCD, V. Kazakov Matrix Models and String Theory, I. Klebanov Black Hole Evaporation and Quantum Gravity, H. Verlinde Barriers in Quantum Gravity, J. Ambjorn Two-Dimensional Black Hole and Nonperturbative String Theory, A. Dhar U(N) Gauge Theory and Lattice Strings, I. Kostov Applications of 0(d,d) Transformations to Generate New Geometries, J. Maharana Quantization of Mirror Symmetry, H. Ooguri W-Strings 93, C. Pope and other papers.
CERN1
TL;DR: In this article, the special geometry for twisted $N=2$ strings is derived as consistency conditions of a new contact term algebra, where the dilaton appears in the contact terms of topological and antitopological operators.
Abstract: The special geometry ($(t,{\bar t})$-equations) for twisted $N=2$ strings are derived as consistency conditions of a new contact term algebra. The dilaton appears in the contact terms of topological and antitopological operators. The holomorphic anomaly, which can be interpreted as measuring the background dependence, is obtained from the contact algebra relations.