arXiv subjects

Christian Fronsdal

Publications and source records attributed to Christian Fronsdal.

25 records · Page 2Linked to original sources

arXiv1999

Singletons and Neutrinos

The first half is a rapid review of 30 years of work on physics in anti-De Sitter space, with heavy emphasis on singletons. Principal topics are the kinematical basis for regarding singletons as the constituents of massless particles, and the effect of (negative) curvature in the infrared domain. Ideas that lead to an alternative to Big Bang cosmology are merely sketched. The second half presents new ideas inspired by experimental results on neutrino oscillations. Since leptons are massless before symmetry breaking it is natural to view them as composite states consisting of one Bose singleton (the Rac) and one Fermi singleton (the Di). This gives rise to a particular formulation of the phenomenology of electroweak physics, and strong suggestions for an expansion of the Standard model. An expansion of the Higgs sector seems inevitable, and flavor changing symmetry, complete with a new set of heavy vector mesons, is a very attractive possibility.

hep-th↗

arXiv1999

Singleton physics

We review the developments in the past twenty years (which are based on our deformation philosophy of physical theories) dealing with elementary particles composed of singletons in anti De Sitter space-time. The study starts with the kinematical aspects (especially for massless particles) and extends to the beginning of a field theory of composite elementary particles and its relations with conformal field theory (including very recent developments).

hep-th↗

arXiv1998

On N=8 Supergravity on $AdS_5$ and N=4 Superconformal Yang-Mills theory

We discuss the spectrum of states of IIB supergravity on $AdS_5\times S^5$ in a manifest $SU(2,2/4)$ invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in $AdS_5$ and superconformal invariant singleton theory at the boundary is formulated in an N=4 superfield covariant language.

hep-th↗

arXiv1998

Interacting singletons

There is a chance that singleton fields, that in the context of strings and membranes have been regarded as topological gauge fields that can interact only at the boundary of anti-De Sitter space, at spatial infinity, may have a more physical manifestation as costituents of massless fields in space time. The composite character of massless fields is expressed by field - current identities that relate ordinary massless field operators to singleton currents and stress-energy tensors. Naive versions of such identities do not make sense, but when the singletons are described in terms of dipole structures, then such constructions are at least formally possible. The new proposal includes and generalizes an early composite version of QED, and includes quantum gravity, super gravity and models of QCD. Unitarity of such theories is conjectural.

hep-th↗

arXiv1996

Generalization and Exact Deformations of Quantum Groups

A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Algebraic surfaces in parameter space are characterized by the appearance of certain ideals; in this case the universal R-matrix exists on the associated algebraic quotient. In special cases the quotient is a "standard" quantum group; all familiar quantum groups including twisted ones are obtained in this way. In other special cases one finds new types of coboundary bi-algebras. The "standard" universal R-matrix is shown to be the unique solution of a very simple, linear recursion relation. The classical limit is obtained in the case of quantized Kac-Moody algebras of finite and affine type. Returning to the general case, we study deformations of the standard R-matrix and the associated Hopf algebras. A preliminary investigation of the first order deformations uncovers a class of deformations that incompasses the quantization of all Kac-Moody algebras of finite and affine type. The corresponding exact deformations are described as generalized twists, $ R_ε= (F^t)^{-1}RF$, where $R$ is the standard R-matrix and the cocycle $F$ (a power series in the deformation parameter $ε$) is the solution of a linear recursion relation of the same type as that which determines $R$. Included here is the universal R-matrix for the elliptic quantum groups associated with $sl(n)$, a big surprise! Specializing again, to the case of quantized Kac-Moody algebras, and taking the classical limit of these esoteric quantum groups, one re-discovers all the trigonometric and elliptic r-matrices of Belavin and Drinfeld. The formulas obtained here are easier to use than the original ones, and the structure of the space of classical r-matrices is more transparent. The r-matrices obtained here are more general in that they are defined on the full Kac-Moody algebras, the central extensions of the loop groups.

q-alg↗

arXiv1995

Universal T-matrix for Twisted Quantum gl(N)

The Universal T-matrix is the capstone of the structure that consists of a quantum group and its dual, and the central object from which spring the T-matrices (monodromies) of all the associated integrable models. A closed expression is obtained for the case of multiparameter (twisted) quantum $gl(N)$. The factorized nature of standard quantum groups, that allows the explicit expression for $U\hskip-1mm T $ to be obtained with relative ease, extends to some nonstandard quantum groups, such as those based on $A_n^{(2)}$, and perhaps to all. The paper is mostly concerned with parameters in general position, but the extension to roots of unity is also explored, in the case of $g\ell(N)$. The structure of the dual is now radically different, and an interesting generalization of the $q$-exponential appears in the formulas for the Universal T- and R-matrices. The projection to quantum $sl(N)$ is simple and direct; this allows, in particular, to apply recent results concerning deformations of twisted $gl(N)$ to the semisimple quotient.

q-alg↗

arXiv1995

Cohomology of Quantum Groups

Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the esoteric forms of quantum gl(N) by deformation theory.

q-alg↗