Differential Calculus on Fuzzy Sphere and Scalar Field

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.Comment: LaTeX 12 page

Noncommutative Geometry and Gauge Theory on Fuzzy Sphere

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left $U(N+1)$ transformation of the field, where a field is a bimodule over the quantized algebra \CA_N. The interaction with a complex scalar field is also given.Comment: LaTeX 26 pages, final version (Dec.1999) accepted in CMP. An extra term in the gauge action is discusse

Boundary state analysis on the equivalence of T-duality and Nahm transformation in superstring theory

We investigated the equivalence of the T-duality for a bound state of D2 and D0-branes with the Nahm transformation of the corresponding gauge theory on a 2-dimensional torus, using the boundary state analysis in superstring theory. In contrast to the case of a 4-dimensional torus, it changes a sign in a topological charge, which seems puzzling when regarded as a D-brane charge. Nevertheless, it is shown that it agrees with the T-duality of the boundary state, including a minus sign. We reformulated boundary states in the RR-sector using a new representation of zeromodes, and show that the RR-coupling is invariant under the T-duality. Finally, the T-duality invariance at the level of the Chern-Simon coupling is shown by deriving the Buscher rule for the RR-potentials, known as the 'Hori formula', including the correct sign.Comment: 31 pages. v2: references added, typos correcte

Metric Algebroid and Poisson-Lie T-duality in DFT

In this article we investigate the gauge invariance and duality properties of DFT based on a metric algebroid formulation given previously in [1]. The derivation of the general action given in this paper does not employ the section condition. Instead, the action is determined by requiring a pre-Bianchi identity on the structure functions of the metric algebroid and also for the dilaton flux. The pre-Bianchi identity is also a sufficient condition for a generalized Lichnerowicz formula to hold. The reduction to the D-dimensional space is achieved by a dimensional reduction of the fluctuations. The result contains the theory on the group manifold, or the theory extending to the GSE, depending on the chosen background. As an explicit example we apply our formulation to the Poisson-Lie T-duality in the effective theory on a group manifold. It is formulated as a 2D-dimensional diffeomorphism including the fluctuations.Comment: 61 page

DFT in supermanifold formulation and group manifold as background geometry

We develop the formulation of DFT on pre-QP-manifold. The consistency conditions like section condition and closure constraint are unified by a weak master equation. The Bianchi identities are also characterized by the pre-Bianchi identity. Then, the background metric and connections are formulated by using covariantized pre-QP-manifold. An application to the analysis of the DFT on group manifold is given.Comment: 52 pages, 2 tabels. Several references adde

Monopole Bundles over Fuzzy Complex Projective Spaces

We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N -> infinity limit, where N labels the representation of the fuzzy algebra.Comment: 30 pages, LaTeX, published version; extended discussion on asymptotic Chern number