Duality Invariance Research Articles

Nonlinear arcsin‐electrodynamics and asymptotic Reissner‐Nordström black holes

A model of nonlinear electrodynamics with the Lagrangian density is proposed. The scale invariance and the dual invariance of electromagnetic fields are broken in the model. In the limit one comes to Maxwell's electrodynamics and the scale and dual invariances are recovered. We investigate the effect of coupling electromagnetic fields with the gravitational field. The asymptotic black hole solution is found which is similar to the Reissner‐Nordström solution. We obtain corrections to Coulomb's law and to the Reissner‐Nordström solution in the model proposed. The existence of the regular asymptotic at was demonstrated. The mass of the black hole is calculated possessing the electromagnetic origin. It was shown that there are not superluminal fluctuations and principles of causality and unitarity take place.

Nilpotent chiral superfield in N = 2 $$ \mathcal{N}=2 $$ supergravity and partial rigid supersymmetry breaking

In the framework of N=2 conformal supergravity in four dimensions, we introduce a nilpotent chiral superfield suitable for the description of partial supersymmetry breaking in maximally supersymmetric spacetimes. As an application, we construct Maxwell-Goldstone multiplet actions for partial N=2 --> N=1 supersymmetry breaking on R x S^3, AdS_3 x S^1 (or its covering AdS_3 x R), and a pp-wave spacetime. In each of these cases, the action coincides with a unique curved-superspace extension of the N=1 supersymmetric Born-Infeld action, which is singled out by the requirement of U(1) duality invariance.

Chiral theories of class S $$ \mathcal{S} $$

We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. We explicitly check this from the 't Hooft anomalies of the global symmetries and central charges.

Duality invariance in massive theories

In this work, we show that duality symmetry can be implemented for massive theories at the level of the action, whenever we can formulate appropriate gauge invariant actions. For a massive vectorial field, we use a known gauge invariant description, while for a massive graviton, we introduce a novel gauge invariant action in order to show duality invariance.

Manifest duality invariance for the partially massless graviton

For a special value of the mass, a massive graviton on de Sitter space acquires an enhanced scalar gauge symmetry, and is called partially massless. The partially massless graviton possesses a duality invariance akin to electromagnetic duality. We display this duality in its manifestly local and covariant form, in which it acts to interchange the first-order field equations and Bianchi identities of a gauge invariant field strength.

Duality invariance of [formula omitted] fermions in AdS

We show that in D=4 AdS, s≥3/2 partially massless (PM) fermions retain the duality invariances of their flat space massless counterparts. They have tuned ratios m2/M2≠0 that turn them into sums of effectively massless unconstrained helicity ±(s,⋯,32) excitations, shorn of the lowest (non-dual) helicity ±12-rung and — more generally — of succeeding higher rung as well. Each helicity mode is separately duality invariant, like its flat space counterpart.

Supersymmetric electric-magnetic duality of hypergravity

Hypergravity is the theory in which the graviton, of spin-2, has a supersymmetric partner of spin-$5/2$. There are ``no-go'' theorems that prevent interactions in these higher spin theories. However, it appears that one can circumvent them by bringing in an infinite tower of higher spin fields. With this possibility in mind, we study herein the electric-magnetic duality invariance of hypergravity. The analysis is carried out in detail for the free theory of the spin-$(2,5/2)$ multiplet, and it is indicated how it may be extended to the infinite tower of higher spins. Interactions are not considered. The procedure is the same that was employed recently for the spin-$(3/2,2)$ multiplet of supergravity. One introduces new potentials (``prepotentials'') by solving the constraints of the Hamiltonian formulation. In terms of the prepotentials, the action is written in a form in which its electric-magnetic duality invariance is manifest. The prepotential action is local, but the spacetime invariance is not manifest. Just as for the spin-2 and spin-$(3/2,2)$ cases, the gauge symmetries of the prepotential action take a form similar to those of the free conformal theory of the same multiplet. The automatic emergence of gauge conformal invariance, out of demand for manifest duality invariance, is yet more evidence of the subtle interplay between duality invariance and spacetime symmetry. We also compare and contrast the formulation with that of the analogous spin-$(1,3/2)$ multiplet.

Self-dual $ \mathcal{N} $ = 2 Born-Infeld theory through auxiliary superfields

There is an evidence that the N=2 Born-Infeld theory with spontaneously broken N=4 supersymmetry exhibits self-duality. We perform a further check of this hypothesis by constructing a new representation for the N=2 Born-Infeld action through the auxiliary chiral superfield U. In such a formulation, self-duality is equivalent to U(1) invariance of the U interaction. We explicitly calculate the auxiliary interaction up to the 10th order and show its U(1) duality invariance, thus proving that the original action is self-dual to the same order. We also suggest a new method of recursive computation of the N=2 Born-Infeld action in the standard formulation, based solely on the nonlinear realization of the N=4 central charge on the N=2 superfield strengths W, \bar W.

Angle Estimation in Bistatic MIMO Radar System based on Unitary ESPRIT

Angle estimation for a bistatic MIMO radar system based on Unitary Esprit techniques is proposed in this study. The algorithm exploits the dual invariance in distinct directions and centrosymmetry of the bistatic MIMO radar system to provide real valued computations and automatically paired Directions of Departures (DOD) and Directions of Arrival (DOA) estimates. Simulation results show the effectiveness of this method.

