Electromagnetic instability of vacuum with instantons in the holographic plasma

TL;DR

This work investigates how instantons in a holographic plasma modify electromagnetic instability and Schwinger-like pair production. Using the D(-1)-D3 background with D7-brane flavors, the vacuum decay rate is computed from the imaginary part of the flavored Lagrangian $\mathcal{L}$ under static external fields, revealing that increasing instanton density $q$ raises the critical field $E_c$ and induces a mass gap. The results show $E_c \propto q^{2}$ for small $q$ and $E_c \propto \sqrt{q}$ for large $q$, and the corresponding V-A curve indicates an insulating vacuum for subcritical $E$ and a conductivity that becomes less sensitive to $q$ at large $E$. Overall, the paper establishes a link between instanton topology and electromagnetic response in strongly coupled gauge theories, highlighting an insulating/conductive phase transition controlled by instanton density.

Abstract

Using the gauge-gravity duality, we study the electromagnetic instability of vacuum with instantons in holographic plasma. The model we employ is the D(-1)-D3 brane system in which the D(-1)-branes correspond to the instantons in holography. To take into account the flavored quarks, the coincident probe D7-branes as flavors are embedded into the bulk geometry so that the effective electromagnetic Lagrangian with flavors corresponds to the action of the D7-branes according to gauge-gravity duality. We numerically evaluate the vacuum decay rate, the critical electric field and the V-A curve of the vacuum by using the D7-brane action with various values of the electromagnetic field. It implies the particles in the plasma acquire an effective mass in the presence of instantons as it is expected in the quantum field theory, and the plasma trends to become insulating when the electric field is small. This work reveals the relation between electromagnetic and instantonic properties of the vacuum in the plasma.

Figures (5)

• Figure 1: The imaginary part of effective Lagrangian as a function of $E,B_{\parallel}$ and $E,B_{\perp}$ with various instanton charge $q$. $B_{\parallel},B_{\perp}$ refers respectively to the cases that the magnetic field is parallel and perpendicular to the electric field. The parameters are chosen as $z_{H}=R=2\pi\alpha^{\prime}=1,d=0,j=0$. The yellow, blue, green and red colors correspond respectively to the case of $q=0,3,6,9$.
• Figure 2: The imaginary part of effective Lagrangian as a function of $E$ with various instanton charge $q$. The parameters are chosen as $z_{H}=R=2\pi\alpha^{\prime}=1,j=0,B_{i}=0$.
• Figure 3: The critical electric field $E_{c}$ as a function of the instanton charge $q$. The parameters are chosen as $z_{H}=R=2\pi\alpha^{\prime}=1,j=0$.
• Figure 4: The imaginary part of effective Lagrangian as a function of $q$ with fixed external fields. The parameters are chosen as $z_{H}=R=2\pi\alpha^{\prime}=1,j=0$.
• Figure 5: The vacuum V-A curve in holography with vanished magnetic field. The stable current becomes non-zero at $E>E_{c}$.