Showing papers on "Topological string theory published in 2001"

Fluxbranes in String Theory

Abstract: A flux p-brane in D dimensions has (p+1)-dimensional Poincare invariance and a nonzero rank (D-p-1) field strength tangent to the transverse dimensions. We find a family of such solutions in string theory and M-theory and investigate their properties.

Polynomial invariants for torus knots and topological strings

Abstract: We make a precision test of a recently proposed conjecture relating Chern–Simons gauge theory to topological string theory on the resolution of the conifold First, we develop a systematic procedure to extract string amplitudes from vacuum expectation values (vevs) of Wilson loops in Chern–Simons gauge theory, and then we evaluate these vevs in arbitrary irreducible representations of SU(N) for torus knots We find complete agreement with the predictions derived from the target space interpretation of the string amplitudes We also show that the structure of the free energy of topological open string theory gives further constraints on the Chern–Simons vevs Our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems

Split string field theory II

Abstract: We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string functionals. These BRST operators were postulated by Rastelli, Sen, and Zwiebach to give a description of cubic string field theory in the closed string vacuum arising from condensation of a D25-brane in the original tachyonic theory. We find a class of solutions for the ghost equations of motion using the pure ghost BRST operators. We find a vanishing action for these solutions, and discuss possible interpretations of this result. The form of the solutions we find in the pure ghost theory suggests an analogous class of solutions in the original theory on the D25-brane with BRST operator QB coupling the matter and ghost sectors.

N=1 mirror symmetry and open / closed string duality

Abstract: We show that the exact N = 1 superpotential of a class of 4d string compactications is computed by the closed topological string compactied to two dimensions. A relation to the open topological string is used to dene a special geometry for N = 1 mirror symmetry. Flat coordinates, an N = 1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of dierential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov{Witten invariants of one Calabi{Yau geometry with the open string invariants of the dual Calabi{Yau .

Open string Gromov-Witten invariants: Calculations and a mirror 'theorem'

Abstract: We propose localization techniques for computing Gromov-WitteninvariantsofmapsfromRiemannsurfaceswith boundariesintoaCalabi-Yau, with the boundaries mapped to a Lagrangian submanifold. Thecomputations can be expressed in terms of Gromov-Witten invariantsof one-pointed maps. In genus zero, an equivariant version of the mir-ror theorem allows us to write down a hypergeometric series, whichtogether with a mirror map allows one to compute the invariants to allorders, similar to the closed string model or the physics approach viamirror symmetry. In the noncompact example where the Calabi-Yau isK P 2 ,our results agree with physics predictions at genus zero obtainedusing mirror symmetry for open strings. At higher genera, our resultssatisfy strong integrality checks conjectured from physics. 1 Introduction 1.1 The Physics Mirror symmetry is famous for being able to predict Gromov-Witten invari-ants of Calabi-Yau manifolds. The basic conjecture is that there is a dualitybetween string theories on mirror Calabi-Yau manifolds. As a consequence,the topological field theory defined from the A-twist of one Calabi-Yau man-ifold is equal to the topological B-twist of the mirror. Both twists can beperformed on Calabi-Yau target manifolds. From a practical point of view,in order to obtain enumerative predictions, one needs to know the theoryon the B-model (in this case, defined through classical period integrals) aswell as an identification of the parameter spaces for both theories – the“mirror map.” To extract integer-valued invariants, one needs an all-genus“multiple-cover” formula. The technology for finding mirror manifolds [3]1

String field theory and brane superpotentials

Abstract: I discuss tree-level amplitudes in cubic topological string field theory, showing that a certain family of gauge conditions leads to an A∞ algebra of tree-level string products which define a potential describing the dynamics of physical states Upon using results of modern deformation theory, I show that the string moduli space admits two equivalent descriptions, one given in standard Maurer-Cartan fashion and another given in terms of a `homotopy Maurer-Cartan problem', which describes the critical set of the potential By applying this construction to the topological A and B models, I obtain an intrinsic formulation of `D-brane superpotentials' in terms of string field theory data This gives a prescription for computing such quantities to all orders, and proves the equivalence of this formulation with the fundamental description in terms of string field moduli In particular, it clarifies the relation between the Chern-Simons/holomorphic Chern-Simons actions and the superpotential for A/B-type branes

