Yasunari Tosa

Global anomalies and algebraic topology

The algebraic topology aspect of the global pure gauge anomaly calculation is investigated. In particular, the use of a cohomology sequence clarifies the method initiated by Witten [Nucl. Phys. 223, 422, 433 (1983)] and Elitzur and Nair [Nucl. Phys. B 243, 205 (1984)]. Examples in SU(N), Sp(N), and SO(N) are discussed.

Explicit construction of nontrivial elements for homotopy groups of classical Lie groups

Nontrivial elements of homotopy groups for unitary, orthogonal, and symplectic groups are given explicitly. In particular, (a) representatives of generators of nontrivial homotopy groups of stable special unitary, orthogonal, and symplectic groups are constructed using Clifford algebras; (b) the values for ‘‘winding numbers’’ for stable SU, SO, and Sp are calculated for generators of homotopy groups; and (c) representatives of generators of homotopy groups Πn−2(O(n−1)), Π2n−2(U(n−1)), Π4n−2(Sp(n−1)) are given.

Temperature in Kaluza-Klein cosmologies☆

Abstract The temperature behavior is discussed for three typical equations of state in Kaluza-Klein cosmologies: (i) p = p ′ = ( λ − 1) ϱ , (ii) ϱ = − p = p ′, (iii) ϱ = p = − p ′.

NEW ANOMALY FREE THEORIES BEYOND SUPERSTRINGS

Abstract Many new anomaly-free configurations are found group-theoretically, assuming that they contain N = 1 supergravity and Yang-Mills matter with a simple group and allowing the existence of many Yang-Mills singlets (shadow matter).

Anomaly-free supergravity theories remain anomaly-free after dimensional reduction

Abstract We show that the anomaly after compactification of a supergravity theory coupled to Yang-Mills matter is usually given by an integral of the original anomaly over the compact space, as long as there are no isometries for the compact space. This means that a supergravity theory, whose anomaly vanishes identically (i.e., without the addition of local counter terms to the action), will remain anomaly-free after compactification to any lower dimension, subject to some restrictions on self-dual antisymmetric tensors. We next consider the case where the original anomaly cancels by the Green-Schwarz mechanism. In this case, again subject to the restrictions on self-dual antisymmetric tensors, the anomaly will still cancel after compactification to any lower dimension D > 2, provided that: (1) There are no U(1) gauge groups after compactification. (2) There exists a three-form field strength H such that d H = (Tr R 0 2 + k Tr F 0 2 ), or that the compact space is chosen such that (Tr R 0 2 + k Tr F 0 2 ) = 0.