Topological structures in string theory

@article{Segal2001TopologicalSI,
  title={Topological structures in string theory},
  author={Guy Segal},
  journal={Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  year={2001},
  volume={359},
  pages={1389 - 1398}
}
  • G. Segal
  • Published 15 July 2001
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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… Expand

Figures from this paper

Topological and conformal field theory as Frobenius algebras
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets alongExpand
Gerbes, (twisted) K-theory, and the supersymmetric WZW model
The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifestsExpand
Homological Quantum Field Theory
We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal $d$-algebra. We construct a structure of transversalExpand
Categorification and correlation functions in conformal field theory
Amodular tensor category provides the appropriate data for the construction of a threedimensional topological field theory. We describe the following analogue for two-dimensional conformal fieldExpand
MORSE THEORY, GRAPHS, AND STRING TOPOLOGY
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done byExpand
A Prehistory of n-Categorical Physics
This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifestExpand
Exotic smooth Bbb R4 and quantum matter
We follow the point of view that superstring theory, as the theory of quantum gravity in the number of spacetime dimensions bigger than 4, serves as mathematics for both, 4 dimensional QG and exoticExpand
Categorical Aspects of Topological Quantum Field Theories
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topologicalExpand
Twisted K-theory
Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twistingExpand
Notes on string topology
This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views aboutExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 10 REFERENCES
D-branes, B fields and twisted K theory
In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C*-algebra. In the case of B-fieldsExpand
Self-duality, Ramond-Ramond fields, and K-theory
Just as D-brane charge of type-IIA and type-IIB superstrings is classified, respectively, by K-1(X) and K(X), Ramond-Ramond fields in these theories are classified, respectively, by K(X) and K-1(X).Expand
Homotopy field theory in dimension 2 and group-algebras
We apply the idea of a topological quantum field theory (TQFT) to maps from manifolds into topological spaces. This leads to a notion of a (d+1)-dimensional homotopy quantum field theory (HQFT) whichExpand
Quantum Fields and Strings: A Course for Mathematicians
Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics. InExpand
Lectures on Special Lagrangian Submanifolds
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us toExpand
Topological quantum field theories
© Publications mathematiques de l’I.H.E.S., 1988, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.Expand
Graded brauer groups and K-theory with local coefficients
© Publications mathematiques de l’I.H.E.S., 1970, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.Expand
String Theory
DEE struggles to uphold her political ideals in the face of her very proper mother, THERESA, and her long-time, over-achieving friend, LEENA. She makes stands that shock and antagonize both women,Expand
String theory. In Quantum fields and strings: a course for mathematicians (ed
  • P. Deligne et al .),
  • 1999