The Dual Embedding Method in D = 3

Physics Letters B, 2018

We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n > 3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partially-massless case, where the duality has been previously discussed in covariant form only at the level of the equations of motion. The nature of the dual graviton is therefore clarified for all values of the mass and of the cosmological constant.

Physical Review D, 1996

The technique of extended dualization developed in this paper is used to bosonize quantized fermion systems in arbitrary dimension D in the low energy regime. In its original (minimal) form, dualization is restricted to models wherein it is possible to define a dynamical quantized conserved charge. We generalize the usual dualization prescription to include systems with dynamical non-conserved quantum currents.

Physical Review D, 2021

Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space IR 3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ansätz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ansätz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields.

Physical Review D, 2010

2006

Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual model interacting with a matter superfield, which turns out to be not the Maxwell-Chern-Simons theory coupled to matter, but a more complicated model, with a "restricted" gauge invariance. We stress the difficulties in dualizing the self-dual field coupled to matter into a theory with complete gauge invariance. After that, we show that the duality, achieved between these two models at the tree level, also holds up to the lowest order quantum corrections. * Electronic address: alysson,mgomes,[email protected] † Electronic address: jroberto,[email protected]

Il Nuovo Cimento A, 1979

Physics Letters B, 2011

Using the compatibility of the DBI and the Chern-Simons actions with the Tduality transformations, the curvature corrections to these actions have been recently extended to include the quadratic B-field couplings at order O(α ′2 ). In this paper, we use the compatibility of the couplings on D 3 -brane with the S-duality to find the nonlinear RR couplings at order O(α ′2 ). We confirm the quadratic RR couplings in the DBI part with the disk-level scattering amplitude. Using the regularized nonholomorphic Eisenstein series E 1 , we then write the results in SL(2, Z) invariant form.

International Journal of Modern Physics A, 2011

We study the connection, at the quantum level, between (d = 2+1)-dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity ±2 massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing us to establish dual maps among relevant vacuum expectation values. We check consistency of these vacuum expectation values with the gauge invariance gained in each mapping.

We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed in previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to analyze compatibility and extend a symmetry from one sector to another. * Electronic address: [email protected] arXiv:1411.4909v1 [hep-ph] 18 Nov 2014 2 discrete symmetries, the Smith Normal Form (SNF) method has been used successfully in various contexts to find discrete symmetries arising from the breaking of continuous gauge symmetries [6], find useful R-symmetries in supersymmetric extensions of the SM [7], justify two-zero textures in the neutrino mass matrix with symmetries [8] and classify abelian symmetries in multi-Higgs-doublets models . The latter class of models will be the focus of this work.

Nuclear Physics B, 2010

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral n-form gauge theories, for n = 2p in D = 4p + 2 dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into (D − 1) dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into D ′ and D ′′ = D − D ′ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.

Physical Review D, 1999

We show that the connection between partial breaking of supersymmetry and nonlinear actions is not accidental and has to do with constraints that lead directly to nonlinear actions of the Born-Infeld type. We develop a constrained superfield approach that gives a universal way of deriving and using these actions. In particular, we find the manifestly supersymmetric form of the action of the 3-brane in 6-dimensional space in terms of N = 1 superfields by using the tensor multiplet as a tool. We explain the relation between the Born-Infeld action and the model of partial N = 2 supersymmetry breaking by a dual D-term. We represent the Born-Infeld action in a novel form quadratic in the gauge field strengths by introducing two auxiliary complex scalar fields; this makes duality covariance and the connection with the N = 1 supersymmetric extension of the action very transparent. We also suggest a general procedure for deriving manifestly duality symmetric actions, explaining in a systematic way relations between previously discussed Lorentz-covariant and noncovariant actions.

Advances in High Energy Physics, 2016

We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions,ω1(|ϕ|)andω(|ϕ|), which split the kinetic term of the Higgs field,|Dμϕ|2→ω1(|ϕ|)|D0ϕ|2-ω(|ϕ|)|Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whetherω(|ϕ|)∝β|ϕ|2β-2withβ≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing functionω1(|ϕ|)which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual|ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.

2021

In the old spirit of Kaluza-Klein, we consider a spacetime of the form P = M4×K, where K is the Lie group SU(3) equipped with a left-invariant metric that is not fully rightinvariant. This metric has a U(1)× SU(3) isometry group, corresponding to the massless gauge bosons, and depends on a parameter φ with values in a subspace of su(3) isomorphic to C. It is shown that the classical Einstein-Hilbert Lagrangian density RP − 2Λ on the higher-dimensional manifold P , after integration over K, encodes not only the Yang-Mills terms of the Standard Model over M4, as in the usual Kaluza-Klein calculation, but also a kinetic term |dφ| identical to the covariant derivative of the Higgs field. For Λ in an appropriate range, it also encodes a potential V (|φ|) having absolute minima with |φ0| 6= 0, thereby inducing mass terms for the remaining gauge bosons. The classical masses of the resulting Higgs-like and gauge bosons are explicitly calculated as functions of the vacuum value |φ0| in the s...

2016

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral n-form gauge theories, for n = 2p in D = 4p + 2 dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into (D − 1) dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into D ′ and D ′′ = D − D ′ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.

Physics Letters B, 1996

We consider E 8 × E 8 heterotic compactifications on K3 and K3 ×T 2 . The idea of heterotic/heterotic duality in D = 6 has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both E 8 's . We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to D = 4, we find that the duals in the DMW case correspond to N = 2 models in which the β-function of the different group factors verify β α = 12 whereas the asymmetric solutions that we propose have β α = 24. We check the consistency of these dualities by studying the different large T, S limits of the gauge kinetic function. Dual N = 1, D = 4 models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.