Noncommutative geometry and string field theory pdf

Edward witten, noncommutative geometry and string field theory, nucl. Noncommutative geometry and string field theory inspire. General properties of noncommutative field theories. We identify a limit in which the entire string dynamics is described by a minimally coupled supersymmetric gauge theory on a noncommutative space, and discuss the corrections away from this limit. Pdf string theory, matrix model, and noncommutative geometry. Noncommutative geometry and vacuum string field theory y. Noncommutative field theories and superstring field theories. Pdf string theory and noncommutative geometry semantic. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. Heisenberg and the noncommutative algebra of physical quantities 40 2. An attempt is made to interpret the interactions of bosonic open strings as defining a noncummulative, associative algebra, and to formulate the classical nonlinear field theory of such strings in the language of noncommulative geometry. One can take ato be an abstract noncommutative associative algebra awith a multiplication. We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero b field.

In chapter 2 we explain basic ideas of noncommutative field theory, its stringy origin and various interesting properties. Statistical state of a macroscopic system and quantum statistical mechanics 45 3. String theory and noncommutative gauge theory semantic scholar. A course on noncommutative geometry in string theory. Comments on noncommutative field theories 1 1 1 lectures presented at the 9th adriatic meeting in dubrovnik croatia, september 2003 l. Compactification of matrix model on a noncommutative torus is obtained from strings ending on dbranes with background b field. The point of departure is the brst approach to string field theory. In the search for the exact minimum of the tachyon potential in the wittens cubic string field theory we try to learn as much as possible from the string field theory in the large bfield background. Noncommutative geometry uses a generalization of the known duality between a space and the algebra of functions on it 2, 3.

A brief history of vsft purely cubic theory 85 noncommutative geometry dbrane as nc soliton vsft dbrane charge k theory osft noncommutative geometry 99. In the field theory limit, these are yangmills instantons, that is, solutions. Noncommutative geometry and string field theory core. The metric aspect of noncommutative geometry 34 chapter 1. The bps spectrum of the system and a novel sl2,z symmetry are. The original application of noncommutative yangmills theory to string theory 2 was. Noncommutative geometry and string field theory sciencedirect. String field theory at large bfield and noncommutative geometry. Noncommutative geometry and vacuum string field theory. In string theory the use of noncommutative geometry was pioneered by witten 7. In mathematics, more specifically abstract algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative. String field theory at large bfield and noncommutative. Pdf noncommutative geometry and string field theory.