Topic
Topological string theory
About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.
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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: 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
TL;DR: In this article, the authors study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology.
Abstract: We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the Cl(n)-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond-Ramond fields in Type II string theory in terms of topological K-chains.
17 citations
TL;DR: In this article, the integrals over the 3-chains on the compact Calabi-Yau 3-folds were studied in the context of the open mirror symmetry analysis of the topological B-model.
Abstract: We develop some computational methods for the integrals over the 3-chains on the compact Calabi–Yau 3-folds that play a prominent role in the analysis of the topological B-model in the context of the open mirror symmetry. We discuss such 3-chain integrals in two approaches. In the first approach, we provide an algorithm to obtain the inhomogeneous Picard–Fuchs equations. In the second approach, we discuss the analytic continuation of the period integral to compute the 3-chain integral directly. The latter direct integration method is applicable for both on-shell and off-shell formalisms.
17 citations
TL;DR: In this article, the integrable structure in a modified melting crystal model of topological string theory on the resolved conifold has been studied and it is shown that the partition function (deformed by external potentials) is essentially a tau function of 2D Toda hierarchy.
Abstract: This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the Fock space of 2D complex free fermion fields. The quantum torus algebra of fermion bilinears behind this expression is shown to have an extended set of ?shift symmetries?. They are used to prove that the partition function (deformed by external potentials) is essentially a tau function of the 2D Toda hierarchy. This special solution of the 2D Toda hierarchy can also be characterized by a factorization problem of matrices. The associated Lax operators turn out to be quotients of first-order difference operators. This implies that the solution of the 2D Toda hierarchy in question is actually a solution of the Ablowitz?Ladik (equivalently, the relativistic Toda) hierarchy. As a byproduct, the shift symmetries are shown to be related to matrix-valued quantum dilogarithmic functions.
17 citations