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14
DIFFERENTIAL TWISTED KTHEORY AND APPLICATIONS
, 2007
"... In this paper, we develop differential characters in twisted Ktheory and use them to define a twisted Chern character. In the usual formalism the ‘twist’ is given by a degree three Čech class while we work with differential twisted Ktheory with twisting given by a degree 3 Deligne class. This res ..."
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In this paper, we develop differential characters in twisted Ktheory and use them to define a twisted Chern character. In the usual formalism the ‘twist’ is given by a degree three Čech class while we work with differential twisted Ktheory with twisting given by a degree 3 Deligne class. This resolves an unsatisfactory dependence on choices of representatives of differential forms in the definition of the Chern character map for twisted Ktheory in the current literature. Twisted eta forms and twisted spin c structures are also defined. To show the efficacy of our point of view we use our approach to study Dbrane charges on a compact Lie group with nontrivial twisting by a Deligne class.
Families index theorem in supersymmetric WZW model and twisted Ktheory: The SU(2) case
, 2005
"... The construction of twisted Ktheory classes on a compact Lie group is reviewed using the supersymmetric WessZuminoWitten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed ..."
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Cited by 3 (3 self)
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The construction of twisted Ktheory classes on a compact Lie group is reviewed using the supersymmetric WessZuminoWitten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a Dbrane.
Westerland: The symplectic Verlinde algebras and string Ktheory, arXiv:0901.2109
"... Abstract. We construct string topology operations in twisted Ktheory. We study the examples given by symplectic Grassmannians, computing K τ ∗ (LHP ℓ) in detail. Via the work of FreedHopkinsTeleman, these computations are related to completions of the Verlinde algebras of Sp(n). We compute these ..."
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Abstract. We construct string topology operations in twisted Ktheory. We study the examples given by symplectic Grassmannians, computing K τ ∗ (LHP ℓ) in detail. Via the work of FreedHopkinsTeleman, these computations are related to completions of the Verlinde algebras of Sp(n). We compute these completions, and other relevant information about the Verlinde algebras. We also identify the completions with the twisted Ktheory of the GruherSalvatore prospectra. Further comments on the field theoretic nature of these constructions are made. Much of the recent history of algebraic topology has been concerned with manifestations of ideas from mathematical physics within topology. A stunning example is ChasSullivan’s theory of string topology [4], which provides a family of algebraic structures analogous to conformal field theory on the homology H∗(LM) of the free loop space LM of a closed orientable manifold M ([16]). The work of Chas and Sullivan started an entirely new field of algebraic topology, and led to papers too numerous to quote. Equally interesting as this analogy however is the fact that it is not quite precise: while the notion of conformal field theory is supposed to be completely selfdual, the string topology coproduct in H∗LM has no counit. The inspiration for this paper came from two sources: one is the paper of Cohen and Jones [6], generalizing string topology to an arbitrary Moriented generalized cohomology theory. The other is the work of Freed, Hopkins, and Teleman [14] which identified the famous Verlinde algebra of a compact Lie group G with its equivariant twisted Ktheory. It follows that a completion of the Verlinde algebra is isomorphic to the (nonequivariant) twisted Ktheory of LBG. In more detail, in [14], FreedHopkinsTeleman establish a ring isomorphism
On the structure of the fusion ideal
 Comm. Math. Phys
"... Abstract. We prove that there is a finite levelindependent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the fusion ring of G2 at all levels. 1. ..."
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Abstract. We prove that there is a finite levelindependent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the fusion ring of G2 at all levels. 1.
Dbrane charges on
 SO(3), JHEP 11 (2004) 082 [hepth/0404017
"... Preprint typeset in JHEP style HYPER VERSION hepth/0504007 ..."
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Preprint typeset in JHEP style HYPER VERSION hepth/0504007
FUSION RINGS OF LOOP GROUP REPRESENTATIONS
, 901
"... Abstract. We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups. ..."
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Abstract. We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.
Contents
, 2006
"... 2. Preliminaries: spaces and functionals 6 2.1. Marcinkiewicz function and sequence spaces 6 2.2. Singular symmetric functionals on Marcinkiewicz spaces. 7 ..."
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2. Preliminaries: spaces and functionals 6 2.1. Marcinkiewicz function and sequence spaces 6 2.2. Singular symmetric functionals on Marcinkiewicz spaces. 7
Type IIB string theory, Sduality, and generalized cohomology
, 2004
"... In the presence of background NeveuSchwarz flux, the description of the RamondRamond fields of type IIB string theory using twisted Ktheory is not compatible with Sduality. We argue that other possible variants of twisted Ktheory would still not resolve this issue. We propose instead a possible ..."
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In the presence of background NeveuSchwarz flux, the description of the RamondRamond fields of type IIB string theory using twisted Ktheory is not compatible with Sduality. We argue that other possible variants of twisted Ktheory would still not resolve this issue. We propose instead a possible path to a solution using elliptic cohomology. We also discuss Tduality relation of this to a previous proposal for IIA theory, and higherdimensional limits.
KCLMTH0511 Generalised permutation branes
, 2005
"... We propose a new class of nonfactorising Dbranes in the product group G × G where the fluxes and metrics on the two factors do not necessarily coincide. They generalise the maximally symmetric permutation branes which are known to exist when the fluxes agree, but break the symmetry down to the dia ..."
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We propose a new class of nonfactorising Dbranes in the product group G × G where the fluxes and metrics on the two factors do not necessarily coincide. They generalise the maximally symmetric permutation branes which are known to exist when the fluxes agree, but break the symmetry down to the diagonal current algebra in the generic case. Evidence for the existence of these branes comes from a Lagrangian description for the open string worldsheet and from effective DiracBornInfeld theory. We state the geometry, gauge fields and, in the case of SU(2) × SU(2), tensions and partial results on the open string spectrum. In the latter case the generalised permutation branes provide a natural and complete explanation for the charges predicted by Ktheory including their torsion. Contents