The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds

It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the ${\overline{\partial} \partial}It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized K?hler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the -lemma, we establish the equivariant formality theorem. If in addition, the manifold satisfies the generalized K?hler condition, we prove the Kirwan injectivity in this setting. We then consider the Hamiltonian action of a torus on an H-twisted generalized Calabi-Yau manifold and extend to this case the Duistermaat-Heckman theorem for the push-forward measure. As a side result, we show in this paper that the generalized K?hler quotient of a generalized K?hler vector space can never have a (cohomologically) non-trivial twisting. This gives a negative answer to a question asked by physicists whether one can construct (2, 2) gauged linear sigma models with non-trivial fluxes.     

Real Forms of the Complex Twisted N=2 Supersymmetric Toda Chain Hierarchy in Real N=1 and Twisted N=2 Superspaces

Abstract

Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a new superfield basis in which the supersymmetry transformations are local. Furthermore, a representation of this hierarchy is given in terms of two twisted chiral N=2 superfields. The relations to the s-Toda hierarchy by H. Aratyn, E. Nissimov and S. Pacheva (solv-int/9801021) as well as to the modified and derivative NLS hierarchies are established.     

Constant and Equivariant Cyclic Cohomology

In this note, we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.     

Local Anomalies and Local Equivariant Cohomology

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology. This interpretation allows us to solve the problem proposed by Singer in [31], and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. Moreover, using the relation between local cohomology and the cohomology of jet bundles studied in [19] we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.     

Chiral BRST Cohomology of N= 2 Strings at Arbitrary Ghost and Picture Number

We compute the BRST cohomology of the holomorphic part of the N= 1 string at arbitrary ghost and picture number. We confirm the expectation that the relative cohomology at non-zero momentum consists of a single massless state in each picture. The absolute cohomology is obtained by an independent method based on homological algebra. For vanishing momentum, the relative and absolute cohomologies both display a picture dependence – a phenomenon discovered recently also in the relative Ramond sector of N= 1 strings by Berkovits and Zwiebach [1]. Received: 5 January 1998 / Accepted: 16 November 1998     

Chern Character in Twisted K-Theory: Equivariant and Holomorphic Cases

 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     

Lattice models with N=2 supersymmetry

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.     

Supersymmetry and electromagneticE2 transitions

We discuss the quadrupole electric transitions in the frame of the supersymmetric model for light nuclei (s —d shell). We present the construction of an isoscalar transition operator based on the assumption of the dynamicalSO ^BF (6) symmetry. Theoretical transition probabilities for nuclei belonging to the supermultiplet characterized by a particle numberN=5 show quite a good agreement with experimental data.     

Harmonic N=2 superfields with finite attenuation

In the harmonic N=2 superspace we construct the self-action for the attenuated hypermultiplet of matter with a finite number of auxiliary fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 64–67, October, 1988.We thank V. I. Ogievetskii, K. S. Stello, and I. V. Tyutin for useful discussions.     

Algebraic renormalization of twisted N=2 supersymmetry with Z=2 central extension

We study the renormalizability of (massive) topological QCD based on the algebraic BRST technique by adopting a noncovariant Landau type gauge and making use of the full topological superalgebra. The most general local counter terms are determined and it is shown that in the presence of central charges the BRST cohomology remains trivial. By imposing an additional set of stability constraints it is proven that the matter action of topological QCD is perturbatively finite.     

Twisted baryon number in N = 2 supersymmetric QCD

We show that the baryon number of N = 2 supersymmetric QCD can be twisted in order to couple the topological field theory of non-abelian monopoles to Spin^c-structures. To motivate the construction, we also consider some aspects of the twisting procedure as a gauging of global currents in two and four dimensions, in particular the rôle played by anomalies.     

c=3, N=2 超共形场论的Z2 Orbifold-Prime模型

讨论了二维环面上中心荷c=3, N=2 的超共形场论. 特别给出该理论的配分函数. 进一步,为了产生新的模型,回顾了一般的orbifold方法. 然后构造了模不变的Z2 Orbifold-Prime模型.     

N=2 affine superalgebras and Hamiltonian reduction inN=2 superspace

We constructN=2 affine current algebras for the superalgebrassl(n/n-1)⁽¹⁾ in terms ofN=2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction inN=2 superspace at the classical level. We consider in detail the simplest case ofN=2sl(2/1)⁽¹⁾ and show howN=2 superconformal algebra inN=2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case ofN=2sl(3/2)⁽¹⁾, we find two new extendedN=2 superconformal algebras in a manifestly supersymmetricN=2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively,u(2/1) andu(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how theN=2 superfield formulations ofN=2W ₃ andN=2W ₃ ⁽²⁾ superconformal algebras come out in this framework, as well as some unusual extendedN=2 superconformal algebras containing constrainedN=2 stress tensor and/or spin 0 supercurrents.     

Charge Distribution and Spin Textures in Magic-Angle Twisted Bilayer Graphene

JETP Letters - The spin density wave existing on the background of the inhomogeneous charge distribution is examined as a possible ground state of the magic-angle twisted bilayer graphene. When...