Abstract
We have obtained exact three dimensional BTZ type solutions with gauge fields, for string theory on a gauge symmetric gravitational background constructed from semi-simple extension of the Poincaré algebra (and the Maxwell algebra) in \(2+1\) dimensions. We have studied the models for two non-Abelian and Abelian gauge fields solutions and shown that the related sigma model for each of these backgrounds is a \(\mathrm{SL}(2,R)\) Wess–Zumino–Witten model and that these models are classically canonically equivalent. We have also obtained the dual solution for the Abelian case and by interpreting the new field strength tensors of the Abelian solution as electromagnetic field strength tensors shown that dual models coincide with the charged black string solution.
Highlights
The Maxwell [9,10] and semi-simple extension of Poincaré symmetries were applied to the construction of gauge symmetric gravity models in 3 + 1 [11,12] and 2 + 1 [13] dimensions
We show that two sigma models corresponding to the two nonAbelian and Abelian solutions are classically canonically equivalent
We have presented a 2 + 1 dimensional low energy string effective action containing gauge fields term which has a gauge symmetry coming from a semi-simple extension of the Poincaré (Maxwell) gauge group
Summary
The Maxwell [9,10] and semi-simple extension of Poincaré symmetries were applied to the construction of gauge symmetric gravity models in 3 + 1 [11,12] and 2 + 1 [13] dimensions (see [14,15]) We apply these symmetries to obtain an exact three dimensional black hole with gauge fields in string theory by introducing a new extended antisymmetric B-field and try to obtain some solutions for the equations of motion of the low energy string effective action [16,17]. Where xμ (μ = 0, 1, 2) and a, b = 0, 1, 2 are spacetime coordinates and Lie algebra indices, respectively Using these gauge fields (eμa(x), ωμa(x), Aμa(x)), one can write the new field strengths Fμνa as follows [13]: Fμνa = ∂[μ Aνa] +.
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