Perturbative c-theorem in d-dimensions

Yonekura, Kazuya

doi:10.1007/jhep04(2013)011

Cited by 20 publications

(16 citation statements)

References 89 publications

(189 reference statements)

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“…which correctly reduces to the free energies for odd d. They show as d approaches to even integers 2 (see also [10] (1) for small . This is because one has to add a local counter term 5) to the partition function to obtain the renormalized partition function log Z…”

Section: Jhep12(2014)161mentioning

confidence: 75%

Holographic interpolation between a and F

Kawano

Nakaguchi

Nishioka

2014

J. High Energ. Phys.

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An interpolating functionF between the a-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension d. We examineF in the large-N CFT's in d dimensions holographically described by the Einstein-Hilbert gravity in the AdS d+1 space. We show thatF is a smooth function of d and correctly interpolates the a coefficients and the free energies. The monotonicity ofF along an RG flow follows from the analytic continuation of the holographic c-theorem to continuous d, which completes the proof of the conjecture.

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Section: Jhep12(2014)161mentioning

confidence: 75%

Holographic interpolation between a and F

Kawano

Nakaguchi

Nishioka

2014

J. High Energ. Phys.

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“…Other arguments for a c, or a, theorem in six dimensions are given in [41]. This relates the variation of the free energy on a sphere as the radius varies to the metric defined by the two point function.…”

Section: Jhep04(2015)157mentioning

confidence: 99%

Structures on the conformal manifold in six dimensional theories

Osborn

Stergiou

2015

J. High Energ. Phys.

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The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown that there are three symmetric two index tensors only one of which satisfies any positivity conditions. The general results are specialised to the six dimensional conformal theory defined by free two-forms and also to the interacting scalar φ 3 theory at two loops which preserves conformal invariance to this order. All three two index tensor contributions are present.

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“…See, for example, Refs. [16][17][18][19] for recent in-depth studies of the OðNÞ symmetric ϕ 3 theory. For instance, the fixed point structure has been comprehensively studied perturbatively to three loops in Refs.…”

Section: Introductionmentioning

confidence: 98%

Four loop renormalization ofϕ3theory in six dimensions

2015

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We renormalize six-dimensional ϕ 3 theory in the modified minimal subtraction (MS) scheme at four loops. From the resulting β-function, anomalous dimension, and mass anomalous dimension, we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two-dimensional conformal field theory, we obtain estimates for exponents in dimensions 3, 4, and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an OðNÞ symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this OðNÞ analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigenexponents are in agreement with the mass exponents computed at Oð1=N 2 Þ in the nonperturbative large N expansion.

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Perturbative c-theorem in d-dimensions

Cited by 20 publications

References 89 publications

Holographic interpolation between a and F

Holographic interpolation between a and F

Structures on the conformal manifold in six dimensional theories

Four loop renormalization ofϕ3theory in six dimensions

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