Brane/anti-Brane Systems and U(N|M) Supergroup

Abstract: We show that in the context of topological string theories N branes and M anti-branes give rise to Chern-Simons gauge theory with the gauge supergroup $U(N|M)$. We also identify a deformation of the theory which corresponds to brane/anti-brane annihilation. Furthermore we show that when $N=M$ all open string states are BRST trivial in the deformed theory.

New topological field theories in two-dimensions

Abstract: It is shown that two (1 + 1)-dimensional (2D) free Abelian and self-interacting non-Abelian gauge theories (without any interaction with matter fields) belong to a new class of topological field theories (TFTs). These new theories capture together some of the key features of Witten and Schwarz types of TFT because they are endowed with symmetries that are reminiscent of the Schwarz-type theories but their Lagrangian density has the appearance of the Witten-type theories. The topological invariants for these theories are computed on a 2D compact manifold and their recursion relations are obtained. These new theories are shown to provide a class of tractable field theoretical models for the Hodge theory in two dimensions of flat (Minkowski) spacetime where there are no propagating degrees of freedom associated with the 2D gauge boson.

Topological structures in string theory

Abstract: In string theory space–time comes equipped with an additional geometric structure called a B –field or ‘gerbe’. I describe this structure, mention its relationship with noncommutative geometry, and explain how to use the B –field to define a twisted version of the K –theory of space–time. String–theoretical space–time can contain topologically non–trivial dynamical structures called D–branes. These are simply accounted for in the framework of conformal field theory. In a highly simplified limiting casetopological field theory with a finite gauge group—the D–branes naturally represent elements of the twisted K –theory of space–time: the K –theory class is the ‘charge’ of the D–brane.

Some properties of string field algebra

Abstract: We examine string field algebra which is generated by star product in Witten's string field theory including ghost part. We perform calculations using oscillator representation consistently. We construct wedge like states in ghost part and investigate algebras among them. As a by-product we have obtained some solutions of vacuum string field theory. We also discuss some problems about identity state. We hope these calculations will be useful for further investigation of Witten type string field theory.

String Theory on AdS Orbifolds

Abstract: We consider worldsheet string theory on $Z_N$ orbifolds of $AdS_3$ associated with conical singularities. If the orbifold action includes a similar twist of $S^3$, supersymmetry is preserved, and there is a moduli space of vacua arising from blowup modes of the orbifold singularity. We exhibit the spectrum, including the properties of twisted sectors and states obtained by fractional spectral flow. A subalgebra of the spacetime superconformal symmetry remains intact after the $Z_N$ quotient, and serves as the spacetime symmetry algebra of the orbifold.

Enhanced D-Brane Categories from String Field Theory

Abstract: We construct D-brane categories in B-type topological string theory as solutions to string field equations of motion. Using the formalism of superconnections, we show that these solutions form a variant of a construction of Bondal and Kapranov. This analysis is an elaboration on recent work of Lazaroiu. We also comment on the relation between string field theory and the derived category approach of Douglas, and Aspinwall and Lawrence. Non-holomorphic deformations make a somewhat unexpected appearance in this construction.

Enhanced D-Brane Categories From String Field Theory

Abstract: We construct D-brane categories in B-type topological string theory as solutions to string field equations of motion. Using the formalism of superconnections, we show that these solutions form an enhanced triangulated category as defined by Bondal and Kapranov. This analysis is an elaboration on recent work of Lazaroiu. We also comment on the relation between string field theory and the derived category approach of Douglas, and Aspinwall and Lawrence. Non-holomorphic deformations make a somewhat unexpected appearance in this construction.

