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Ultraviolet and Infrared Finiteness in Two Dimensional Curved Space-Time

✍ Scribed by H. Zerrouki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
254 KB
Volume
263
Category
Article
ISSN
0003-4916

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✦ Synopsis

Different models of field theories in two dimensions can be described by the action Tr .F. In the presence of a curved background, we construct local supersymmetry-like transformations under which the action is invariant. Furthermore, by analyzing the cohomology of the theory we show the absence of anomalies. Also the ultraviolet and the infrared finiteness of the theory are proven at all orders of perturbation theory.

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Let GF(q) be the Galois field of order q"pF, and let m53 be an integer. An explicit formula for the number of GF(qK)-rational points of the Fermat curve XL#Β½L#ZL"0 is given when n divides (qK!1)/(q!1) and p is sufficiently large with respect to (qK!1)/(n(q!1)).