Deconfining phase transition in 2+1 D: the Georgi-Glashow model

Dunne, Gerald V.; Kogan, Ian I.; Kovner, Alex; Tekin, Bayram

doi:10.1088/1126-6708/2001/01/032

Cited by 60 publications

(185 citation statements)

References 14 publications

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“…If (3.5) was all that was relevant in this temperature range, it would lead to a high-temperature phase with an infinite correlation length -while we expect to have finite correlation length above the deconfinement transition due to Debye screening of electric charges. It has already been noted [11], in the context of the 3d Polyakov model, that the BKT behavior described above is not the one expected of a confinement-deconfinement transition.…”

Section: Jhep04(2012)040mentioning

confidence: 86%

“…13 Thus, in the limit of large T 2 , the ground state of the Hamiltonian may not be an eigenstate of Z 2 as in (2.17), but may be a linear superposition between even and odd sectors corresponding to a fixed value of e iσ/2 = ±1 instead; we shall see in the next section that this is indeed the case in the SO(3) theory. 11 In the full theory, the Z2-odd ("half-integer" in our convention) flux sector is constructed by considering SO(3) bundles on T 2 twisted along one of the non contractible loops on T 2 by gauge transformations in the topologically nontrivial class π1(SO(3)) = Z2. This way to construct discrete flux sectors on tori is explained in [36]; see [37] for different perspectives.…”

Section: Jhep04(2012)040mentioning

confidence: 99%

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2d affine XY-spin model/4d gauge theory duality and deconfinement

Anber

Poppitz

Ünsal

2012

J. High Energ. Phys.

103

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We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2)/Z 2 gauge theories, compactified on a small spatial circle R 1,2 × S 1 , and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R 2 × T 2 . Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multicomponent electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopoleinstantons or magnetic bions, and the vortices in the spin system map to the electrically charged W -bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N c ) gauge theories with n f ≥1 adjoint Weyl fermions.

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Section: Jhep04(2012)040mentioning

confidence: 86%

Section: Jhep04(2012)040mentioning

confidence: 99%

2d affine XY-spin model/4d gauge theory duality and deconfinement

Anber

Poppitz

Ünsal

2012

J. High Energ. Phys.

103

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“…Ref. [16] (see also the earlier work of [43] on a similar description in the Polyakov model, and also the work [44] for other perspective) argued that the thermal partition function of dYM reduces to a two-dimensional "classical" electricmagnetic Coulomb gas of W -bosons and monopole-instantons and that this gas exhibits a deconfinement phase transition at T c = g 2 4πL . Qualitatively, at low-temperatures magnetic charges (the monopole-instantons) are dominant, causing screening of magnetic charge and confinement of electric charges.…”

Section: Jhep10(2015)051mentioning

confidence: 93%

On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$

Anber

Poppitz

2015

J. High Energ. Phys.

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Spatial compactification on R 3 ×S 1 L at small S 1 -size L often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the center and discrete chiral symmetries. Within this semiclassically calculable framework, we study how distinct theories with the same SU(N c )/Z k gauge group (labeled by "discrete θ-angles") arise upon gauging of appropriate Z k subgroups of the oneform global center symmetry of an SU(N c ) gauge theory. We determine the possible Z k actions on the local electric and magnetic effective degrees of freedom, find the ground states, and use domain walls and confining strings to give a physical picture of the vacuum structure of the different SU(N c )/Z k theories. Some of our results reproduce ones from earlier supersymmetric studies, but most are new and do not invoke supersymmetry. We also study a further finite-temperature compactification to R 2 × S 1 β × S 1 L . We argue that, in deformed Yang-Mills theory, the effective theory near the deconfinement temperature β c L exhibits an emergent Kramers-Wannier duality and that it exchanges high-and low-temperature theories with different global structure, sharing features with both the Ising model and S-duality in N = 4 supersymmetric Yang-Mills theory.

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“…As it has already been discussed in the Introduction, this phase transition occurs when the density of monopoles, approximately equal to 2ξ, becomes of the same order of magnitude as the density of W-bosons [3]. The latter can be evaluated as follows (see e.g.…”

Section: Critical Temperatures Of the Deconfining Phase Transitionmentioning

confidence: 92%

“…Then, in the case T in < T 1 , the situation is identical to the one discussed in ref. [3], namely µ becomes irrelevant and decreases to zero. Indeed, from the evolution equation for µ there follows the equation for dµ/dt, by virtue of which one can determine the sign of this quantity.…”

Section: Critical Temperatures Of the Deconfining Phase Transitionmentioning

confidence: 99%

Deconfining phase transition in the 3D Georgi–Glashow model with finite Higgs-boson mass

Antonov

2002

Physics Letters B

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The (2+1)D Georgi-Glashow model is explored at finite temperature in the regime when the Higgs boson is not infinitely heavy. The resulting Higgs-mediated interaction of monopoles leads to the appearance of a certain upper bound for the parameter of the weak-coupling approximation. Namely, when this bound is exceeded, the cumulant expansion used for the average over the Higgs field breaks down. The finite-temperature deconfining phase transition with the account for the same Higgs-mediated interaction of monopoles is further analysed. It is demonstrated that in the general case, accounting for this interaction leads to the existence of two distinct phase transitions separated by the temperature region where W-bosons exist in both, molecular and plasma, phases. The dependence of possible ranges of the critical temperatures corresponding to these phase transitions on the parameters of the Georgi-Glashow model is discussed. The difference in the RG behaviour of the fugacity of W-bosons from the respective behaviour of this quantity in the compact-QED limit of the model is finally pointed out.

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Deconfining phase transition in 2+1 D: the Georgi-Glashow model

Cited by 60 publications

References 14 publications

2d affine XY-spin model/4d gauge theory duality and deconfinement

2d affine XY-spin model/4d gauge theory duality and deconfinement

On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$

Deconfining phase transition in the 3D Georgi–Glashow model with finite Higgs-boson mass

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