Topological sectors and gauge invariance in massive vector-tensor theories in D ≥ 4

Arias, Pio J.; Leal, Lorenzo

doi:10.1016/s0370-2693(97)00518-2

Cited by 5 publications

(2 citation statements)

References 40 publications

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“…In this sense, this type of dual projection method enables to isolate the physical content of the theory in a gauge-invariant way, the entire gauge-variant contributions residing only in the second sector of the action which reduces to a pure topological field theory. The relevance of our conclusions for general TMGT is confirmed by some results already achieved for particular types of TMGT within the path-integral framework [10,19].…”

Section: Discussionsupporting

confidence: 82%

“…This decoupled TFT sector thus ensures that the gauge structure of the original theory is preserved through dual factorization. Moreover, as in the MCS case, the presence of this topological term, so far hardly evoked in the literature for very particular types of TMGT [19], has dramatic consequences. First, as described in [6] within the context of canonical quantization, this term controls the degeneracy of the physical spectrum of the original TMGT through topological invariants of the space manifold when it is of non-trivial topology.…”

Section: The First Contribution S Dyn [E G] Consisting Of Dynamical G...mentioning

confidence: 99%

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Topologically massive gauge theories and their dual factorized gauge-invariant formulation

Bertrand¹,

Govaerts²

2007

J. Phys. A: Math. Theor.

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There exists a well-known duality between the Maxwell-Chern-Simons theory and the "self-dual" massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the "master" theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.

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Section: Discussionsupporting

confidence: 82%

Section: The First Contribution S Dyn [E G] Consisting Of Dynamical G...mentioning

confidence: 99%

Topologically massive gauge theories and their dual factorized gauge-invariant formulation

Bertrand¹,

Govaerts²

2007

J. Phys. A: Math. Theor.

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Duality and massive gauge-invariant theories

Harikumar

Sivakumar

1998

Phys. Rev. D

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Two different massive gauge invariant spin-one theories in 3 + 1 dimensions, one Stuckelberg formulation and the other 'B ∧ F ' theory, with Kalb-Ramond field are shown to be related by duality. This is demonstrated by gauging the global symmetry in the model and constraining the corresponding dual field strength to be zero by a Lagrange multiplier, which becomes a field in the dual theory. Implication of this equivalence to the 5 dimensional theories from which these theories can be obtained is discussed. The self-dual Deser-Jackiw model in 2 + 1 dimensions, is also shown to result by applying this procedure to Maxwell-Chern-Simon theory.

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Topological mass mechanism from dimensional reduction

Khoudeir

1998

Phys. Rev. D

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We show that the Abelian topological mass mechanism in four dimensions, described by the CremmerSherk action, can be obtained from dimensional reduction in five dimensions. Starting from a gauge invariant action in five dimensions, where the dual equivalence between a massless vector field and a massless secondrank antisymmetric field is established, the dimensional reduction is performed keeping only one massive mode. ͓S0556-2821͑98͒03324-4͔ PACS number͑s͒: 11.10. Lm, 11.25.Mj Several alternatives of the Higgs mechanism, based on the coupling of vector fields with antisymmetric fields through topological terms, have been developed in the last years. In particular, the Abelian Cremmer-Sherk theory ͓1͔ has been studied extensively ͓2͔ as an appropriate model for this proposal. Its non-Abelian extension is a Freedman-Townsend theory ͓3͔ that can be derived using the self-interaction mechanism ͓4͔. Also, other attempts to search a non-Abelian generalization have been formulated ͓5͔; however, serious problems with renormalizability in all these non-Abelian generalizations has been pointed out in Ref.͓6͔. An interesting aspect is the fact that the Cremmer-Sherk theory is related by duality ͓7,4͔ with the Kalb-Ramond theory ͓8͔, where the latter can be obtained by dimensional reduction of the second-rank antisymmetric theory in five dimensions keeping only one massive mode ͓9,10͔. It is worth recalling that the Kalb-Ramond theory provides mass in a nontopological way and can be understood as the resulting theory after condensation of magnetic monopoles in four dimensions QED ͓11͔. In this Brief Report, we show that it is possible to obtain the Cremmer-Sherk theory in four dimensions by dimensional reduction, despite Barcelos-Neto's claim that the Cremmer-Sherk theory cannot come from dimensional reduction of any gauge theory in five dimensions ͓10͔.Let us describe briefly the dual equivalence between the Cremmer-Sherk and Kalb-Ramond theories in four dimensions. The Cremmer-Sherk action, which provides mass to spin-1 fields without spoil gauge invariance, is written down asmn Ϫ 1 12 H mnp H mnp Ϫ 1 4 ⑀ mnpq B mn F pqͬ , ͑1͒ where F mn ϵ‫ץ‬ m A n Ϫ‫ץ‬ n A m and H mnp ϵ‫ץ‬ m B np ϩ‫ץ‬ n B pm ϩ‫ץ‬ p B mn are the field strengths associated with the A m and B mn fields. This action is invariant under gauge transformations: ␦A m ϭ‫ץ‬ m and ␦B mn ϭ‫ץ‬ m n Ϫ‫ץ‬ n m . We observe that this action has global symmetries, for instance, A m →A m Ϫ⑀ m , with ⑀ m the global parameter. A useful way to obtainthe dual theory relies on gauging this local symmetry ͓12͔ by introducing an antisymmetric field a mn , such that the field strength F mn is modified by F mn ϵ‫ץ‬ m A n Ϫ‫ץ‬ n A m ϩ 1 2 (a mn Ϫa nm ) and adding a BF term, which assures the nonpropagation of a mn . Then, we have the following action:and we now have new gauge symmetries, given by ␦A m ϭϪ⑀ m(x) , ␦a m ϭ‫ץ‬ m ␣, and ␦a mn ϭ‫ץ‬ m ⑀ n Ϫ‫ץ‬ n ⑀ m , which allow us to fix the gauge A m ϭ0. After fixing this gauge, the action becomes1 4 a mn a mn Ϫ 1 12 H mnp H mnp Ϫ 1 4 ⑀...

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Topological sectors and gauge invariance in massive vector-tensor theories in D ≥ 4

Cited by 5 publications

References 40 publications

Topologically massive gauge theories and their dual factorized gauge-invariant formulation

Topologically massive gauge theories and their dual factorized gauge-invariant formulation

Duality and massive gauge-invariant theories

Topological mass mechanism from dimensional reduction

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