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ModMax meets Susy
TL;DR: In this article, the authors give a prescription for N=1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that relates to semi-classical unitarity.
Abstract: We give a prescription for 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.
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TL;DR: In this article, a new generalized ModMax model of nonlinear electrodynamics with four parameters is proposed, and it is shown that a singularity of the electric field at the center of point-like charged particles is absent.
21 citations
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TL;DR: In this paper, a duality-invariant model for an Abelian vector multiplet coupled to conformal supergravity was proposed. But this model is based on a Minkowski framework and does not capture the dynamics of the super-Yang-Mills (SYM) theory.
Abstract: We present $\mathcal{N}=2$ superconformal $\mathsf{U}(1)$ duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $\mathcal{N}=4$ $\mathsf{SU}(N)$ super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group $\mathsf{SU}(N)$ is spontaneously broken to $\mathsf{SU}(N-1) \times \mathsf{U}(1)$; and (ii) the dynamics is captured by a single $\mathcal{N}=2$ vector multiplet associated with the $\mathsf{U}(1)$ factor of the unbroken group. Additionally, a local $\mathsf{U}(1)$ duality-invariant action generating the $\mathcal{N}=2$ super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed $\mathsf{U}(1)$ duality-invariant $\mathcal{N}=1$ superconformal electrodynamics, we introduce its $\mathsf{SL}(2,{\mathbb R})$ duality-invariant coupling to the dilaton-axion multiplet.
1 citations
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TL;DR: In this article, a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$ in a conformally flat four-dimensional spacetime, was developed.
Abstract: We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalised by Ivanov and Zupnik. For each integer spin $s\geq 2$ we demonstrate the existence of families of conformal $\mathsf{U}(1)$ duality-invariant models, including a generalisation of the so called ModMax Electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2, n/2)$, for positive integers $m $ and $n$.
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TL;DR: In this paper, it was shown that a brane-like construction can be coupled to scalars in the same way to obtain a DBI-like action, and that Ra\~nada's knotted solutions are still valid both in the ModMax theory and in its precursor.
Abstract: Recently, the most general theory of electromagnetism invariant under duality and conformal invariance was written, and dubbed ModMax. It arises from a generalization of Born-Infeld (BI) theory by taking the infinite tension limit, $T\rightarrow\infty$. In this note we show that this generalization can be obtained from a brane-like construction, just like BI, and can thus be coupled to scalars in the same way to obtain a DBI-like action. All the BIon and catenoid solutions, and their interpolations, are still solutions of the generalized DBI-like action, suggesting that an interpretation within string theory could be possible. We also show that Ra\~nada's knotted solutions (with nonzero helicities) are still valid, both in the ModMax theory, and in its precursor.
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TL;DR: In this paper, a phenomenological Lagrangian is constructed to describe an interaction of the neutrino with itself and with other particles, based on the hypothesis that neutrinos are goldstone particles.
1,365 citations
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23 Feb 1995TL;DR: In this paper, the Poincar-D'e group, the Lorentz group and the supergroup of general coordinate transformations on R^Tp/q were studied.
Abstract: Preface. Mathematical background: The Poincar^D'e group, the Lorentz group Finite-dimensional representations of ^ISpin(3,1) The Lorentz algebra Two-component and four-component spinors Representations of the Poincar^D'e group Elements of differential geometry and gravity The conformal group The mass-shell field representation Elements of algebra with supernumbers Elements of analysis with supernumbers The supergroup of general coordinate transformations on R^Tp/q. Supersymmetry and superspace: Introduction: from R^Tp/q to supersymmetry Superalgebras, Grassmann-shells and super Lie groups The Poincar^D'e superalgebra Unitary representation of the Poincar^D'e superalgebra Real superspace R^T4/4 and superfields Complex superspace C^T4/2, chiral superfields and covariant derivatives The on-shell massive superfield representations The on-shell massless superfield representations From superfields to component fields The superconformal group. Field theory in superspace: Supersymmetric field theory Wess-Zumino model Supersymmetric nonlinear sigma-models Vector multiplet models Supersymmetric Yang-Mills theories Geometric approach to super Yang-Mills theories Classically equivalent theories. Quantized superfields: Picture-change operators Equivalence of component field and superfield perturbation theories Effective action (super) funtional The Wess-Zumino model: perturbative analysis Note about gauge theories Feynman rules for super Yang-Mills theories Renormalization Examples of counterterm calculations: an alternative technique Superfield effective potential. Superspace geometry of supergravity: Gauge group of supergravity and supergravity fields Superspace differential geometry Supergeometry with conformal supergravity constraints Prepotentials Einstein supergravity Prepotential de formations Supercurrent and supertrace Supergravity in components. Dynamics in supergravity: Pure supergravity dynamics Linearized supergravity Superg
640 citations
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CERN1
TL;DR: In this paper, the authors study the properties of interacting field theories which are invariant under duality rotations which transform a vector field strength into its dual, and show that the largest group for n interacting field strengths is the non-compact Sp(2 n,R), which has U( n ) as its maximal compact subgroup.
559 citations
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TL;DR: In this paper, it was shown that there is a function of one variable's worth of Lagrangians for a single Maxwell field coupled to gravity whose equations of motion admit electric-magnetic duality.
465 citations