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Download e-book for iPad: 2-Tori in E8 by Adams J. F.

By Adams J. F.

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There is in fact a smaller supermultiplet, which we discard because it contains gravitini but no graviton states. Finally, we turn to the case of (N+ , N− ) = (2, 2). The smallest supermultiplet is given by the tensor product of the smallest (2, 0) and (0, 2) supermultiplets. This yields the 128 + 128 states of the (2, 2) supergravity multiplet. These states transform according to representations of U Sp(4) × U Sp(4). In principle, one can continue and classify representations for other values of (N+ , N− ).

However, conventional supergravity theories are not of this kind. e. in Table 5) to list supermultiplets with states transforming in higher-helicity representations. The fact that an infinite number of fields can cure certain inconsistencies is by itself not new.

Table 9 reflects also the so-called periodicity theorem [26], according to which there exists an isomorphism between the Clifford algebras C(p+8, q) (or C(p, q+8)) and C(p, q) times the 16 × 16 real matrices. Therefore, the dimension of the representations of C(p+8, q) (or C(p, q +8)) and C(p, q) differs by a factor 16. Finally the table lists the branching of the Clifford algebra representation into SO(p, q) spinor representations. When r = 0 the Clifford algebra representation decomposes into two chiral spinors.

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2-Tori in E8 by Adams J. F.

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