Critical non-linearO(N) ?-Models at 2&lt;d&lt;4: The degeneracy of quasi-primary fields and its resolution

Lang, K.; Rühl, W.

doi:10.1007/bf01413189

Cited by 31 publications

(22 citation statements)

References 10 publications

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“…Consequently, these two theories correspond to different universality classes in 2<d<4 although strong evidence indicates that they coincide for d=4. The results (4.33) for the coupling g ,,O and (4.25) for C J agree with previously obtained results in [11].…”

Section: Discussion and Concluding Remarkssupporting

confidence: 93%

“…The consistency relations in this case provide a non-trivial check for the associativity of the OPE in d>2. Our detailed calculations are in many respects similar to those of Lang and Ru hl [10,11] and in large part we agree on their results, however our perspective is rather different. Discussions concerning possible implications of our result and concluding remarks are presented in Section 6.…”

Section: Introductionsupporting

confidence: 83%

See 1 more Smart Citation

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model

1996

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We discuss conserved currents and operator product expansions (OPE's) in the context of a O(N) invariant conformal field theory. Using OPE's we find explicit expressions for the first few terms in suitable short-distance limits for various four-point functions involving the fundamental N-component scalar field ,: (x), :=1, 2, ..., N. We propose an alternative evaluation of these four-point functions based on graphical expansions. Requiring consistency of the algebraic and graphical treatments of the four-point functions we obtain the values of the dynamical parameters in either a free theory of N massless fields or a non-trivial conformally invariant O(N) vector model in 2

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Section: Discussion and Concluding Remarkssupporting

confidence: 93%

Section: Introductionsupporting

confidence: 83%

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model

1996

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“…(3.33) in [21]. It is remarkable that for d = 3 the quadratic dependence of the anomalous dimension on n reduces to a linear one, and that we get the special case l = t = 0 of (55).…”

Section: Anomalous Dimensions At D =mentioning

confidence: 84%

“…We can use eqs. (3.28)-(3.42) and (3.17) of [21] to check the case d = 3. We find indeed (55) with the degeneracy lifted presumably at O(1/N 2 ).…”

Section: Anomalous Dimensions At D =mentioning

confidence: 99%

The minimal conformalO(N) vector sigma model atd= 3

Leonhardt¹,

Rühl²

2004

J. Phys. A: Math. Gen.

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For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order of differentiation.

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“…From the critical nonlinear O(N) sigma model a similar behavior is known, where the effective expansion parameter is k N 1/2 [16], where k denotes the number of fusions of fundamental fields.…”

Section: The Second Examplementioning

confidence: 98%