Axial Anomaly in Noncommutative QED on R^4

The axial anomaly of the noncommutative U(1) gauge theory is calculated by a number of methods and compared with the commutative one. It is found to be given by the corresponding Chern class.Comment: LaTeX, axodraw.sty; v2: typos are fixed; v3: version to appear in Int. J. Mod. Phys. A. (2001

Central Charge for 2D Gravity on AdS(2) and AdS(2)/CFT(1) Correspondence

We study 2D Maxwell-dilaton gravity on AdS(2). We distinguish two distinctive cases depending on whether the AdS(2) solution can be lifted to an AdS(3) geometry. In both cases, in order to get a consistent boundary condition we need to work with a twisted energy momentum tensor which has non-zero central charge. With this central charge and the explicit form of the twisted Virasoro generators we compute the entropy of the system using the Cardy formula. The entropy is found to be the same as that obtained from gravity calculations for a specific value of the level of the U(1) current. The agreement is an indication of $AdS(2)/CFT(1) correspondence.Comment: 12 pages, latex file; V2: typos corrected, refs added. V3: Corrections and clarifications in section two; conclusion didn't change, few comments added, typos correcte

Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields.Comment: 28 pages, Latex, axodraw.sty; v2: version to appear in Int. J. Mod. Phys. A. (2001