Asymptotic freedom as a spin effect

Nielsen, N.K.

doi:10.1119/1.12565

Cited by 98 publications

(102 citation statements)

References 0 publications

Supporting

Mentioning

101

Contrasting

Order By: Relevance

“…The purpose of the present work is to describe the nature of this unusual phase transition and to make some (probably not very accurate) estimates of some of the numbers involved, such as the critical value k c of k. The essence of this phase transition is the analog [5,6,18] of asymptotic freedom in four dimensions, as indicated by a crucial sign coming from the spin-dependent gauge-boson couplings [19]. Of course, there is no renormalization group in d = 3 gauge theory, so the usual calculation of a β-function which reveals this sign structure in d = 4 cannot be done.…”

Section: Introductionmentioning

confidence: 99%

Phase transition inD=3Yang-Mills Chern-Simons gauge theory

Cornwall

1996

Phys. Rev. D

View full text Add to dashboard Cite

SU(N) Yang-Mills theory in three dimensions, with a Chern-Simons term of level k (an integer) added, has two dimensionful coupling constants, g 2 k and g 2 N; its possible phases depend on the size of k relative to N. For k ≫ N, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For k = 0, the theory is badly infrared singular in perturbation theory, a non-perturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of k, called k c , with k c /N ≈ 2 ± .7. Three lines of evidence are given: First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if k ≤ 29N/12. The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the k = 0 case. Second, we study in a rough approximation the free energy and show that for k ≤ k c there is a non-trivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass M, while both the condensate and M vanish for k ≥ k c . Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass m and a (gauge-invariant) dynamical mass M. We show that if M > ∼ 0.5m, there are finite-action quantum sphalerons, while none survive in the classical limit M = 0, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as M → 0.

show abstract

Section: Introductionmentioning

confidence: 99%

Phase transition inD=3Yang-Mills Chern-Simons gauge theory

Cornwall

1996

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…For QED, the sum over the charge(s) is simply 1, so we obtain 4πχ → + e 2 12π 2 log 2eH Λ 2 , again in accordance with eq.(2). Having outlined the calculation of [1,2], we now proceed to the main part of the paper and switch on temperature.…”

Section: The Zero Temperature Casementioning

confidence: 99%

“…[1,2]. To obtain a scale-dependent µ, let us look at the change in the energy E of the vacuum when an external magnetic field H is applied:…”

Section: The Zero Temperature Casementioning

confidence: 99%

“…In this work, we extend the approach of [1,2] to finite temperature and calculate an effective coupling constant α eff (k, T ). Instead of a loop expansion, we evaluate the energy shift of the vacuum to order e 2 after applying an external (chromo)magnetic field H. The connection of magnetic permeability and dielectric permittivity at finite temperature is made by invoking a renormalization group argument.…”

Section: Introductionmentioning

confidence: 99%

“…In refs. [1,2], it has been shown that the running of a coupling constant at T = 0 can be understood in physical terms by the polarizability of the vacuum. The effects of fluctuations can be incorporated to a certain extent in a scale dependent dielectric permittivity ǫ that defines an effective charge α eff = α/ǫ.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Debye screening at finite temperature reexamined

Schneider

2002

Phys. Rev. D

View full text Add to dashboard Cite

We present an alternative way to calculate the screening of the static potential between two charges in (non)abelian gauge theories at high temperatures. Instead of a loop expansion of a gauge boson self-energy, we evaluate the energy shift of the vacuum to order e 2 after applying an external static magnetic field and extract a temperature-and momentum-dependent dielectric permittivity. The Hard Thermal Loop (HTL) gluon and photon Debye masses are recovered from the lowest lying Landau levels of the perturbed vacuum. In QED, the complete calculation exhibits an interesting cancellation of terms, resulting in a logarithmic running α(T ). In QCD, a Landau pole in αs arises in the infrared from the sign of the gluon contribution, as in more sophisticated thermal renormalization group calculations.

show abstract

One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

Avramidi

1999

Fortschr. Phys.

View full text Add to dashboard Cite

We study the effective action in Euclidean Yang‐Mills theory with a compact simple gauge group in one‐loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many “magnetic fields” in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of “magnetic fields” do not differ much from each other. In the present paper we exactly calculate the relevant zeta‐functions in the case of equal amplitudes of “magnetic fields”. For two “magnetic fields” with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4,5,6,7 (8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9,10,11 (8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non‐perturbative stable vacuum with nonvanishing “magnetic fields”. The critical value of the coupling constant and the amplitudes of the vacuum “magnetic fields” are evaluated exactly. PACS numbers: 11.10Kk, 11.15Tk, 11.15.‐q, 12.38Aw, 12.38Lg

show abstract

Asymptotic freedom as a spin effect

Cited by 98 publications

References 0 publications

Phase transition inD=3Yang-Mills Chern-Simons gauge theory

Phase transition inD=3Yang-Mills Chern-Simons gauge theory

Debye screening at finite temperature reexamined

One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

Contact Info

Product

Resources

About