Implications of Seiberg-Witten map on type-I superconductors

We incorporate the Seiberg-Witten map of noncommutative theory in the classical London theory of type-I superconductivity when an external magnetic field is applied. After defining the noncommutative Maxwell potentials, we derive the London equation for the supercurrent as a function of the noncommutative parameter, up to second order in gauge fields expansion. Keeping track of the effects of noncommutative gauge fields, we argue that noncommutative magnetic field effects can be cast in the permeability of the superconductor as an emergent property of the material, measurable in possible not-so-far ultra-high-energy experimental setups. Another consequence of the Seiberg-Witten map is the London penetration length that acquires corrections in the expansion. Also, we show that the flux quantization remains consistent relative to the commutative case. Our effective magnetic permeability and London penetration length reduce to the standard ones in the commutative limit.