The nonlinear electrodynamics proposed by Bandos, Lechner, Sorokin and Townsend is a remarkable theory that unifies Maxwell, Bialynicki-Birula and ModMax theories, which are known theories invariant under conformal transformations and electromagnetic duality transformations. In the Bandos-Lechner-Sorokin-Townsend nonlinear electrodynamics, we calculate the energy flux density, dispersion relations, refractive indices, phase and group velocities of plane waves as well as the changes of the photon wavelength in the Compton scattering process in the presence of a constant uniform electromagnetic background. Our results are useful for testing and constraining this new theory of nonlinear electrodynamics.

China

Yang Shi

Towe Wang

Compton scattering in Bandos-Lechner-Sorokin-Townsend nonlinear electrodynamics

In six dimensions there exists a unique one-parameter family of nonlinear conformal electrodynamics for a chiral 2-form gauge field that includes (in a free-field limit) the linear chiral 2-form theory and is related, by dimensional reduction, to the four-dimensional ModMax electrodynamics. In this work, we present the first exact solutions of this theory in presence of gravity. In particular, we will consider plane wave, Robinson-Trautman, and self-dual dyonic string configurations, generalizing well-known solutions of this type in six-dimensional supergravities with linear chiral 2-form multiplets.

Türkiye

Nihat Sadik Deger

Italy

Ángel J. Murcia

Dmitri Sorokin

Waves and strings in an interacting conformal chiral 2-form theory in six dimensions

In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -like flows. To lay the background for this study, we elaborate on the relationship between different Lagrangian formulations of duality-invariant p-form theories and corresponding   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -like flows in various dimensions. To this end we propose a new formulation which (i) is a generalization of the four-dimensional construction by Ivanov, Nurmagambetov and Zupnik (INZ) and (ii) turns into the PST formulation upon integrating out an auxiliary self-dual field. We elucidate space-time covariant properties of the PST formulation by clarifying and making use of its relation to the INZ-type formulation and to a so-called “clone” construction.

United States

Christian Ferko

Australia

Sergei Kuzenko

Kurt Lechner

Gabriele Tartaglino-Mazzucchelli

Interacting chiral form field theories and   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -like flows in six and higher dimensions

We prove several universal properties of charge transport in generic conformal field theories holographic to nonminimal extensions of four-dimensional Einstein-Maxwell theory with exact electromagnetic duality invariance. First, we explicitly verify that the conductivity of these theories at zero momentum is a universal frequency-independent constant. Then, we derive the analytical expressions for the conductivities at nonzero momentum in any holographic duality-invariant theory for large frequencies and in the limit of small frequencies and momenta. Next, in the absence of terms that couple covariant derivatives of the curvature to gauge field strengths, two universal features are proven. On the one hand, it is shown that for a general-relativity neutral black-hole background the conductivities at any frequency and momentum are independent of the choice of duality-invariant theory, thus coinciding with those in the Einstein-Maxwell case. On the other hand, if higher-curvature terms affect the gravitational background, the conductivities get modified, but the contributions from nonminimal couplings of the gauge field to gravity are subleading. We illustrate this feature with an example.

Universal aspects of holographic quantum critical transport with self-duality

The Hamiltonian formulation for nonlinear chiral 2-form electrodynamics in six-dimensional Minkowski spacetime is used to show that small-amplitude plane-wave perturbations of a generic uniform constant ‘magnetic’ background exhibit trirefringence: all three independent wave-polarisations have distinct dispersion relations. While two coincide for Lorentz invariant theories, all three coincide uniquely for the chiral 2-form theory on the worldvolume of the M5-brane of M-theory. We argue that this is because, in this M-theory context, the waves propagate in a planar M5-M2-M2 bound-state preserving 16 supersymmetries. We also show how our results imply analogous results for nonlinear electrodynamics in a Minkowski spacetime of five and four dimensions.

Spain

Igor Bandos

United Kingdom

Paul Townsend

Trirefringence and the M5-brane

In this paper the harmonic superspace action of the tensor multiplet of N = (1, 0), d = 6 supersymmetry is constructed which in the bosonic limit reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field. The action involves, besides the potential containing the dynamical fields, also an auxiliary tensor multiplet and a set of analytic superfields with gauge PST scalar among them. For each of gauge symmetries of the PST action, a superfield analog is found. The equations of motion are calculated and it is shown that no extra degrees of freedom appear.

JINR

Nikolay Kozyrev

Supersymmetrizing the Pasti-Sorokin-Tonin action

We consider couplings of electrically and magnetically charged sources to the maximally symmetric nonlinear extension of Maxwell’s theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell’s electrodynamics. We find that, in contrast to generic models of nonlinear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon, are exact solutions of the ModMax equations of motion. We then study whether and how ModMax nonlinearity affects properties of electromagnetic interactions of charged objects, in particular the Lorentz force, the Coulomb law, the Lienard-Wiechert fields, Dirac’s and Schwinger’s quantization of electric and magnetic charges, and the Compton Effect. In passing we also present an alternative form of the ModMax Lagrangian in terms of the coupling of Maxwell’s theory to axion-dilaton-like auxiliary scalar fields which may be relevant for revealing the effective field theory origin of ModMax.

Pieralberto Marchetti

Andrea Sainaghi

Maximally symmetric nonlinear extension of electrodynamics and charged particles

We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. As an example, we perform the explicit dualisation of the <math><mrow><mi>OSp</mi></mrow><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> principal chiral model, and, whilst the target superspace of this model is a three-dimensional supergravity background, we find that its super non-Abelian T-dual falls outside the class of such backgrounds.

Daniele Bielli

Silvia Penati

Martin Wolf

Super non-Abelian T-duality

We give a prescription for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.

ModMax meets Susy

Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2n − 1)-form electrodynamics and chiral 2n-form electrodynamics in Minkowski spacetime of dimension D = 4n and D = 4n + 2, respectively. We exhibit a new family of chiral 2-form electrodynamics in D = 6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell’s equations. For n &gt; 1 we show that the chiral ‘strong-field’ 2n-form electrodynamics is related by dimensional reduction to a new Sl(2; ℝ)-duality invariant theory of (2n − 1)-form electrodynamics.