Chiral helix in AdS/CFT with flavor

TL;DR

This paper explores new phases in the D3/D7 holographic model of QCD, revealing a chiral helix and spontaneous rotation phases driven by anomalies and external fields, enriching the understanding of chiral phenomena in holography.

Contribution

It uncovers previously overlooked phases induced by the Wess-Zumino term, including a chiral helix and spontaneous rotation, in the finite temperature D3/D7 model with external fields.

Findings

Discovery of a chiral helix phase under magnetic field and chemical potential.

Identification of a spontaneous rotation phase with time-dependent U(1)_A angle.

Emphasis on the importance of the WZ term in the phase diagram analysis.

Abstract

The D3/D7 holographic model aims at a better approximation to QCD by adding to N=4 SYM theory N_f of N=2 supersymmetric hypermultiplets in the fundamental representation of SU(N_c) -- the "flavor fields" representing the quarks. Motivated by a recent observation of the importance of the Wess-Zumino-like (WZ) term for realizing the chiral magnetic effect within this model, we revisit the phase diagram of the finite temperature, massless D3/D7 model in the presence of external electric/magnetic fields and at finite chemical potential. We point out that the A-V-V triangle anomaly represented by the WZ term in the D7 brane probe action implies the existence of new phases that have been overlooked in the previous studies. In the case of an external magnetic field and at finite chemical potential, we find a "chiral helix" phase in which the U(1)_A angle of D7 brane embedding increases monotonically along the direction of the magnetic field -- this is a geometric realization of the chiral spiral phase in QCD. We also show that in the case of parallel electric and magnetic fields (E,B) there exists a phase in which the D7 brane spontaneously begins to rotate, so that the U(1)_A angle changes as a function of time -- this may be called the "spontaneous rotation" phase; it is a geometrical realization of a phase with non-zero chiral chemical potential. Our results call for a more thorough study of the (T,B,E,\mu) phase diagram of the massless D3/D7 model taking a complete account of the WZ term. We also speculate about the possible phase diagram in the massive case.