By David I. Olive, Peter C. West

ISBN-10: 0521641586

ISBN-13: 9780521641586

This is often the 1st systematic advent to electromagnetic duality and its generalizations. The authors, prime figures during this fascinating new sector of mathematical physics, describe the basic rules, most modern advancements, and a few previous paintings whose importance has only in the near past turn into obvious. This quantity should be crucial studying for all these operating in mathematical physics.

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6) The third corresponds t o a = d = 0, 6 = — 1/c, c arbitrary, which gives 1 G' = —cF, F' = cG, = 1 = S 5^ = S ^ . ( 6 . 2) we find ¿ ( S i , 5 2 , F ) - ^ F G = ¿ ( 5 i + b, S 2 , F ) - l-F (Ó + 6F) . 14). This choice for the constant b is allowed because this part of the Lagrangian, which does JVonlinear Electromagnetic Self-Duality and Legendre Transformations 45 not include the kinetic term for the scalar fields, does not contain derivatives of the scalar fields. , ¿(S,,S2,F) = L (a2S,,a2S2, ^ F ) .

B365: 87 (1996). H. Schwarz and A. Sen, Phys. Lett. B312: 105 (1993) and Nucl. Phys. B 4 1 1 : 35 (1994); M. Duff, Nucl. Phys. B442: 47 (1995); E. Witten, Nucl. Phys. B443: 85 (1995). [19] S. Cecotti, S. Ferrara and L. Girardello, Nucl. Phys. B308: 436 (1988). Supersymmetric cr-Models in 2 Dimensions Bruno 1 Zumino The bosonic cr-model I have been asked to give a brief introduction to supersymmetric c-models in two space-time dimensions. Let us recali first the properties of the bosonic c-models.

In the case of the Born-Infeld theory, just as for Maxwell's theory, one complex scalar field suffices to enhance the i / ( l ) = 5 0 ( 2 ) invariance to the SU( 1,1) = 5 L ( 2 , R ) noncompact duality invariance. This is pointed out in [5], but it also follows from the considérations of our paper [2]. In the example under considération, K is a single complex field, not a n n x n matrix. 1) where cf> is the dilaton and a is the axion. For 5 L ( 2 , R ) = 5 p ( 2 , R ) , the matrices A, B, C, D are real numbers and A = -D, B and C are independent.

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