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1.
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2.
  • Cederwall, Martin, 1961, et al. (författare)
  • Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra
  • 2020
  • Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708.
  • Tidskriftsartikel (refereegranskat)abstract
    • Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics, especially in extended geometry and gauged supergravity. We further develop the recently proposed definition of tensor hierarchy algebras in terms of generators and relations encoded in a Dynkin diagram (which coincides with the diagram for a related Borcherds superalgebra). We apply it to cases where a grey node is added to the Dynkin diagram of a rank r + 1 Kac-Moody algebra g(+), which in turn is an extension of a rank r finite-dimensional semisimple simply laced Lie algebra g. The algebras are specified by g together with a dominant integral weight lambda. As a by-product, a remarkable identity involving representation matrices for arbitrary integral highest weight representations of g is proven. An accompanying paper [1] describes the application of tensor hierarchy algebras to the gauge structure and dynamics in models of extended geometry.
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3.
  • Cederwall, Martin, 1961, et al. (författare)
  • Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics
  • 2020
  • Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2020:2
  • Tidskriftsartikel (refereegranskat)abstract
    • The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns out to be a tensor hierarchy algebra rather than a Borcherds superalgebra. This tensor hierarchy algebra is a non-contragredient superalgebra, generically infinite-dimensional, which is a double extension of the structure algebra of the extended geometry. We use it to perform a (partial) analysis of the gauge structure in terms of an L∞ algebra for extended geometries based on finite-dimensional structure groups. An invariant pseudo-action is also given in these cases. We comment on the continuation to infinite-dimensional structure groups. An accompanying paper [1] deals with the mathematical construction of the tensor hierarchy algebras.
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4.
  • Adawi, Tom, 1970, et al. (författare)
  • Goldstone tensor modes
  • 1998
  • Ingår i: J. High Energy Phys. 9902:001,1999.
  • Tidskriftsartikel (refereegranskat)abstract
    • In the context of brane solutions of supergravity, we discuss a general method to introduce collective modes of any spin by exploiting a particular way of breaking symmetries. The method is applied to the D3, M2 and M5 branes and we derive explicit expressions for how the zero-modes enter the target space fields, verify normalisability in the transverse directions and derive the corresponding field equations on the brane. In particular, the method provides a clear understanding of scalar, spinor, and rank r tensorial Goldstone modes, chiral as well as non-chiral, and how they arise from the gravity, Rarita-Schwinger, and rank r+1 Kalb-Ramond tensor gauge fields, respectively. Some additional observations concerning the chiral tensor modes on the M5 brane are discussed.
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5.
  • Adawi, Tom, 1970, et al. (författare)
  • Superembeddings, nonlinear supersymmetry and five-branes
  • 1997
  • Ingår i: Int.J.Mod.Phys.A13:4691-4716,1998.
  • Tidskriftsartikel (refereegranskat)abstract
    • We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in 7 dimensions, containing a self-dual 3-form world-volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.
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6.
  • Bandos, Igor, et al. (författare)
  • Towards a complete twistorization of the heterotic string
  • 1994
  • Ingår i: Mod.Phys.Lett.A9 (1994) 2987.
  • Tidskriftsartikel (refereegranskat)abstract
    • In D=3,4,6 and 10 space-time dimensions considered is a string model invariant under transformations of N=1 space-time supersymmetry and n=D-2 local worldsheet supersymmetry with the both Virasoro constraints solved in the twistor form. The twistor solution survives in a modified form even in the presence of the heterotic fermions.
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7.
  • Bao, Ling, 1980, et al. (författare)
  • A note on topological M5-branes and string-fivebrane duality
  • 2008
  • Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; :6, s. 11-
  • Tidskriftsartikel (refereegranskat)abstract
    • We derive the stability conditions for the M5-brane in topological M-theory using k-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) subset of G(2). The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.
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8.
  • Bao, Ling, 1980, et al. (författare)
  • A Note on Topological M5-branes and String-Fivebrane Duality
  • 2006
  • Tidskriftsartikel (övrigt vetenskapligt)abstract
    • We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.
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9.
  • Bao, Ling, 1980, et al. (författare)
  • Aspects of higher curvature terms and U-duality
  • 2007
  • Ingår i: Classical and Quantum Gravity. - 0264-9381. ; 25:9
  • Tidskriftsartikel (refereegranskat)abstract
    • We discuss various aspects of dimensional reduction of gravity with theEinstein-Hilbert action supplemented by a lowest order deformation formed asthe Riemann tensor raised to powers two, three or four. In the case of R^2 wegive an explicit expression, and discuss the possibility of extended cosetsymmetries, especially SL(n+1,Z) for reduction on an n-torus to threedimensions. Then we start an investigation of the dimensional reduction of R^3and R^4 by calculating some terms relevant for the coset formulation, aiming inparticular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and aninvestigation of the derivative structure. We emphasise some issues concerningthe need for the introduction of non-scalar automorphic forms in order torealise certain expected enhanced symmetries.
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10.
  • Bao, Ling, 1980, et al. (författare)
  • Membranes for Topological M-Theory
  • 2005
  • Ingår i: Journal of High Energy Physics.
  • Tidskriftsartikel (refereegranskat)abstract
    • We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.
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tidskriftsartikel (90)
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