2020/02/29 by Ali Eghbali, Reza Naderi, Adel Rezaei-Aghdam
Mathematics · Physics and Astronomy · #Abelian group #Action (physics) #Axion #Black Holes and Theoretical Physics #Dilaton #Dual polyhedron #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Space (punctuation) #String (physics) #String theory #hep-th
paper · pdf · doi:10.1140/epjc/s10052-020-08797-9
published as Eur. Phys. J. C 81, 68(2021) · 44 pages; two references and three Tables added
openalex created_date 2020/02/07 · openalex publication_date 2021/01/01 · arxiv created 2021/01/21 · arxiv updated 2021/01/25 · openalex updated_date 2026/08/05
Abstract Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in α ' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>α</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to α ' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>α</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> -corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as A2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , A2 ⊕ A1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>⊕</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> and SL(2, \mathbb R) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . In this way, the PL self-duality of AdS3 × \mathbb R <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> space is discussed.