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1.
Peter Bouwknegt Alan L. Carey Varghese Mathai Michael K. Murray Danny Stevenson 《Communications in Mathematical Physics》2002,228(1):17-49
In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of K-brane charges in nontrivial backgrounds are briefly discussed.
Received: 29 June 2001 / Accepted: 15 October 2001 相似文献
2.
Kiyonori Gomi 《Communications in Mathematical Physics》2010,294(3):863-889
We provide a finite-dimensional model of the twisted K-group twisted by any degree three integral cohomology class of a CW complex. One key to the model is Furuta’s generalized
vector bundle, and the other is a finite-dimensional approximation of Fredholm operators. 相似文献
3.
We give a finite-dimensional and geometric construction of a Chern character for twisted K-theory, introducing a notion of connection on a twisted vectorial bundle which can be considered as a finite-dimensional
approximation of a twisted family of Fredholm operators. Our construction is applicable to the case of any classes giving
the twisting, and agrees with the Chern character of bundle gerbe modules in the case of torsion classes. 相似文献
4.
We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes
stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the
low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond
fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond
couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated
to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials
on orbifolds. 相似文献
5.
We study the structure of abelian extensions of the group L
q
G of q-differentiable loops (in the Sobolev sense), generalizing from the case of the central extension of the smooth loop group.
This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules
are constructed for the Lie algebra. The construction is extended to the current algebra of the supersymmetric Wess-Zumino-Witten
model. An application to the twisted K-theory on G is discussed. 相似文献
6.
In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X. We show how from its curvature we can obtain its characteristic class in H3(X) via Chern-Weil theory. For an arbitrary gerbe , a twisting Korb(X) of the orbifold K-theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold.The first author was partially supported by the National Science Foundation and Conacyt-México 相似文献
7.
Ralph M. Kaufmann 《Letters in Mathematical Physics》2010,94(2):165-195
There are two approaches to constructing stringy multiplications for global quotients. The first one is given by first pulling back and then pushing forward. The second one is given by first pushing forward and then pulling back. The first approach has been used to define a global stringy extension of the functors K 0 and K top by Jarvis–Kaufmann–Kimura, A* by Abramovich–Graber–Vistoli, and H* by Chen–Ruan and Fantechi–Göttsche. The second approach has been applied by the author in the case of cyclic twisted sector and in particular for singularities with symmetries and for symmetric products. The second type of construction has also been discussed in the de Rham setting for Abelian quotients by Chen–Hu. We give a rigorous formulation of de Rham theory for any global quotient from both points of view. We also show that the pull–push formalism has a solution by the push–pull equations in the setting case of cyclic twisted sectors. In the general, not necessarily cyclic case, we introduce ring extensions and treat all the stringy extension of the functors mentioned above also from the second point of view. A first extension provides formal sections and a second extension fractional Euler classes. The formal sections allow us to give a pull–push solution while fractional Euler classes give a trivialization of the co-cycles of the pull–push formalism. The main tool is the formula for the obstruction bundle of Jarvis–Kaufmann–Kimura. This trivialization can be interpreted as defining the physics notion of twist fields. We end with an outlook on applications to singularities with symmetries aka. orbifold Landau–Ginzburg models. 相似文献
8.
It was argued in [25, 5] that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are classified by twisted K-theory. In [4], it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary Hilbert bundles on a principal projective unitary bundle, with an action of the bundle
gerbe determined by the principal projective unitary bundle. The principal projective unitary bundle is in turn determined
by the twist. This paper studies in detail the Chern-Weil representative of the Chern character of bundle gerbe K-theory that was introduced in [4], extending the construction to the equivariant and the holomorphic cases. Included is a
discussion of interesting examples.
Received: 10 January 2002 / Accepted: 9 December 2002
Published online: 25 February 2003
RID="⋆"
ID="⋆" The authors acknowledge the support of the Australian Research Council
Communicated by R.H. Dijkgraaf 相似文献
9.
Feng Xu 《Communications in Mathematical Physics》1994,166(2):237-253
We use the lattice models to determine the obstructions to the flatness of the orbifold connections in some finite depth subsfactors. 相似文献
10.
In this paper, we try to answer the following question: given a modular tensor category ? with an action of a compact group
G, is it possible to describe in a suitable sense the “quotient” category ?/G? We give a full answer in the case when ?=?ℯ? is the category of vector spaces; in this case, ?ℯ?/G turns out to be the category of representation of Drinfeld's double D(G). This should be considered as the category theory analog of the topological identity {pt}/G=BG.
This implies a conjecture of Dijkgraaf, Vafa, E. Verlinde and H. Verlinde regarding so-called orbifold conformal field theories:
if ? is a vertex operator algebra which has a unique irreducible module, ? itself, and G is a compact group of automorphisms of ?, and some not too restrictive technical conditions are satisfied, then G is finite, and the category of representations of the algebra of invariants, ?
G
, is equivalent as a tensor category to the category of representations of Drinfeld's double D(G). We also get some partial results in the non-holomorphic case, i.e. when ? has more than one simple module.
Received: 27 August 2001 / Accepted: 1 March 2002 相似文献
11.