Deformations of closed strings and topological open membranes

Abstract: We study deformations of topological closed strings. A well-known example is the perturbation of a topological closed string by itself, where the associative OPE product is deformed, and which is governed by the WDVV equations. Our main interest will be closed strings that arise as the boundary theory for topological open membranes, where the boundary string is deformed by the bulk membrane operators. The main example is the topological open membrane theory with a nonzero 3-form field in the bulk. In this case the Lie bracket of the current algebra is deformed, leading in general to a correction of the Jacobi identity. We identify these deformations in terms of deformation theory. To this end we describe the deformation of the algebraic structure of the closed string, given by the BRST operator, the associative product and the Lie bracket. Quite remarkably, we find that there are three classes of deformations for the closed string, two of which are exemplified by the WDVV theory and the topological open membrane. The third class remains largely mysterious, as we have no explicit example.

Notes on soliton bound state problems in gauge theory and string theory

Abstract: We review four basic examples where string theory and/or field theory dualities predict the existence of soliton bound-states. These include the existence of threshold bound-states of D0 branes required by IIA/M duality and the closely-related bound-states of instantons in the maximally supersymmetric five dimensional gauge theory. In the IIB theory we discuss (p,q)-strings as bound-states of D and F strings, as well as the corresponding bound-states of monopoles and dyons in N=4 supersymmetric Yang-Mills theory whose existence was predicted by Sen. In particular we consider the L^2-index theory relevant for counting these states. In each case we show that the bulk contribution to the index can be evaluated by relating it to an instanton effect in the corresponding theory with a compact Euclidean time dimension. The boundary contribution to the index can be determined by considering the asymptotic regions of the relevant moduli space.

Lecture notes on Chern-Simons-Witten theory

Abstract: Examples of quantizations classical solutions of gauge field theory quantization of Chern-Simons action Chern-Simons-Witten theory and three manifold invariant renormalized perturbation series of Chern-Simons-Witten theory topological sigma model and localization. Appendices: complex manifold without potential theory, S.S. Chern geometric quantization of Chern-Simons gauge theory, S. Axelrod, S.D. Pietra and E. Witten on holomorphic factorization of WZW and Coset models, E. Witten.

A-infinity structure and superpotentials

Abstract: A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.

On non-abelian structures in open string field theory

Abstract: Multi-brane backgrounds are studied in the framework of the background independent open string field theory. A simple description of the non-abelian degrees of freedom is given. Algebra of the differential operators acting on the space of functions on the space-time provides a natural tool for the discussion of this phenomena.

Topologically Induced Instability in String Theory

Abstract: Using the generalised AdS/CFT correspondence, we show that there are certain ten-dimensional differentiable manifolds such that string theory on such a manifold is unstable [to the emission of "large branes"] no matter what the metric may be. The instability is thus due to the [differential] topology of the manifold, not to any particular choice of its geometry. We propose a precise criterion for this "topology selection mechanism", and prove it in many cases. The techniques employed may be useful in more general cases.

String field theory, non-commutative Chern-Simons theory and Lie algebra cohomology

Abstract: Motivated by non-commutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We demonstrate the existence of non-trivial classical solutions. We find Wilson loop-like observables in these examples.

Yang-Mills theory as a quantum gravity with 'aether'

Abstract: Quantum Yang–Mills theory can be rewritten in terms of gauge-invariant variables: it has the form of the so-called BF gravity, with an additional ‘aether’ term. The BF gravity based on the gauge group SU(N) is actually a theory of high spin fields (up to J = N ) with high local symmetry mixing up fields with different spins — as in supergravity but without fermions. As N → ∞ , one gets a theory with an infinite tower of spins related by local symmetry, similar to what one has in string theory. We thus outline a way of deriving a string theory from the local Yang–Mills theory in the large N limit.