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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 analogy between topological string theory and equivariant cohomology was examined, and it was shown that the equivariance of a topological conformal field theory carries a certain algebraic structure, which is called a gravity algebra.
Abstract: In this paper, we examine the analogy between topological string theory and equivariant cohomology. We also show that the equivariant cohomology of a topological conformal field theory carries a certain algebraic structure, which we call a gravity algebra. (Error on page 9 corrected: BRS current contains total derivatives.)
2 citations
TL;DR: In this paper, the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and quantum gravity are described.
Abstract: We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and quantum gravity. Its partition function can be computed by enumerating the contributions from noncommutative instantons to a six-dimensional cohomological gauge theory, which yields a dynamical realization of the crystal as a discretization of spacetime at the Planck scale. We describe analogous relations between a melting crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory in four dimensions. We elaborate on some mathematical details of the construction of the quantum geometry which combines methods from toric geometry, isospectral deformation theory and noncommutative geometry in braided monoidal categories. In particular, we relate the construction of noncommutative instantons to deformed ADHM data, torsion-free modules and a noncommutative twistor correspondence.
2 citations
TL;DR: In this article, the supersymmetric structure present in W-gravities was derived in the geometrical framework of Zucchini, which necessitates the introduction of an appropriate new basis of variables which replace the canonical fields and their derivatives.
Abstract: We derive the supersymmetric structure present in W-gravities which has been already observed in various contexts as Yang-Mills theory, topological field theories, bosonic string and chiral -gravity. This derivation which is made in the geometrical framework of Zucchini, necessitates the introduction of an appropriate new basis of variables which replace the canonical fields and their derivatives. This construction is used, in the -case, to deduce from the Chern-Simons action the Wess-Zumino-Polyakov action.
2 citations
TL;DR: In this article, a double BRST structure for topological matter theories is found. But the implementation of the topological symmetry in non-critical (super) string theories depends on the matter content of the two realizations connected by the mirror transformation.
2 citations
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.
2 citations