Abstract
To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the energy of the ρ-meson field. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the ρ through scattering, suggesting that the ρ and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.
Highlights
Non-BPS systems, including the Skyrme model, are more complicated
We propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson
The N -instanton moduli space is 8N dimensional, in disagreement with the 7N modes found numerically. What explains this discrepancy? Physically, what do the additional modes describe? In this paper we show that these questions are resolved by the addition of vector mesons to the Skyrme model
Summary
We study the Skyrme model coupled to a tower of vector mesons, with the interactions fixed by a holographic construction. We can use the fields (3.6) and (3.7) to study the energy of the instanton-generated Skyrme and ρ-meson configurations as a function of the moduli space parameters. Applying a gauge transformation to the instanton gauge field A modifies the Skyrme-meson Lagrangian (2.6) and the solutions (3.7). This can be seen explicitly in [15] and [16], where the N = 1 calculation is done in the definite-parity and a no-parity gauge. In contrast the meson profiles ki do depend on H and so the energy density EV (r)+EI (r) does change We plot this density for a variety of H and a fixed λ = 1.2 in figure 2. There are two non-zero modes: the overall size (λ) and the energy of the meson field (H)
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