4 research outputs found
Quantum D-branes and exotic smooth R^4
In this paper, we present the idea that the formalism of string theory is
connected with the dimension 4 in a new way, not covered by phenomenological or
model-building approaches. The main connection is given by structures induced
by small exotic smooth R^4's having intrinsic meaning for physics in dimension
4. We extend the notion of stable quantum D-branes in a separable
noncommutative C* algebras over convolution algebras corresponding to the
codimension-1 foliations of S^3 which are mainly connected to small exotic R^4.
The tools of topological K-homology and K-theory as well KK-theory describe
stable quantum branes in the C* algebras when naturally extended to algebras.
In case of convolution algebras, small exotic smooth R^4's embedded in exotic
R^4 correspond to a generalized quantum branes on the algebras. These results
extend the correspondence between exotic R^4 and classical D and NS branes from
our previous work.Comment: 16 pages, no figure, see arXiv/1101.3169 for Part 1 This is part 2 of
the work based on the talk "Small exotic smooth and string
theory" given at the International Congress of Mathematicians, ICM2010,
19-28.08.2010, Hyderabad, Indi
Exotic R^4 and quantum field theory
Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic
differential structure, shows the connection of 4-exotics with the
codimension-1 foliations of , SU(2) WZW models and twisted K-theory
, . These results made it possible
to explicate some physical effects of exotic 4-smoothness. Here we present a
relation between exotic smooth R^4 and operator algebras. The correspondence
uses the leaf space of the codimension-1 foliation of S^3 inducing a von
Neumann algebra as description. This algebra is a type III_1 factor
lying at the heart of any observable algebra of QFT. By using the relation to
factor II, we showed that the algebra can be interpreted as
Drinfeld-Turaev deformation quantization of the space of flat SL(2,\mathbb{C})
connections (or holonomies). Thus, we obtain a natural relation to quantum
field theory. Finally we discuss the appearance of concrete action functionals
for fermions or gauge fields and its connection to quantum-field-theoretical
models like the Tree QFT of Rivasseau.Comment: 15 pages, 2 figures, Based on the talk presented at Quantum Theory
and Symmetries 7, Prague, August 7-13, 2011, JPconf styl
Hochaufloesende lineare Infrarot-Array-Module 'LINAR'. Teilvorhaben: Ungekuehlte Arrays Schlussbericht
SIGLEAvailable from TIB Hannover: F03B756+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Bildung und Forschung, Berlin (Germany)DEGerman