Flavoured Large N Gauge Theory in an External Magnetic Field

TL;DR

The paper investigates a flavored large-$N$ gauge theory in an external magnetic field using a D7-brane probe in $AdS_5\times S^5$, where a pure gauge $B$-field couples to fundamental matter and induces a nonzero fermionic condensate, signaling spontaneous chiral symmetry breaking. It develops the embedding dynamics via the DBI and Wess–Zumino actions, mapping the D7 profile $L(\rho)$ to the bare quark mass $m_q$ and condensate $\langle\bar{\psi}\psi\rangle$, and analyzes the meson spectrum through quadratic fluctuations that couple scalar and vector modes. In the weak-field limit, a Zeeman-like splitting of the meson states is found, with $M_±=M_0\pm\frac{H}{m}\sqrt{1+\frac{k_{23}^2}{M_0^2}}$, while in the strong-field regime numerical methods reveal a $\sqrt{m_q}$ dependence for the ground state and a Goldstone mode at zero quark mass; excited states tend toward finite values and the AdS$_5\times S^5$ spectrum in the large-mass limit. Overall, the work demonstrates magnetic catalysis of chiral symmetry breaking and elucidates the qualitative structure of the meson spectrum in holographic QCD-like theories under external magnetic fields. The results enhance understanding of how external electromagnetic fields influence flavor dynamics in gauge/gravity duals and offer a controlled framework to study chiral symmetry breaking and hadron spectra in strongly coupled plasmas.

Abstract

We consider a D7-brane probe of AdS$_{5}\times S^5$ in the presence of pure gauge $B$-field. In the dual gauge theory, the $B$-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The $B$-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic $\sqrt{m_{q}}$ dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry.

Figures (7)

• Figure 1: The black line corresponds to (\ref{['1/m']}), one can observe that the analytic result is valid for large $\tilde{m}$. It is also evident that for $\tilde{m}=0$$\langle\bar{\psi}\psi\rangle\neq0$. The corresponding value of the condensate is $\tilde{c}_{\rm cr}=0.226$
• Figure 2: A plot of the magnitude of the fermionic condensate at zero bare quark mass $c_{\rm cr}$ as function of $R^2H$, the black curve represents equation (\ref{['Ccr']}).
• Figure 3: A magnification of figure \ref{['fig:fig1']} to show the spiral behavior near the origin of the $(-\tilde{c},\tilde{m})$-plane.
• Figure 4: Plot of $\bar{M}=M{R^2}/{m}$ vs. $H/m$ for the first three states. The dashed black lines correspond to the spectrum given by equation (\ref{['degen']})
• Figure 5: Spectrum of $\tilde{m}_{23}$ vs. $\tilde{m}$. The dashed line represents the lowest level of the meson spectrum for pure AdS$_{5}\times S^5$ space