Overview of K theory applied to strings
By E. Witten. 2000
172 citations recorded by the source corpus.
K-theory provides a framework for classifying Ramond-Ramond (RR) charges and fields. K-theory of manifolds has a natural extension to K-theory of noncommutative algebras, such as the algebras considered in noncommutative Yang-Mills theory or in open string field theory. In a number of concrete problems, the K-theory analysis proceeds most naturally if one starts out with an infinite set of D-branes, reduced by tachyon condensation to a finite set. This suggests that string field theory should be reconsidered for N=∞.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
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Citations in the corpus
- Dirac Charge Quantization and Generalized Differential Cohomology (2000, background): “K-theory elements of finite rank, but the rank is constrained to be a multiple of N. Elements of virtual rank zero exist for any twisting; one might instead formally consider them to have infinite rank [W1]. Explicit formulas for twisted Kˇ-theory are difficult to write in general, but can be written if”
- Half-strings, projectors and multiple D-branes (2001, background): “While no doubt technical complications related to normalization and regularization would be encountered in discussing concretely such background, it is interesting to note that a background with infinite number of Dbranes is natural for a general K-theory analysis of D-brane states [23].”
- Exact noncommutative solitons (2000, background): “2 Similar issues arise in the proposal of [42].”
- D-brane Deconstructions in IIB Orientifolds (2008, background): “A sampling of papers on this topic is [90, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 117, 118, 119].”
- D-Brane Instantons and K-Theory Charges (2001, background): “) While these discussions fit in well with our current understanding of D-branes, as discussed in [12,13], they do not demonstrate the physical relevance of K H(X).”
- Split string field theory I (2001, background): “I. It may be that the solutions (5.10) with ˆ χ a rank one projector correspond to single D-branes, while the solution with ˆ χ = I may represent a U(∞) theory of an infinite number of space-filling D25-branes, such as is useful in K-theory constructions [ 45 ].”
- Phases Of N=2 Theories In 1+1 Dimensions With Boundary (2008, background): “(iii) Infinite size Chan-Paton factors which are effectively finite for the same reason as above had been discussed earlier in [54, 55].”
- Twisted K-Theory and K-Theory of Bundle Gerbes (2001, methodology): “The picture of D-brane charges taking values in (twisted) K-theory has received further support from an analysis of M -theory [7], noncommutative tachyons [37, 13] and explicit examples (see, e.”
- Brane tilings and their applications (2008, methodology): “If you are familiar with K-theory in the context of tachyon condensation [227, 228], then you can think of derived categories as an more elaborate version of K-theory.”
- A paradigm of open/closed duality Liouville D-branes and the Kontsevich model (2003, background): “(20)Open string field theory on an infinite number of branes has been conjectured [82] to be relevant for the issue of background independence in string theory.”
- Komaba Lectures on Noncommutative Solitons and D-Branes (2001, methodology): “interesting connections to some more exotic aspects of K-theory and noncommutative geometry [85,86,57].”
- Chiral 4d string vacua with D branes and NSNS and RR fluxes (2003, background): “This has been argued mainly when the cohomology class [H3] is torsion [41, 42], and there have been attempts at defining it properly for non-torsion [H3] [43].”
- D-branes and K-theory in 2D topological field theory (2006, unknown): “(Indeed, Witten has suggested in [5] that one should use something analogous to stabilization of C∗ algebras, namely one should replace the string field algebra by Oaa ⊗ K where K is the algebra of compact operators.”