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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: In this article, the authors describe some recent progress in understanding and formulating string theory which is based on extensive studies of strings in lower (D=2) dimension At the center is a large $W_{\infty}$ symmetry that appears most simply in the matrix model picture In turn the symmetry defines the dynamics giving Ward identities and the complete S-matrix.
Abstract: We describe some recent progress in understanding and formulating string theory which is based on extensive studies of strings in lower (D=2) dimension At the center is a large $W_{\infty}$ symmetry that appears most simply in the matrix model picture In turn the symmetry defines the dynamics giving Ward identities and the complete S-matrix The integrability aspect where nonlinear string phenomena emerges from linear matrix model dynamics is emphasized Extensions involving couplings of discrete topological fields to the tachyon are also described

3 citations

Book ChapterDOI
TL;DR: In this paper, it was suggested that D-brane charges are classified by K-theory and not just by homology as was first proposed by Minasian and Moore.
Abstract: In quantum field theories, we are often confronted with the situation that there are extended field configurations that are topologically different, for example, instantons and monopoles. They can carry charges that are topological invariants and so are conserved under small fluctuations. Similarly in string theory, D-branes carry topological charges. In the semiclassical geometric description, these charges can be understood as sources of Ramond–Ramond (RR) fields, higher form fields that couple electrically and magnetically to the D-branes. These charges have to be quantized, similar to the Dirac quantization of electric and magnetic charges in electrodynamics. The classification of D-branes and their charges was a topic of great importance since their discovery. Minasian and Moore (1997) suggested that D-brane charges are classified by K-theory and not just by homology as was proposed first. See Chap. 4 and 9 for K-theory and cohomology as well as their connection in Part 3.

3 citations

Journal ArticleDOI
TL;DR: In this paper, topological invariant terms in the first quantization of strings associated with nonzero elements of the second cohomology group of space-time are investigated, and the direct effect of such terms is C -violation.

2 citations

Book ChapterDOI
01 Jan 1988
TL;DR: In this article, Gomez, Reina, Moore and Vafa developed an operator formalism describing high orders of string perturbation theory, as well as conformal field theories on Riemann Surfaces of genus bigger than one.
Abstract: These lectures are based on joint work with C. Gomez, C. Reina, G. Moore and C. Vafa [1], [2], [3]. The motivation is two-fold. On the one hand we would like to develop an operator formalism describing high orders of string perturbation theory, as well as conformal field theories on Riemann Surfaces of genus bigger than one. On the other hand, developments in the theory of soliton solutions of the K-P hierarchy (KadomtsevPetviashvili equations); for a detailed geometrical account of this theory and references to the literature see for example [4], [5]) made it clear that many of the geometrical features of Riemann Surfaces and their moduli spaces can be formulated in terms of the properties of certain two dimensional quantum field theories [6], so that the geometrical complexity of a Riemann Surface with a field on it can be coded into a state in the standard Fork space of the field theory [1], [7], [8], [9], [10], [11], [12]. This approach gives an important understanding of the action of the Virasoro algebra on the moduli space of surfaces [13], [14] . The space of solutions of the K.P. equation can be described in terms of an infinite dimensional grassmannian GT. To any algebraic curve X with a point P selected on it, a local coordinate around P, and a line bundle L over X, we can associate a point in Gr Krichever construction [4], [5]). Moreover, the collection of all those points in Gr is a dense set. It is thus plausible to expect that some subspace of Gr provides an explicit model for the Universal Moduli Space of Friedan and Shenker [15, 16] which plays a central role in their non-perturbative approach to string theory.

2 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
20228
202115
202012
201915
201817