Probing the supersymmetric O(N) α-model to : Critical exponent η

Counterterms that are not reducible to ζ n are generated by 3 F 2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 8 19 and (5, 3) = 10 124 , are found in anomalous dimensions at O(1/N 3 ) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Padé resummations of ε-expansions, which are compared with analytical results in 3 dimensions. The O(1/N 3 ) results entail knots generated by three dressed propagators in the master two-loop two-point diagram. At higher orders in 1/N one encounters the uniquely positive hyperbolic 11-crossing knot, associated with an irreducible triple sum. At 12 crossings, a pair of 3-braid knots is generated, corresponding to a pair of irreducible double sums with alternating signs. The hyperbolic positive knots 10 139 and 10 152 are not generated by such self-energy insertions. * ) Work supported in part by grant CHRX-CT94-0579, from HUCAM.

show abstract

“…for the σ-model in 2 − 2ε dimensions. Using (59) to shift the dimensionality by two units, we obtain the ε-expansions…”

Section: Bosonic σ-Model and φ 4 -Theorymentioning

confidence: 99%

Beyond the triangle and uniqueness relations: non-zeta counterterms at large $N$ from positive knots

Broadhurst

Gracey

Kreimer

1997

Zeitschrift f�r Physik C Particles and Fields

Self Cite

124

210

View full text Add to dashboard Cite

show abstract

“…Otherwise the calculation is almost identical. We find small discrepancies with [20] in some of the diagrams, mostly factors of 2 and some minus signs. The most notable difference is Φ 1 , where the residue has a different denominator.…”

Section: Calculation Of the Graphs Needed For ηmentioning

confidence: 96%

“…Only bosonic propagators are shown. Similar identities with fermions can which are used in our calculation can be found in [20] which when antisymmetrizing to get the wedge product returns zero. So R 2 ∧ R 2 = 0 in our case, and we do not have to worry about the gravitational anomalies.…”

Section: A Anomaliesmentioning

confidence: 96%

See 1 more Smart Citation

Heterotic non-linear sigma models with anti-de Sitter target spaces

Michalogiorgakis

Gubser

2006

Nuclear Physics B

View full text Add to dashboard Cite

We calculate the beta function of non-linear sigma models with S D+1 and AdS D+1 target spaces in a 1/D expansion up to order 1/D 2 and to all orders in α ′ . This beta function encodes partial information about the spacetime effective action for the heterotic string to all orders in α ′ . We argue that a zero of the beta function, corresponding to a worldsheet CFT with AdS D+1 target space, arises from competition between the one-loop and higherloop terms, similarly to the bosonic and supersymmetric cases studied previously in [1]. Various critical exponents of the non-linear sigma model are calculated, and checks of the calculation are presented.

show abstract

“…In the N = 1 SUSY O(N) nonlinear sigma model in three dimensions, the next-to-leading order term in the β-function turned out to be absent modulo power divergences in the 1/N expansion [6] and in the critical exponent technique [7]. In the N = 2 SUSY CP N −1 model in three dimensions, the next-to-leading order term in the β-function was found to vanish [8,9].…”

Section: Introductionmentioning

confidence: 99%