In this thesis we take a superspace perspective on Tduality, focusing on sigma models defined on background geometries that are constructed in terms of Lie supergroups. We briefly review Abelian bosonic and fermionic Tduality and the derivation of Buscher’s rules, moving then to the dualisation of principal chiral models on group manifolds. Extension of the latter to the case of supergroup manifolds represents the starting point of our analysis, which features an extended discussion about the explicit dualisation of the supergroup OSp(12). While the initial model represents an appropriate threedimensional supergravity background, the Tdual one hints in the opposite direction, as the ansatz adopted to construct the dual veilbeine fails to satisfy the supegravity torsion constraints. Such result, together with the complexity of the ansatzbased approach, suggests that a more abstract and general point of view should be taken on the dualisation procedure. This represents the next step of our analysis and allows a simpler dualisation of principal chiral models and a clearer argument that the above Tdual model falls outside the class of threedimensional supergravity backgrounds. Extension of the dualisation procedure to symmetric and semisymmetric coset space sigma models based on Lie supergroups G/H is also favored by the more abstract perspective, which allows to recover the wellknown exchange of equations of motion and Maurer Cartan equations typically observed in purely bosonic settings, hence leading to the construction of a dual Lax connection and ensuring preservation of classical integrability. While dualisation of principal chiral models can be performed in full generality, for coset models the procedure might be affected by impediments appearing in the process of integrating out the gauge fields in favor of the dual variables, and thus requires a case by case analysis. We proceed by solving those gauge fields equations of motion that allow for a general solution, thus confining the potential obstruction to a single equation, whose solvability depends on the invertibility of two linear operators. We conclude by discussing two explicit examples in which dualisation goes through, the first based on the symmetric space SO(4)/SO(3), wellknown for its dualisability, the second on the semisymmetric space OSp(12)/SO(1,1) already approached in the literature from the point of view of holography and representing a GreenSchwarzlike sigma model satisfying the supergravity torsion constraints.
In this thesis we take a superspace perspective on Tduality, focusing on sigma models defined on background geometries that are constructed in terms of Lie supergroups. We briefly review Abelian bosonic and fermionic Tduality and the derivation of Buscher’s rules, moving then to the dualisation of principal chiral models on group manifolds. Extension of the latter to the case of supergroup manifolds represents the starting point of our analysis, which features an extended discussion about the explicit dualisation of the supergroup OSp(12). While the initial model represents an appropriate threedimensional supergravity background, the Tdual one hints in the opposite direction, as the ansatz adopted to construct the dual veilbeine fails to satisfy the supegravity torsion constraints. Such result, together with the complexity of the ansatzbased approach, suggests that a more abstract and general point of view should be taken on the dualisation procedure. This represents the next step of our analysis and allows a simpler dualisation of principal chiral models and a clearer argument that the above Tdual model falls outside the class of threedimensional supergravity backgrounds. Extension of the dualisation procedure to symmetric and semisymmetric coset space sigma models based on Lie supergroups G/H is also favored by the more abstract perspective, which allows to recover the wellknown exchange of equations of motion and Maurer Cartan equations typically observed in purely bosonic settings, hence leading to the construction of a dual Lax connection and ensuring preservation of classical integrability. While dualisation of principal chiral models can be performed in full generality, for coset models the procedure might be affected by impediments appearing in the process of integrating out the gauge fields in favor of the dual variables, and thus requires a case by case analysis. We proceed by solving those gauge fields equations of motion that allow for a general solution, thus confining the potential obstruction to a single equation, whose solvability depends on the invertibility of two linear operators. We conclude by discussing two explicit examples in which dualisation goes through, the first based on the symmetric space SO(4)/SO(3), wellknown for its dualisability, the second on the semisymmetric space OSp(12)/SO(1,1) already approached in the literature from the point of view of holography and representing a GreenSchwarzlike sigma model satisfying the supergravity torsion constraints.
(2023). NonAbelian Tduality in Superspace. (Tesi di dottorato, Università degli Studi di MilanoBicocca, 2023).
NonAbelian Tduality in Superspace
BIELLI, DANIELE
2023
Abstract
In this thesis we take a superspace perspective on Tduality, focusing on sigma models defined on background geometries that are constructed in terms of Lie supergroups. We briefly review Abelian bosonic and fermionic Tduality and the derivation of Buscher’s rules, moving then to the dualisation of principal chiral models on group manifolds. Extension of the latter to the case of supergroup manifolds represents the starting point of our analysis, which features an extended discussion about the explicit dualisation of the supergroup OSp(12). While the initial model represents an appropriate threedimensional supergravity background, the Tdual one hints in the opposite direction, as the ansatz adopted to construct the dual veilbeine fails to satisfy the supegravity torsion constraints. Such result, together with the complexity of the ansatzbased approach, suggests that a more abstract and general point of view should be taken on the dualisation procedure. This represents the next step of our analysis and allows a simpler dualisation of principal chiral models and a clearer argument that the above Tdual model falls outside the class of threedimensional supergravity backgrounds. Extension of the dualisation procedure to symmetric and semisymmetric coset space sigma models based on Lie supergroups G/H is also favored by the more abstract perspective, which allows to recover the wellknown exchange of equations of motion and Maurer Cartan equations typically observed in purely bosonic settings, hence leading to the construction of a dual Lax connection and ensuring preservation of classical integrability. While dualisation of principal chiral models can be performed in full generality, for coset models the procedure might be affected by impediments appearing in the process of integrating out the gauge fields in favor of the dual variables, and thus requires a case by case analysis. We proceed by solving those gauge fields equations of motion that allow for a general solution, thus confining the potential obstruction to a single equation, whose solvability depends on the invertibility of two linear operators. We conclude by discussing two explicit examples in which dualisation goes through, the first based on the symmetric space SO(4)/SO(3), wellknown for its dualisability, the second on the semisymmetric space OSp(12)/SO(1,1) already approached in the literature from the point of view of holography and representing a GreenSchwarzlike sigma model satisfying the supergravity torsion constraints.File  Dimensione  Formato  

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Descrizione: Tesi di Bielli Daniele  856546
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