On p-form gauge theories and their conformal limits
TL;DR: In this article, the relationship between nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits is clarified, with a focus on duality invariant (2n − 1)-form electdynamics and chiral 2n-forms in Minkowski spacetime.
Abstract: 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 > 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.
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TL;DR: In this paper , the deformation of the ModMax theory was investigated under the flow invariance for Born-Infeld theories, and it was shown that the deformed theory is the generalized non-linear Born-infeld electrodynamics.
61 citations
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TL;DR: In this paper, a supersymmetrization of any four-dimensional nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that relates to semi-classical unitarity is proposed.
Abstract: We give a prescription for $$ \mathcal{N} $$
= 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.
44 citations
DOI•
TL;DR: In this article , it was shown that the ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equationdriven by a quadratic combination of stress-energy tensors.
Abstract: We show that the recently introduced ModMax theory of electrodynamics
and its Born-Infeld-like generalization are related by a flow equation
driven by a quadratic combination of stress-energy tensors. The operator
associated to this flow is a 4d4d
analogue of the T\overline{T}TT¯
deformation in two dimensions. This result generalizes the observation
that the ordinary Born-Infeld Lagrangian is related to the free Maxwell
theory by a current-squared flow. As in that case, we show that no
analogous relationship holds in any other dimension besides
d=4d=4.
We also demonstrate that the \mathcal{N}=1𝒩=1
supersymmetric version of the ModMax-Born-Infeld theory obeys a related
supercurrent-squared flow which is formulated directly in
\mathcal{N} = 1𝒩=1
superspace.
23 citations
TL;DR: In this article , the authors propose a solution to solve the problem of the problem: this article ] of "uniformity" and "uncertainty" of the solution.
Abstract: ,
23 citations
TL;DR: In this article, a flow equation for non-linear electrodynamic theories in D(2n)-dimensional spacetime was derived from a simple integration technique, and it was shown that this flow equation is compatible with the classical free action in higher dimensions.
Abstract: We investigate the $$ T\overline{T} $$
-like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$
operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$
deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$
flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$
operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$
= 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$
operator and quadratic form of the energy-momentum tensor in D = 4.
20 citations
References
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Book•
01 Jan 1974
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Abstract: Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid bodies. Part 3 Hamiltonian mechanics: differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
11,008 citations
TL;DR: The equations of dynamics were put into a general form by Lagrange, who expressed them in terms of a set of generalized coordinates and velocities as discussed by the authors, and an alternative general form was later given by Hamilton, in the form of coordinates and momenta.
Abstract: 1. Introduction. The equations of dynamics were put into a general form
by Lagrange, who expressed them in terms of a set of generalized coordinates
and velocities. An alternative general form was later given by Hamilton, in
terms of coordinates and momenta. Let us consider the relative merits of the
two forms.
1,725 citations
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
TL;DR: In this paper, the authors propose a complete, $d\phantom{\rule{0ex}{0ex}} = \phantom''rule {0ex}0ex''6$ covariant and kappa-symmetric, action for the $M$ theory five-brane propagating in a supergravity background, which can be used for studying corresponding dualities and nonperturbative aspects of these theories.
Abstract: We propose a complete, $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6$ covariant and kappa-symmetric, action for the $M$ theory five-brane propagating in $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11$ supergravity background. This opens a direct way of relating a wide class of super- $p$-brane solutions of string theory with the five-brane of $M$ theory, which should be useful for studying corresponding dualities and nonperturbative aspects of these theories.
501 citations
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