D-Branes in Noncommutative Field Theory

  title={D-Branes in Noncommutative Field Theory},
  author={Richard J Szabo},
  journal={arXiv: High Energy Physics - Theory},
  • R. Szabo
  • Published 5 December 2005
  • Physics
  • arXiv: High Energy Physics - Theory
A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory on Moyal spaces are extensively studied. Instantons in Yang-Mills theory on the two-dimensional noncommutative torus and the fuzzy sphere are also constructed. In some instances the connection to D-brane physics is provided by a mapping of noncommutative… 

Symmetry, gravity and noncommutativity

We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of

Rank two quiver gauge theory, graded connections and noncommutative vortices

We consider equivariant dimensional reduction of Yang-Mills theory on K?hler manifolds of the form M ? P1 ? P1. This induces a rank two quiver gauge theory on M which can be formulated as a

Notes on exact multi-soliton solutions of noncommutative integrable hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh.

Conformal twists, Yang–Baxter σ-models & holographic noncommutativity

Expanding upon earlier results (Araujo et al 2017 Phys. Rev. D 95 105006), we present a compendium of σ-models associated with integrable deformations of AdS5 generated by solutions to homogenous

Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane ?

In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenewold-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and

Towards a T-dual Emergent Gravity

Darboux theorem in symplectic geometry is the crux of emergent gravity in which the gravitational metric emerges from a noncommutative U(1)-theory. Topological T-duality, on the other hand, is a

Virasoro Action on Pseudo-Differential Symbols and (Noncommutative) Supersymmetric Peakon Type Integrable Systems

Using Grozman’s formalism of invariant differential operators we demonstrate the derivation of N=2 Camassa-Holm equation from the action of Vect(S1|2) on the space of pseudo-differential symbols. We

Graded Hopf Maps and Fuzzy Superspheres

A ug 2 01 1 Graded Hopf Maps and Fuzzy Superspheres

It is shown that fuzzy supersPheres are represented as a “superposition” of fuzzy superspheres with lower supersymmetries, and algebraic structures of fuzzy twoand four-superspheres are investigated to identify su(2|N) and su(4|N).



Komaba Lectures on Noncommutative Solitons and D-Branes

These lectures provide an introduction to noncommutative geometry and its origins in quantum mechanics and to the construction of solitons in noncommutative field theory. These ideas are applied to

Quantum field theory on noncommutative spaces

Noncommutative tachyons and K-theory

We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and

Noncommutative geometry from strings and branes

Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a non-vanishing background B field. We

Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two

D-branes and strings as non-commutative solitons

The non-commutative geometry of a large auxiliary B-field simplifies the construction of D-branes as solitons in open string field theory. Similarly, fundamental strings are constructed as localized

Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization

These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum

Noncommutative Solitons on Orbifolds

In the noncommutative field theory of open strings in a B-field, D-branes arise as solitons described as projection operators or partial isometries in a $C^*$ algebra. We discuss how D-branes on

String theory and noncommutative geometry

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally