Solitons in noncommutative gauge theory

By D. Gross, N. Nekrasov. 2000

154 citations recorded by the source corpus.

We present a unified treatment of classical solutions of non-commutative gauge theories. We find all solutions of the non-commutative Yang-Mills equations of motion in 2 dimensions; and show that they are labeled by two integers --- the rank of the gauge group and the magnetic charge. The magnetic vortex solutions are unstable in 2+1 dimensions, but correspond to the full, stable BPS solutions of = 4 U(1) non-commutative gauge theory in 4 dimensions, that describes N infinite D1 strings that pierce a D3-brane at various points, in the presence of a background B-field in the Seiberg-Witten α'→0 limit. We discuss the behavior of gauge invariant observables in the background of the solitons. We use these solutions to construct a panoply of BPS and non-BPS solutions of supersymmetric gauge theories that describe various configurations of D-branes. We analyze the instabilites of the non-BPS solitons. We also present an exact analytic solution of non-commutative gauge theory that describes a U(2) monopole.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7e014df44218a8646d2e5b1136178b2c83437d04

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Komaba Lectures on Noncommutative Solitons and D-Branes (2001, background): “Results along these lines can be found in [43,44,45,46,47,48,49,50].”
Noncommutative field theory (2001, methodology): “…ψ † ψ, ψ † D i ψ and so on will be gauge invariant and can be used in the action and to define new observables, either by enforcing an equation of motion on ψ or doing a functional integral over ψ (Ambjorn, Makeenko , Nishimura, and Szabo 2000; Gross and Nekrasov 2001; Rajaraman and Rozali 2000).”
Quantum field theory on noncommutative spaces (2001, methodology): “1) may be interpreted as gauge fields appropriate to the splitting of covariant derivatives on a generic Aθ-module into a free part Hm (represented by the gauge field Ai) and a twisted part of constant magnetic flux corresponding to copies of the Fock module Hq [38, 155].”
BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field (2000, background): “) Which solution we want is quite clear from several recent papers [6-11].”