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Thu, 05 Apr 2001 00:00:00 +0200Thu, 05 Apr 2001 00:00:00 +0200Critical O(N) -vector nonlinear sigma-models: a resume of their field structure
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1191
Abstract: The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N)-Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d = 2 and d = 4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so. (To appear in the Proceedings of the XXII Conference on Differential Geometry Methods in Theoretical Physics, Ixtapa, Mexico, September 20-24, 1993)Klaus Lang; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1191Thu, 05 Apr 2001 00:00:00 +0200Aspects of the conformal operator product expansion in AdS/CFT correspondence
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1073
We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.Werner Rühl; Anastasios C. Petkou; Laurent Hoffmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1073Thu, 06 Apr 2000 00:00:00 +0200A note on the analyticity of AdS scalar exchange graphs in the crossed channel
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1074
We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.Werner Rühl; Anastasios C. Petkou; Laurent Hoffmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1074Thu, 06 Apr 2000 00:00:00 +0200The construction of trigonometric invariants for Weyl groups and the derivation of corresponding exactly solvable Sutherland models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1075
Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the coroot space and lead to an exactly solvable model of Sutherland type. We apply this construction to the \(F_4\) case.Oliver Haschke; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1075Thu, 06 Apr 2000 00:00:00 +0200An exactly solvable model of the Calogero type for the icosahedral group
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1076
We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.Oliver Haschke; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1076Thu, 06 Apr 2000 00:00:00 +0200Is it possible to construct exactly solvable models?
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1077
We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schrödinger operator. We prove the feasibility of our method by constructing a new "\(AG_3\) model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the \(B_3\) model. In order to better understand features of our construction we exhibit the \(F_4\) rational model with our method.Oliver Haschke; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1077Thu, 06 Apr 2000 00:00:00 +0200Remarks on 'Coloring Random Triangulation'
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1078
We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a 'formal' integral used by these authors as a proper integral. We show also, using their method, that the results obtained for the resolvent and the density are not reliable.S Balaska; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1078Thu, 06 Apr 2000 00:00:00 +0200On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1079
An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.S. Balaska; J. Maeder; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1079Thu, 06 Apr 2000 00:00:00 +0200The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1080
The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.S. Balaska; J. Maeder; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1080Thu, 06 Apr 2000 00:00:00 +0200Perturbative approach to the critical behaviour of two-matrix models in the limit N -> infinity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1081
We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders.S Balaska; J Maeder; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1081Thu, 06 Apr 2000 00:00:00 +0200Greensite-Halpern stabilization of Ak singularities in the N -> infty limit
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1082
The Greensite-Halpern method of stabilizing bottomless Euclidean actions is applied to zerodimensional O(N) sigma models with unstable \(A_k\) singularities in the \( N = \infty\) limit.J. Maeder; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1082Thu, 06 Apr 2000 00:00:00 +0200Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1083
O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N - > infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.Joachim Maeder; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1083Thu, 06 Apr 2000 00:00:00 +0200Double Scaling Limits and Catastrophes of the zerodimensional O(N) Vector Sigma Model: The A-Series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1084
We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1084Thu, 06 Apr 2000 00:00:00 +0200The critical O(N) sigma-model at dimension 2<d<4: Hardy-Ramanujan distribution of quasi-primary fields and a collective fusion approach
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1085
The distribution of quasiprimary fields of fixed classes characterized by their O(N) representations Y and the number p of vector fields from which they are composed at N=infty in dependence on their normal dimension delta is shown to obey a Hardy-Ramanujan law at leading order in a 1/N-expansion. We develop a method of collective fusion of the fundamental fields which yields arbitrary qps and resolves any degeneracy.Klaus Lang; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1085Thu, 06 Apr 2000 00:00:00 +0200Construction of exactly solvable quantum models of Calogero and Sutherland type with translation invariant four-particle interactions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1086
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.Oliver Haschke; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1086Thu, 06 Apr 2000 00:00:00 +0200Exactly solvable dynamical systems in the neighborhood of the Calogero model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1087
The Hamiltonian of the \(N\)-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For \(N = 3\) and \(N = 4\) such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all \(N\).Oliver Haschke; Werner Rühlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1087Thu, 06 Apr 2000 00:00:00 +0200