The critical O(N) σ-model at dimensions 2 &lt; d &lt; 4: a list of quasi-primary fields

Lang, K.; Rühl, W.

doi:10.1016/0550-3213(93)90119-a

Cited by 63 publications

(91 citation statements)

References 6 publications

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“…We will then match our results with the 1/N expansions derived for the [4][5][6][7][8][9][10][11][12], evaluating them in d = 6− . The perfect match of the coefficients in these two 1/N expansions provides convincing evidence that the IR fixed point of the cubic O(N ) theory (1.2) indeed describes the same physics as the UV fixed point of the (φ i φ i ) 2 theory.…”

Section: This Leads To the Well-knownmentioning

confidence: 99%

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CriticalO(N)models in6−εdimensions

2014

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We revisit the classic O(N ) symmetric scalar field theories in d dimensions with interaction (φ i φ i ) 2 . For 2 < d < 4 these theories flow to the Wilson-Fisher fixed points for any N . A standard large N Hubbard-Stratonovich approach also indicates that, for 4 < d < 6, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of N + 1 massless scalars with the cubic interactions σφ i φ i and σ 3 . Our one-loop calculation in 6 − dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for N > 1038. We show that the 1/N expansions of various operator scaling dimensions match the known results for the critical O(N ) theory continued to d = 6 − . These results suggest that, for sufficiently large N , there are 5-dimensional unitary O(N ) symmetric interacting CFT's; they should be dual to the Vasiliev higher-spin theory in AdS 6 with alternate boundary conditions for the bulk scalar. Using these CFT's we provide a new test of the 5-dimensional F -theorem, and also find a new counterexample for the C T theorem.

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Section: This Leads To the Well-knownmentioning

confidence: 99%

“…We first note that the coefficients in the 1/N expansions derived for various quantities in [4][5][6][7][8][9][10][11][12] may be continued to the range (1.1) without any obvious difficulty. Thus, the UV fixed points make sense at least in the 1/N expansion.…”

Section: Introductionmentioning

confidence: 99%

CriticalO(N)models in6−εdimensions

2014

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“…These cases have been considered previously for a = b and S = d − 1, d respectively in [24,5] and results for any ℓ were given in [25].…”

Section: Appendix a Differential Operators For The Operator Product mentioning

confidence: 99%

Conformal four point functions and the operator product expansion

2001

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Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u, v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z, x which are simply related to u, v.

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“…The large N analysis of the interacting O(N ) vector model has been carried out for arbitrary dimension d in [39][40][41][42][43][44][45][46][47][48]. For the two cases studied in this work, d = 5 and d = 5.95, we record that the dimensions for the O(N ) fundamental φ i and the two lowest singlet operators σ and…”

Section: < D <mentioning

confidence: 99%

“…3 We emphasize that the lower bound on ∆ σ 2 (where this lower bound is chosen to be strictly greater than ∆ σ ) must be chosen judiciously if one's goal is to study the interacting O(N ) theories proposed in [55,56]. Indeed, in these theories, one has ∆ σ 2 = 4+O(1/N ), where the leading 1/N correction is negative [39][40][41][42][43][44][45][46][47][48]. At least at large N , one therefore expects the scaling dimension of σ 2 to be slightly less than four.…”

Section: Introductionmentioning

confidence: 99%

BootstrappingO(N)vector models in4<d<6

2015

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We use the conformal bootstrap to study conformal field theories with O(N ) global symmetry in d = 5 and d = 5.95 spacetime dimensions that have a scalar operator φ i transforming as an O(N ) vector. The crossing symmetry of the four-point function of this O(N ) vector operator, along with unitarity assumptions, determine constraints on the scaling dimensions of conformal primary operators in the φ i × φ j OPE. Imposing a lower bound on the second smallest scaling dimension of such an O(N )-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting O(N )-symmetric CFT conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest O(N ) singlet in the φ i × φ j OPE, we observe that this kink disappears in d = 5 for small enough N , suggesting that in this case an interacting O(N ) CFT may cease to exist for N below a certain critical value. *

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The critical O(N) σ-model at dimensions 2 < d < 4: a list of quasi-primary fields

Cited by 63 publications

References 6 publications

CriticalO(N)models in6−εdimensions

CriticalO(N)models in6−εdimensions

Conformal four point functions and the operator product expansion

BootstrappingO(N)vector models in4<d<6

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