Higher dimensional higher derivative 
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 theory

Gracey, J.A.; Simms, R. M.

doi:10.1103/physrevd.96.025022

Cited by 17 publications

(13 citation statements)

References 89 publications

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“…In terms of the dimensionless field ϕ the dimensionless functions (d = d c − and δ = d/2−2) are defined as (18) and their flow equations at quadratic order are…”

Section: Theories Of the Second Type: The Case K =mentioning

confidence: 99%

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Multicritical scalar theories with higher-derivative kinetic terms: A perturbative RG approach with the ε -expansion

Safari

Vacca

2018

Phys. Rev. D

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We employ perturbative RG and -expansion to study multicritical single-scalar field theories with higher derivative kinetic terms of the form φ(− ) k φ. We focus on those with a Z2-symmetric critical point which are characterized by an upper critical dimension dc = 2nk/(n − 1) accumulating at even integers. We distinguish two types of theories depending on whether or not the numbers k and n − 1 are relatively prime. When they are, the critical theory involves a marginal power-like interaction φ 2n and the deformations admit a derivative expansion that at leading order involves only the potential. In this case we present the beta functional of the potential and use this to calculate some anomalous dimensions and OPE coefficients. These confirm some CFT data obtained using conformal-block techniques, while giving new results. In the second case where k and n − 1 have a common divisor, the theories show a much richer structure induced by the presence of marginal derivative operators at criticality. We study the case k = 2 with odd values of n, which fall in the second class, and calculate the functional flows and spectrum. These theories have a phase diagram characterized at leading order in by four fixed points which apart from the Gaussian UV fixed point include an IR fixed point with a purely derivative interaction.

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“…In terms of the dimensionless field ϕ the dimensionless functions (d = d c − and δ = d/2−2) are defined as (18) and their flow equations at quadratic order are…”

Section: Theories Of the Second Type: The Case K =mentioning

confidence: 99%

“…The corresponding free theories had been earlier analysed in [16] mainly motivated by de Sitter holography. Theories with higher derivative kinetic terms in higher dimensions have been considered also in [17] and from a pure RG perspective in [18].…”

Section: Introductionmentioning

confidence: 99%

Multicritical scalar theories with higher-derivative kinetic terms: A perturbative RG approach with the ε -expansion

Safari

Vacca

2018

Phys. Rev. D

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“…One usually needs to resort to some approximations in order to obtain tractable RG equations in the full theory space, but reasonably precise results can be nevertheless obtained, as shown for example in the computation of the critical exponents of the Ising universality class and its O(N )-symmetric extensions [14]. The investigations of several different universality classes -new and old -continues to this day and certainly will not lose momentum any time soon [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Leading order CFT analysis of multi-scalar theories in $$d>2$$ d > 2

et al. 2019

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We investigate multi-field multicritical scalar theories using CFT constraints on two-and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define to admit a Landau-Ginzburg description that includes the most general critical interactions built from monomials of the form φ i 1 . . . φ i m . For all such models we analyze to the leading order of the -expansion the anomalous dimensions of the fields and those of the composite quadratic operators. For models with even m we extend the analysis to an infinite tower of composite operators of arbitrary order. The results are supplemented by the computation of some families of structure constants. We also find the equations which constrain the nontrivial critical theories at leading order and show that they coincide with the ones obtained with functional perturbative RG methods. This is done for the case m = 3 as well as for all the even models. We ultimately specialize to S q symmetric models, which are related to the q-state Potts universality class, and focus on three realizations appearing below the upper critical dimensions 6, 4 and 10 3 , which can thus be nontrivial CFTs in three dimensions.

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“…Another class of scalar theories that further generalizes the above models and has recently received more attention in the literature includes those with a higher derivative kinetic term of the form φ(− ) k φ [17][18][19][20][21][22] or k theories for short, where k is a positive integer. Despite their nonunitary nature, theories with higher derivatives have found interesting physical applications.…”

Section: Introductionmentioning

confidence: 99%

Uncovering novel phase structures in $$\Box ^k$$ □ k scalar theories with the renormalization group

Safari

Vacca

2018

Eur. Phys. J. C

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We present a detailed version of our recent work on the RG approach to multicritical scalar theories with higher derivative kinetic term φ(−) k φ and upper critical dimension d c = 2nk/(n − 1). Depending on whether the numbers k and n have a common divisor two classes of theories have been distinguished. For coprime k and n − 1 the theory admits a Wilson-Fisher type fixed point. We derive in this case the RG equations of the potential and compute the scaling dimensions and some OPE coefficients, mostly at leading order in. While giving new results, the critical data we provide are compared, when possible, and accord with a recent alternative approach using the analytic structure of conformal blocks. Instead when k and n − 1 have a common divisor we unveil a novel interacting structure at criticality. 2 theories with odd n, which fall in this class, are analyzed in detail. Using the RG flows it is shown that a derivative interaction is unavoidable at the critical point. In particular there is an infrared fixed point with a pure derivative interaction at which we compute the scaling dimensions and, for the particular example of 2 theory in d c = 6, also some OPE coefficients. * = 0 pattern of mixing, which includes non-derivative couplings as well, in this case is given by the following table

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Higher dimensional higher derivative ϕ4 theory

Cited by 17 publications

References 89 publications

Multicritical scalar theories with higher-derivative kinetic terms: A perturbative RG approach with the ε -expansion

Multicritical scalar theories with higher-derivative kinetic terms: A perturbative RG approach with the ε -expansion

Leading order CFT analysis of multi-scalar theories in $$d>2$$ d > 2

Uncovering novel phase structures in $$\Box ^k$$ □ k scalar theories with the renormalization group

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