We apply the notion of orbifold models ofSU(N) solvable lattice models to the Hecke algebra subfactors of Wenzl and get a new series of subfactors. In order to distinguish our subfactors from those of Wenzl, we compute the principal graphs for both series of subfactors. An obstruction for flatness of connections arises in this orbifold procedure in the caseN=2 and this eliminates the possibility of the Dynkin diagramsD
2n+1
, but we show that no such obstructions arise in the caseN=3. Our tools are the paragroups of Ocneanu and solutions of Jimbo-Miwa-Okado to the Yang-Baxter equation. 相似文献
12.
《Nuclear Physics B》1988,302(2):291-329
The orbifold models of the heterotic string are constructed on the quotient spaces of generalized tori by translational and rotational discrete symmetries. In order to obtain the consistent orbifold models, the conditions of the modular invariance are derived from a one-loop vacuum amplitude. Z3 orbifold models satisfying such conditions are searched systematically. It is shown that there are infinite possible models with N = 2 supersymmetry. Among these models, two examples having E6 and E7 gauge groups are discussed. The orbifold models with N = 1 supersymmetry are also discussed in detail. It is shown that there are only five consistent models in the class of these models based on E8 ⊗ E′8 heterotic string in which the extra six-dimensional torus and the E8 ⊗ E′8 maximal torus are modded out by the rotational and the translational Z3 symmetries respectively. 相似文献
13.
A New Cohomology Theory of Orbifold 总被引:7,自引:0,他引:7
Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation 相似文献
15.
P. Bantay 《Letters in Mathematical Physics》2008,83(2):163-179
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform
are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of
permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions.
Work supported by grants OTKA T047041, T043582, the János Bolyai Research Scholarship of the Hungarian Academy of Sciences
and EC Marie Curie MRTN-CT-2004-512194. 相似文献
16.
《Physics letters. [Part B]》1988,203(4):367-370
The internal degrees of freedom of twisted heterotic strings are discussed using the theory of Kac-Moody algebras. 相似文献
17.
Sergei Gukov 《Communications in Mathematical Physics》2000,210(3):621-639
We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in Type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in Type I brane systems with p+q=7, as proposed by Witten. 相似文献
18.
The Berezin-Toeplitz deformation quantization of an abelian variety is explicitly computed by the use of Theta-functions. An SL(2n,)-equivariant complex structure dependent equivalence E between the constant Moyal-Weyl product and this family of deformations is given. This equivalence is seen to be convergent on the dense subspace spanned by the pure phase functions. The Toeplitz operators associated to the equivalence E applied to a pure phase function produces a covariant constant section of the endomorphism bundle of the vector bundle of Theta-functions (for each level) over the moduli space of abelian varieties.Applying this to any holonomy function on the symplectic torus one obtains as the moduli space of U(1)-connections on a surface, we provide an explicit geometric construction of the abelian TQFT-operator associated to a simple closed curve on the surface. Using these TQFT-operators we prove an analog of asymptotic faithfulness (see [A1]) in this abelian case. Namely that the intersection of the kernels for the quantum representations is the Toreilli subgroup in this abelian case.Furthermore, we relate this construction to the deformation quantization of the moduli spaces of flat connections constructed in [AMR1] and [AMR2]. In particular we prove that this topologically defined *-product in this abelian case is the Moyal-Weyl product. Finally we combine all of this to give a geometric construction of the abelian TQFT operator associated to any link in the cylinder over the surface and we show the glueing axiom for these operators.This research was conducted in part for the Clay Mathematics Institute at University of California, Berkeley.This work was supported by MaPhySto – A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation 相似文献
19.
The aim of the paper is twofold. First, we show that a quantum field theory A living on the line and having a group G of inner symmetries gives rise to a category G–Loc A of twisted representations. This category is a braided crossed G-category in the sense of Turaev [60]. Its degree zero subcategory is braided and equivalent to the usual representation category
Rep A. Combining this with [29], where Rep A was proven to be modular for a nice class of rational conformal models, and with the construction of invariants of G-manifolds
in [60], we obtain an equivariant version of the following chain of constructions: Rational CFT modular category 3-manifold invariant.
Secondly, we study the relation between G–Loc A and the braided (in the usual sense) representation category Rep AG of the orbifold theory AG. We prove the equivalence RepAG≃(G–Loc A)G, which is a rigorous implementation of the insight that one needs to take the twisted representations of A into account in order to determine Rep AG. In the opposite direction we have is the full subcategory of representations of AG contained in the vacuum representation of A, and ⋊ refers to the Galois extensions of braided tensor categories of [44, 48].
Under the assumptions that A is completely rational and G is finite we prove that A has g-twisted representations for every g∈ G and that the sum over the squared dimensions of the simple g-twisted representations for fixed g equals dim Rep A. In the holomorphic case this allows to classify the possible categories G− Loc A and to clarify the r?le of the twisted quantum doubles Dω(G) in this context, as will be done in a sequel. We conclude with some remarks on non-holomorphic orbifolds and surprising
counterexamples concerning permutation orbifolds.
Supported by NWO through the “pioneer” project no. 616.062.384 of N. P. Landsman.
An erratum to this article can be found at 相似文献
20.
《Journal of Geometry and Physics》2001,38(2):153-170
We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of singularities. We also make explicit conjectures on elliptic genera for the wreath product orbifolds. 相似文献