Phase structure and compactness

Nándori, I.; Nagy, S.; Sailer, K.; Trombettoni, Andrea

doi:10.1007/jhep09(2010)069

Cited by 15 publications

(12 citation statements)

References 76 publications

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“…There are a large number of good reviews [8,9,10,11]. A lot of work has been done on the RG of the Sine-Gordon model over the last few years and many computations have been carried out analytically and numerically [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. This paper primarily studies the application of ERG mainly to two dimensional field theories -the emphasis being on a simple way of writing down the solution to the ERG in terms of an evolution operator.…”

Section: Introductionmentioning

confidence: 99%

Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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Abstract:The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional φ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating cfunctions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.

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Section: Introductionmentioning

confidence: 99%

Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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“…The integration by the momentum q can be performed by choosing the R k (q 2 ) regulator function in such a way that it satisfies all the following requirements: Γ k approaches the bare action in the limit k → Λ and the full quantum effective action when k → 0 [18]. Various types of regulator functions can be chosen, but a more general choice is the so-called Compactly Supported Smooth regulator (CSS) [31][32][33] which recovers all major types of regulators in its appropriate limits. By using a particular normalisation [32,33] and the notation y = q 2 /k 2 , the dimensionless CSS regulator (r k (q 2 ) ≡ R k (q 2 )/q 2 ) has the following form…”

Section: A the Functional Renormalisation Groupmentioning

confidence: 99%

Vanishing beta function curves from the functional renormalization group

Mati

2015

Phys. Rev. D

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In this paper we will discuss the derivation of the so-called vanishing beta function curves which can be used to explore the fixed point structure of the theory under consideration. This can be applied to the O(N ) symmetric theories, essentially, for arbitrary dimensions (D) and field component (N ). We will show the restoration of the Mermin-Wagner theorem for theories defined in D ≤ 2 and the presence of the Wilson-Fisher fixed point in 2 < D < 4. Triviality is found in D > 4. Interestingly, one needs to make an excursion to the complex plane to see the triviality of the four-dimensional O(N ) theories. The large -N analysis shows a new fixed point candidate in 4 < D < 6 dimensions which turns out to define an unbounded fixed point potential supporting the recent results by R. Percacci and G. P. Vacca in: "Are there scaling solutions in the O(N )-models for large -N in D > 4?" [Phys. Rev. D 90, 107702 (2014)].

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“…There is a line of Gaussian fixed points in the asymptotically free phase, too, but these fixed points are UV and their scaling laws are linearizable. The IR scaling is difficult to establish numerically because of the instability of the Fourier expansion [16] in any RG scheme, used so far. Nevertheless it is unambiguous from numerics that z tends to be big as the scale k is decreased, whileũ 1 (12) and (13).…”

mentioning

confidence: 99%