Abstract:The quantum actions of the (4,4) supersymmetric nonlinear sigma
model and its dual in the Abelian case are constructed by using the
background superfield method. The propagators of the quantum superfield
and its dual and the gauge-fixing actions of the original and dual (4,4)
supersymmetric sigma models are determined. On the other hand, the BRST
transformations are used to obtain the quantum dual action of the (4,4)
supersymmetric nonlinear sigma model in the sense of a Poisson-Lie
T-duality.
“…18) and the decomposition of a general group element we choose as 19) which is equivalent to a change of coordinates x 1 = −y 1 , x 2 = . .…”
Section: An Explicit Example Duals Of Bianchi Vmentioning
confidence: 99%
“…Therefore a mistake in the dilaton transformation formula was not discovered. Further quantum properties were studied and discussed in [15,16,17,18,19]. By now Poisson-Lie Tduality is quite well studied and generalizations have been made in several directions.…”
Abstract:We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the litterature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants.
“…18) and the decomposition of a general group element we choose as 19) which is equivalent to a change of coordinates x 1 = −y 1 , x 2 = . .…”
Section: An Explicit Example Duals Of Bianchi Vmentioning
confidence: 99%
“…Therefore a mistake in the dilaton transformation formula was not discovered. Further quantum properties were studied and discussed in [15,16,17,18,19]. By now Poisson-Lie Tduality is quite well studied and generalizations have been made in several directions.…”
Abstract:We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the litterature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants.
“…The quantum setting has been treated in [2,3,4], of which the most relevant reference for our discussion is the path-integral treatment in [3]. Supersymmetric extensions have been discussed in [5,6,7,8,9].…”
We extend the path-integral formulation of Poisson-Lie duality given in [3] to N = 1 supersymmetric σ-models. Using an explicit representation of the generators of the Drinfel'd double corresponding to G⊗U (1) dimG we discuss an application to non-abelian duality. The paper also contains the relevant background and some comments on Poisson-Lie duality. * s.e.hjelmeland@fys.uio.no † ul@physto.se
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