Chern Simons duality with a fundamental boson and fermion

We compute the thermal free energy for all renormalizable Chern Simon theories coupled to a single fundamental bosonic and fermionic field in the 't Hooft large N limit. We use our results to conjecture a strong weak coupling duality invariance for this class of theories. Our conjectured duality reduces to Giveon Kutasov duality when restricted to {\cal N}=2 supersymmetric theories and to an earlier conjectured bosonization duality in an appropriate decoupling limit. Consequently the bosonization duality may be regarded as a deformation of Giveon Kutasov duality, suggesting that it is true even at large but finite N.

Self-dual supersymmetric nonlinear sigma models

In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).

Invariants and divergences in half-maximal supergravity theories

Abstract The invariants in half-maximal supergravity theories in D = 4, 5 are discussed in detail up to dimension eight (e.g. R 4). In D = 4, owing to the anomaly in the rigid SL(2, $ \mathbb{R} $ ) duality symmetry, the restrictions on divergences need careful treatment. In pure $ \mathcal{N}=4 $ supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L ≥ 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same conclusion when vector multiplets are present because of the appearance of F 4 terms in the SL(2, $ \mathbb{R} $ ) anomaly. In D = 5 there is no one-loop anomaly in the shift invariance of the dilaton, and we argue that this implies finiteness at two loops, again subject to the assumption that 16 supercharges can be preserved off-shell.

PM=EM? Partially massless duality invariance

In d=4 de Sitter space, novel conformally invariant photon-like theories consistently couple to charged matter. We show that these higher spin, maximal depth, partially massless systems enjoy a Maxwellian, "electric-magnetic" duality.

Duality rotations in supersymmetric nonlinear electrodynamics revisited

We revisit the U(1) duality-invariant nonlinear models for N=1 and N=2 vector multiplets coupled to off-shell supergravities. For such theories we develop new formulations which make use of auxiliary chiral superfields (spinor in the N=1 case and scalar for N=2) and are characterized by the remarkable property that U(1) duality invariance is equivalent to the manifest U(1) invariance of the self-interaction. Our construction is inspired by the non-supersymmetric approach that was proposed by Ivanov and Zupnik a decade ago and recently re-discovered in the form of twisted self-duality.

Anomalies and divergences in [formula omitted] supergravity

The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L⩾2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that, subject to the assumption that a full off-shell quantisation formalism exists, such marginal invariants are not allowable as counterterms.

Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity

For the free massless spin-one and spin-two field theories one may write the action in a form which is manifestly invariant under electric-magnetic duality. This is achieved by introducing new potentials through solving the constraints of the Hamiltonian formulation. The price for making electric-magnetic duality invariance manifest through this direct procedure is losing manifest Lorentz invariance. Both theories admit supersymmetric extensions, which make the bosonic fields and their corresponding fermionic partners to be parts of the same geometrical object, a supermultiplet. We present in this paper the supersymmetric extension of the manifestly electric-magnetic duality invariant actions for the photon and the photino; and for the graviton and the gravitino. In each case the spinor fields transform under electric-magnetic duality in a chiral manner. For the spin-tree-half field, which possesses a gauge invariance, it is necessary to bring in a spinor ``prepotential.'' As in previous cases the introduction of additional potentials to solve the constraints increases the number of gauge invariances of the action, thus keeping the number of degrees of freedom unaltered. The similarity in the formulations for the photon-photino and graviton-gravitino systems is remarkable.

New E 7(7) invariants and amplitudes

We construct a new class of manifest E77 duality invariants, which generalize the Cartan quartic invariant, familiar from studies of the black hole entropy. The new ones, being four-linear, are designed for studies of the four-vector amplitudes and to be used, upon supersymmetrization, as initial sources of deformation for the non-linear higher-derivative generalizations of the linear twisted self-duality condition. We show, however, that the new invariants are inconsistent with the expected UV divergent amplitudes in extended supergravities with non-degenerate duality groups of type E7. When E77 degenerates into U(1) the new invariants reproduce the recently discovered source of deformation for the Born-Infeld duality invariant model with higher derivatives relevant to UV divergences of the D3 brane action. These facts may explain the UV properties of perturbative supergravity.

Macroscopic quantum electrodynamics in nonlocal and nonreciprocal media

We formulate macroscopic quantum electrodynamics in the most general linear, absorbing media. In particular, Onsager reciprocity is not assumed to hold. The field quantization is based on the source-quantity representation of the electromagnetic field in terms of the dyadic Green's tensor. For media with a nonlocal response, a description in terms of a complex conductivity tensor is employed. As an alternative description, we introduce the permittivity, permeability and magnetoelectric susceptibilities to obtain an explicitly duality-invariant scheme. We find that duality invariance only holds as a continuous symmetry when nonreciprocal responses are allowed for.

FlippedSL(2,R)duality in five-dimensional supergravity

The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two $U(1)$ gauge fields and the dimensionally reduced equations of motion have $SL(2,\mathbb{R})/SO(2)$-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in which the field equations have $SL(2,\mathbb{R})/SO(1,1)$ invariance. In the timelike case, we develop a new duality transformation technique, while in the spacelike case we have done that in the previous work. As an example, by applying it to the Rasheed solutions, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. In general, in contrast to the spacelike case, the resulting dimensionally reduced solution includes the so-called NUT (Newman, Unti, and Tamburino) parameter, and therefore from a four-dimensional point of view, such a spacetime is not asymptotically flat. However, it is shown that in some special cases, it can describe ordinary Kaluza-Klein black holes.

Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.