# A low-dimensional analogue of holographic baryons

## Summary (1 min read)

### 1 Introduction

- As the soliton is small compared to the curvature scale then it can be approximated by a flat space self-dual Yang-Mills instanton with a small size [3, 4].
- Multi-solitons in the Sakai-Sugimoto model (including solitons at finite density) are unlikely to have any continuous symmetries, so numerical field theory computations would require a fully four-dimensional computation that is beyond current capabilities.
- It is argued that, with increasing density, this dyonic salt arrangement turns into a cubic crystal of half-instantons that is dual to the well-known Skyrme crystal.
- The results provide evidence to support the validity of these ideas within the Sakai-Sugimoto model.

### 3 Solitons at finite density

- As mentioned in the introduction, the study of solitons at finite density in the SakaiSugimoto model has attracted some recent attention in attempts to understand dense QCD within a holographic setting.
- These results show that the double chain solution has a lower energy than the single chain solution once the density is greater than about twice the optimal density.
- Both approaches therefore confirm the analogue of baryonic popcorn in their low-dimensional model.
- A minimization over the parameters in such an instanton approximation yields the blue curve in Figure 5, which agrees with the field theory results.
- All these results suggest that as the density is increased further then the number of soliton chains increases and eventually the configuration begins to resemble a portion of a two-dimensional lattice rather than the one-dimensional chain that arises at the optimal density.

### 4 Conclusion

- The advantage of the low-dimensional theory is that several aspects that one would like to study in the Sakai-Sugimoto model, but are currently not tractable, can be investigated exactly.
- This provides further support for the use of self-dual Yang-Mills instantons in approximating bulk solitons in the Sakai-Sugimoto model.
- Analogues of dyonic salt and baryonic popcorn configurations have been found, providing strong evidence for their relevance in the study of holographic baryons.
- Note that the results in that paper show that this can produce similar results to the inclusion of a baby Skyrme term.

Did you find this useful? Give us your feedback

##### Citations

21 citations

##### References

1,679 citations

802 citations

335 citations

268 citations

226 citations

##### Related Papers (5)

##### Frequently Asked Questions (2)

###### Q2. What are the future works in "A low-dimensional analogue of holographic baryons" ?

In this paper the authors have introduced and investigated a holographic baby Skyrme model that can be used to study several low-dimensional analogues of bulk solitons in the Sakai-Sugimoto model, describing holographic baryons. The advantage of the low-dimensional theory is that several aspects that one would like to study in the Sakai-Sugimoto model, but are currently not tractable, can be investigated exactly. This provides further support for the use of self-dual Yang-Mills instantons in approximating bulk solitons in the Sakai-Sugimoto model. As the baby Skyrme model is easier to investigate the authors have chosen this route in the current paper, but it might be of interest to investigate the vector meson model to see if additional phenomena can be obtained.