Introductory Notes on Non‐linear Electrodynamics and its Applications

Abstract

In 1933-1934 Born and Infeld constructed the first non-linear generalization of Maxwell's electrodynamics that turned out to be a remarkable theory in many respects. In 1935 Heisenberg and Euler computed a complete effective action describing non-linear corrections to Maxwell's theory due to quantum electron-positron one-loop effects. Since then, these and a variety of other models of non-linear electrodynamics proposed in the course of decades have been extensively studied and used in a wide range of areas of theoretical physics including string theory, gravity, cosmology and condensed matter (CMT). In these notes I will overview general properties of non-linear electrodynamics and particular models which are distinguished by their symmetries and physical properties, such as a recently discovered unique non-linear modification of Maxwell's electrodynamics which is conformal and duality invariant. I will also sketch how non-linear electromagnetic effects may manifest themselves in physical phenomena (such as vacuum birefringence), in properties of gravitational objects (e.g. charged black holes) and in the evolution of the universe, and can be used, via gravity/CMT holography, for the description of properties of certain conducting and insulating materials.

On the Classical Integrability of Root-$T \overline{T}$ Flows

“…For instance, although it still admits plane waves such as φ µ = n µ e ipν σ ν as solutions, linear combinations of plane waves are not solutions. This is very similar to ModMax theories [12][13][14][15] (see [16] for a review) and in fact the action (1.10) can be obtained as the dimensional reduction of the ModMax action [10]. This non-linear and non-analytic structure makes the quantisation of Root-T T deformed theories, as well as of ModMax theories, an outstanding problem.…”

“…An important outstanding question is how to quantise Root-T T theories (as well as ModMax theories [12][13][14][15][16]). It might be worth undertaking this study on some particular examples which are integrable.…”

“…[26,31]). 16 On top of the obvious physical interest of this study, this would probably allow for the perturbative quantisation of the deformed models once a suitable gauge is fixed. In fact, we would expect the gaugefixed theory to become analytic in the small-field expansion of the transverse modes of the string (like it is the case for the Nambu-Goto action).…”

“…15 In fact, the introduction of the WZ term in the semi-symmetric sigma model by [31] has been a key ingredient in the development of integrability for AdS3/CF T2 [55,56]. 16 It is worth remarking that, even for sigma-model actions, κ-symmetry does not imply Weyl invariance of the action [57], see e.g. [58][59][60][61] for some examples.…”

ModMax meets GCA

“…Notable examples of NLEDs include the famous Born-Infeld theory [2], a crucial component of String Theory in the study of D-branes [3], that makes sure to keep self energy of point particles finite. Other well studied examples include actions involving various functionals of the field tensor and a nice review for these constructions can be found in [4] and references therein. But the main caveat lies in the problem that a generic NLED in 4d is not conformally invariant, neither is it invariant under Hodge duality rotations.…”