Solutions to axion electrodynamics with electric-magnetic duality in supersymmetric Seiberg-Witten theory

TL;DR

The paper develops a calculable UV model of a Peccei–Quinn axion coupled to electric and magnetic charges within $ abla$N=2 Seiberg–Witten theory, exploiting electric–magnetic duality to derive non-linear axion electrodynamics. By using the SW IR Lagrangian, it derives frame-dependent EM equations in both the electric frame (E-frame) and magnetic frame (M-frame), analyzes the moduli-space parameter $u$ to identify reliable regions, and solves the axion Maxwell equations under external magnetic or electric fields, yielding observable axion-induced fields that are most pronounced in the $ abla$-photon sector. The work then outlines detection strategies using LC circuits, providing prospective sensitivities for the axion–photon couplings $g_{a\gamma\gamma}$ and its dual $g_{a\gamma\gamma}^D$, and discusses how duality manifests in measured signals. Overall, it connects non-perturbative instanton effects in SW theory to measurable axion–photon phenomenology, offering concrete experimental paths to probe these couplings in different duality frames.

Abstract

Axion and magnetic monopole are among the most fascinating candidates for physics beyond the Standard Model. The potential connection between axion and magnetic monopole stems from the Witten effect and is revealed by non-standard axion electrodynamics. Non-standard axion electrodynamics under electric-magnetic duality modifies conventional axion Maxwell equations and motivates intriguing axion-photon phenomenology. A calculable ultraviolet model of Peccei-Quinn axion coupled to magnetic monopoles and electric charges was proposed based on $\mathcal{N}=2$ supersymmetric Seiberg-Witten (SW) theory with manifest electric-magnetic duality. In this work, we aim to investigate the solutions to the non-linear axion electrodynamics from SW axion model and propose relevant detection strategies for non-trivial axion-photon couplings. Based on the infrared Lagrangian of SW axion, we derive the electromagetic (EM) equations of motion. We also analyze the moduli space coordinate in SW theory and find out the reliabe parameter space. We then solve the resultant axion Maxwell equations with an external EM field. The observable axion-induced EM fields are obtained analytically and then numerically computed. Finally, we propose the detection strategy with an LC circuit and show the prospective sensitivity to SW axion-photon couplings.

Figures (11)

• Figure 1: The field structure for $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory. The red arrows represent the $\mathcal{N}=1$ sub-supersymmetry generator manifest in the $\mathcal{N}=1$ superfield formalism. The blue arrow indicates a global symmetry $SU(2)_R$ relating the fermions $\lambda,\psi$ within the $\mathcal{N}=2$ multiplet.
• Figure 2: The squared couplings $e^2(u)$ and $e_D^2(u)$ as a function of the coordinate $u$ in the electric frame and magnetic frame.
• Figure 3: BPS states mass spectrum on the Coulomb branch, illustrated for the monopole with $(g,q)=(1,0)$ and its first dyonic excitation with $(g,q)=(1,2)$. The masses of BPS states satisfy the central-charge formula $M_\text{BPS}=|A^v_D(u)g+A^v(u)q|$.
• Figure 4: Absolute values of the expansion terms for $\text{Re}\tau$ (left) and $\text{Im}\tau$ (right) on the real axis of $u$. The regions not shown here correspond to zero. The axion mass is fixed to $m_a=5\times 10^{-9}~\text{eV}$.
• Figure 5: Comparison between the exact $|\tau|$ (blue) and its approximate expansion (orange) for two different axion masses $m_a=2.48\times 10^{-10}~\text{eV}$ (left) and $2.48\times 10^{-11}~\text{eV}$ (right).