Baryon-charge Chemical Potential in AdS/CFT

TL;DR

This paper develops a comprehensive AdS/CFT framework incorporating finite U(1)B-charge chemical potential, clarifies its gauge-invariant definition, and highlights the importance of Minkowski embeddings for a complete phase structure analysis.

Contribution

It introduces a closed, gauge-invariant method to include chemical potential in AdS/CFT and emphasizes the necessity of Minkowski embeddings for accurate phase diagram representation.

Findings

Minkowski embeddings are essential for a complete phase structure.

D3-D7 models with only black-hole embeddings lack low-temperature, low-chemical-potential regions.

Numerical analysis supports the physical significance of Minkowski embeddings.

Abstract

We present a closed framework of AdS/CFT with finite U(1)B-charge chemical potential. We show how the gauge-invariant identification of the chemical potential with the bulk gauge field emerges from the standard AdS/CFT dictionary. Physical importance and necessity of the Minkowski embeddings within the present framework is also shown numerically in the D3-D7 systems. We point out that the D3-D7 model with only the black-hole embeddings does not have the low-temperature and low-chemical-potential region in the grand-canonical ensemble, hence it is incomplete. A physical interpretation that explains these numerical results is also proposed.