Open accessJournal Article

# On p-form gauge theories and their conformal limits

02 Mar 2021-Journal of High Energy Physics (Springer Berlin Heidelberg)-Vol. 2021, Iss: 3, pp 1-42
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.

Topics: Gauge theory (62%), Conformal symmetry (57%), Minkowski space (54%) ... show more
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Abstract: We investigate the $T\bar{T}$-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 $T\bar{T}$ operator from a simple integration technique. We show that this flow equation is compatible with $T\bar{T}$ 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 $T\bar{T}$ 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 $T\bar{T}$ 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 $T\bar{T}$ operator and quadratic form of the energy-momentum tensor in $D\!=\!4$.

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7 Citations

Open accessJournal Article
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.

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7 Citations

Open accessJournal Article
Abstract: The present work deals with two different but subtilely related kinds of conformal mappings: Weyl rescaling in $d>2$ dimensional spaces and SO(2,d) transformations. We express how the difference between the two can be compensated by diffeomorphic transformations. This is well known in the framework of String Theory but in the particular case of $d=2$ spaces. Indeed, the Polyakov formalism describes world-sheets in terms of two-dimensional conformal field theory. On the other hand, B. Zumino had shown that a classical four-dimensional Weyl-invariant field theory restricted to live in Minkowski space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS). This allows us to assert that a classical $SO(2,d)$-invariant field does not distinguish, at least locally, between two different $d$-dimensional CFSs.

6 Citations

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Igor A. Bandos1, Igor A. Bandos2, Kurt Lechner3, Dmitri Sorokin3  +1 moreInstitutions (4)
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.

4 Citations

Open accessJournal Article
Abstract: We explore the properties of polynomial Lagrangians for chiral p-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general p-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

Topics: Polynomial (56%), , Differential form (51%)

3 Citations

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96 results found

Open accessBook
01 Jan 1974-
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.

10,748 Citations

Journal Article
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.

Topics: , , Dirac bracket (53%)

1,661 Citations

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Mary K. Gaillard, Bruno Zumino1Institutions (1)
21 Dec 1981-Nuclear Physics
Abstract: We study the properties of interacting field theories which are invariant under duality rotations which transform a vector field strength into its dual. We consider non-abelian duality groups and find 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. We show that invariance of the equations of motion requires that the lagrangian change in a particular way under duality. We use this property to demonstrate the existence of conserved currents, the invariance of the energy-momentum tensor and the S -matrix, and also in the general construction of the lagrangian. Finally we comment on the existence of zero-mass spin-one bound states in N =8 supergravity, which possesses a non-compact E 7 dual invariance.

517 Citations

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Igor A. Bandos1, Kurt Lechner2, Aleksei Nurmagambetov1, Paolo Pasti2  +2 moreInstitutions (2)
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.

Topics: Brane (50%)

483 Citations

Open accessJournal Article
Gary W. Gibbons1, D.A. Rasheed1Institutions (1)
06 Nov 1995-Nuclear Physics
Abstract: We show 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. Such Lagrangians are given by solutions of the Hamilton-Jacobi equation for timelike geodesics in Witten's two-dimensional black hole. Among them are the Born-Infeld Langrangian which arises in open string theory. We investigate the effect of the axion and the dilaton in the open superstring case and we show that this theory loses its electric-magnetic duality invariance when one considers the higher order electromagnetic field terms. We discuss some implications for black holes in string theory and an extension to 2 k -forms in 4 k spacetime dimensions.

430 Citations

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