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Spontaneous breaking of supersymmetry

Description: There has been recently a revival of interest in supersymmetric gauge theories, stimulated by the hope that supersymmetry might help in clarifying some of the questions which remain unanswered in the so called Grand Unified Theories and in particular the gauge hierarchy problem. In a Grand Unified Theory one has two widely different mass scales: the unification mass M approx. = 10/sup 15/GeV at which the unification group (e.g. SU(5)) breaks down to SU(3) x SU(2) x U(1) and the mass ..mu.. approx. = 100 GeV at which SU(2) x U(1) is broken down to the U(1) of electromagnetism. There is at present no theoretical understanding of the extreme smallness of the ratio ..mu../M of these two numbers. This is the gauge hierarchy problem. This lecture attempts to review the various mechanisms for spontaneous supersymmetry breaking in gauge theories. Most of the discussions are concerned with the tree approximation, but what is presently known about radiative correction is also reviewed.
Date: December 1, 1981
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Prospects for supergravity

Description: Present particle phenomenology appears to be successfully described by a renormalizable gauge theory based on the low-energy group SU(3)/sub color/ x SU(2)/sub left/ x U(1). The three effective coupling constants of this theory vary with energy according to the renormalization group equations and become approximately equal at an energy of about 10/sup 14/ - 10/sup 15/ GeV, where one can attempt a grand unified theory (GUT) based on a gauge group with only one coupling constant and containing the low-energy group. The grand unification energy is very large and not much smaller than the Planck mass m/sub P/approx. = 10/sup 19/ GeV, where gravity becomes important. A natural way to unify gravity with lower-spin fields is provided by supergravity, the supersymmetric extension of Einstein's gravity. The largest supergravity theory (largest theory with a supermultiplet with maximum spin not exceeding two) is the N = 8 theory (N is the number of supersymmetries), which has an SO(8) internal symmetry. A GUT with N = 8 supergravity is considered. (RWR)
Date: August 1, 1980
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

The geometry of the Virasoro group for physicists

Description: Diff(S/sup 1/), the group of reparametrizations of the circle, is known as the Virasoro group in string theory. Reparametrizations keeping fixed a point of the circle form the quotient space Diff(S/sup 1/)S/sup 1/. The geometry of this space is relevant for string theory and string field theory. We describe this space as an infinite dimensional complex manifold with a Kaehler metric and compute ist Riemann tensor and its Ricci tensor. 7 refs
Date: November 1, 1987
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Chiral anomalies and differential geometry

Description: Some properties of chiral anomalies are described from a geometric point of view. Topics include chiral anomalies and differential forms, transformation properties of the anomalies, identification and use of the anomalies, and normalization of the anomalies. 22 references. (WHK)
Date: October 1, 1983
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Duality rotations

Description: Irrespective of supersymmetry, it is interesting to understand the special properties of theories admitting duality rotations. The Lagrangian of such a theory is not invariant under the transformations, nor does it change by a total derivative, but it transforms in a particular way which implies that the system of the equations of motion is invariant and that observables, such as the energy momentum tensor and therefore the total energy and momentum, are invariant. The main results of a recent paper on the properties of theories admitting duality rotations written in collaboration with M. K. Gaillard (1981) are described.
Date: November 1, 1981
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Gravity theories in more than four dimensions

Description: String theories suggest particular forms for gravity interactions in higher dimensions. We consider an interesting class of gravity theories in more than four dimensions, clarify their geometric meaning and discuss their special properties. 9 refs.
Date: March 1, 1985
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Magnetic charge and non-associative algebras

Description: We consider the possibility that the quantum mechanics of a nonrelativistic electron in the magnetic field of a magnetic charge distribution can be described in terms of a non-associative algebra of observables. It appears that the case of a point monopole is excluded, while that of a constant charge distribution is acceptable. 21 references.
Date: February 1, 1985
Creator: Guenaydin, M. & Zumino, B.
Partner: UNT Libraries Government Documents Department

Supersymmetric {sigma}-models in 2-dimensions

Description: The author gives a brief introduction to supersymmetric {sigma}-models in two space-time dimensions. The topics he covers are: the bosonic {sigma}-model; supersymmetry in two dimensions; complex manifolds; the Kaehler and hyper-Kaehler case; and chiral supersymmetries. The lesson to be learned from the lecture is that the number of supersymmetries is intimately related to the geometric structure of the target space manifold: more geometric structure corresponds to more supersymmetries.
Date: February 1, 1997
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Differential calculus on quantum spaces and quantum groups

Description: A review of recent developments in the quantum differential calculus. The quantum group GL[sub q](n) is treated by considering it as a particular quantum space. Functions on SL[sub q] (n) are defined as a subclass of functions on GL[sub q](n). The case of SO[sub q](n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.
Date: December 10, 1992
Creator: Zumino, B.
Partner: UNT Libraries Government Documents Department

Nonlinear electromagnetic self-duality and Legendre transformations

Description: We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of the continuous group are shown to be related to the Legendre transformation with respect to the field strengths.
Date: December 9, 1997
Creator: Gaillard, M.K. & Zumino, B.
Partner: UNT Libraries Government Documents Department

The Seiberg-Witten map for noncommutative gauge theories

Description: The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
Date: June 26, 2002
Creator: Cerchiai, B.L.; Pasqua, A.F. & Zumino, B.
Partner: UNT Libraries Government Documents Department

The Seiberg-Witten map for noncommutative gauge theories

Description: The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
Date: June 26, 2002
Creator: Cerchiai, B.L.; Pasqua, A.F. & Zumino, B.
Partner: UNT Libraries Government Documents Department