# Noncommutative solitons: moduli spaces, quantization, finite θ effects and stability

@article{Hadasz2001NoncommutativeSM,
title={Noncommutative solitons: moduli spaces, quantization, finite $\theta$ effects and stability},
author={Leszek Hadasz and Ulf Lindstrom and Martin Ro{\vc}ek and Rikard von Unge},
journal={Journal of High Energy Physics},
year={2001},
volume={2001},
pages={040-040}
}
• Published 2 April 2001
• Mathematics, Physics
• Journal of High Energy Physics
We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite theta corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite theta, we find…

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## References

SHOWING 1-10 OF 27 REFERENCES

### Noncommutative Solitons

• Mathematics, Physics
• 2000
We ﬁnd classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative ﬁeld theories whose scalar potential, V ( φ ), has at least two minima. These solutions are bubbles of

### The stability of noncommutative scalar solitons

We determine the stability conditions for a radially symmetric non-commutative scalar soliton at finite noncommutivity parameter θ. We find an intriguing relationship between the stability and

### Unstable solitons in noncommutative gauge theory

• Physics, Mathematics
• 2001
We find a class of exact solutions of noncommutative gauge theories corresponding to unstable non-BPS solitons. In the two-dimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find

### Quantum Corrections to Noncommutative Solitons

Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real

### On Noncommutative Multi-Solitons

• Mathematics
• 2001
Abstract: We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is

### Noncommutative Tachyons

• Physics
• 2000
When unstable Dp-branes in type II string theory are placed in a B-ﬁeld, the resulting tachyonic world-volume theory becomes noncommutative. We argue that for large noncommutativity parameter,

### Non-commutative soliton scattering

• Mathematics, Physics
Journal of High Energy Physics
• 2000
We study solitons in three dimensional non-commutative scalar field theory at infinite non-commutativity parameter. We find the metric on the relative moduli space and show that it is Kahler. We then

### Exact Multi-Vortex Solutions in Noncommutative Abelian-Higgs Theory

We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS

### Monopoles and strings in noncommutative gauge theory

• Physics, Mathematics
• 2000
We study some non-perturbative aspects of non-commutative gauge theories. We find analytic solutions of the equations of motion, for non-commutative U(1) gauge theory, that describe magnetic