2019/10/31 by David Osten
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Current (fluid) #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Interpretation (philosophy) #Lagrangian #Lie algebroid #Noncommutative and Quantum Gravity Theories #String (physics) #String theory #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/ab8f3d
49 pages, v2: typos corrected, references added, new result showing the connection of strong constraint and associativity of current algebra in sections 4.3 and 5.2
openalex created_date 2019/10/10 · arxiv created 2019/10/31 · openalex publication_date 2020/05/01 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/05
A Hamiltonian formulation of the classical world-sheet theory in a generic, geometric or non-geometric, NSNS background is proposed. The essence of this formulation is a deformed current algebra, which is solely characterised by the generalised fluxes describing such a background. The construction extends to backgrounds for which there is no Lagrangian description—namely magnetically charged backgrounds or those violating the strong constraint of double field theory—at the cost of violating the Jacobi identity of the current algebra. The known non-commutative and non-associative interpretation of non-geometric flux backgrounds is reproduced by means of the deformed current algebra. Furthermore, the provided framework is used to suggest a generalisation of Poisson–Lie T -duality to generic models with constant generalised fluxes. As a side note, the relation between Lie and Courant algebroid structures of the string current algebra is clarified.