Polyakov loops and the Hosotani mechanism on the lattice

Cossu, Guido; Noaki, J.; Hatanaka, Hisaki; Hosotani, Yutaka

doi:10.1103/physrevd.89.094509

Cited by 51 publications

(62 citation statements)

References 56 publications

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“…Alternatively, the full 4D gauge theory with sufficiently light adjoint fermions could be studied on the lattice. In fact, lattice studies of QCD(adj) on "R 3 " × S 1 L , with a particular focus towards its abelianization at small-L have recently appeared, with promising results [53]. Generally, we expect that the interplay of lattice and analytical methods will be crucial in the study of the transition from the small-L, weakly coupled abelian, to the large-L, strongly coupled nonabelian, regime.…”

Section: Discussionmentioning

confidence: 99%

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model

Anber

Collier

Poppitz

et al. 2013

J. High Energ. Phys.

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We study finite-temperature N = 1 SU (2) super Yang-Mills theory, compactified on a spatial circle of size L with supersymmetric boundary conditions. In the semiclassical small-L regime, a deconfinement transition occurs at T c 1/L. The transition is due to a competition between non-perturbative topological "molecules"-magnetic and neutral bioninstantons-and electrically charged W -bosons and superpartners. Compared to deconfinement in non-supersymmetric QCD(adj) [1], the novelty is the relevance of the light modulus scalar field. It mediates interactions between neutral bions (and W -bosons), serves as an order parameter for the Z (L) 2 center symmetry associated with the non-thermal circle, and explicitly breaks the electric-magnetic (Kramers-Wannier) duality enjoyed by non-supersymmetric QCD(adj) near T c . We show that deconfinement can be studied using an effective twodimensional gas of electric and magnetic charges with (dual) Coulomb and Aharonov-Bohm interactions, or, equivalently, via an XY-spin model with a symmetry-breaking perturbation, where each system couples to the scalar field. To study the realization of the discrete Rsymmetry and the Z remaining unbroken at the transition. Thus, the SYM transition appears similar to the one in SU (2) QCD(adj) [1] and is also likely to be characterized by continuously varying critical exponents.

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Section: Discussionmentioning

confidence: 99%

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model

Anber

Collier

Poppitz

et al. 2013

J. High Energ. Phys.

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“…As mentioned earlier, a particularly simple case which we will focus on is n f = N . For this number of flavors the tree-level constituent quark masses (4.24) become half-integers times m W , 28) with k = a − A + nN and n ∈ Z + 1 2 . The resulting bound state energies are given by…”

Section: Mesonsmentioning

confidence: 99%

QCD on a small circle

et al. 2017

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QCD-like theories can be engineered to remain in a confined phase when compactified on an arbitrarily small circle, where their features may be studied quantitatively in a controlled fashion. Previous work has elucidated the generation of a non-perturbative mass gap and the spontaneous breaking of chiral symmetry in this regime. Here, we study the rich spectrum of hadronic states, including glueball, meson, and baryon resonances. We find an exponentially growing Hagedorn density of states, as well as the emergence of non-perturbative energy scales given by iterated exponentials of the inverse Yang-Mills coupling g 2 .arXiv:1707.08971v1 [hep-th]

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“…It is stressed byÜnsal and his collaborators that these configurations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], which are termed "bions", have two physical significances associated with two types of topologically trivial bion configurations called "magnetic (charged) bions" and "neutral bions", as seen in the following examples: in the weak-coupling regime (L ≪ 1/Λ QCD ) in QCD(adj.) on R 3 × S 1 , or in the U(1) N −1 center-symmetric phase [20][21][22][23][24][25][26][27][28][29], condensation of magnetic bions (zero topological charge and nonzero magnetic charge) causes the confinement [3][4][5][6][7][8][9]. This confinement mechanism may remain responsible for the confinement at strong-coupling regime due to the continuity principle.…”

Section: Introductionmentioning

confidence: 99%

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

Misumi

Nitta

Sakai

2014

J. High Energ. Phys.

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We study classical configurations in the CP N −1 model on R 1 × S 1 with twisted boundary conditions. We focus on specific configurations composed of multiple fractionalized-instantons, termed "neutral bions", which are identified as "perturbative infrared renormalons" byÜnsal and his collaborators. For Z N twisted boundary conditions, we consider an explicit ansatz corresponding to topologically trivial configurations containing one fractionalized instanton (ν = 1/N ) and one fractionalized anti-instanton (ν = −1/N ) at large separations, and exhibit the attractive interaction between the instanton constituents and how they behave at shorter separations. We show that the bosonic interaction potential between the constituents as a function of both the separation and N is consistent with the standard separated-instanton calculus even from short to large separations, which indicates that the ansatz enables us to study bions and the related physics for a wide range of separations. We also propose different bion ansatze in a certain non-Z N twisted boundary condition corresponding to the "split" vacuum for N = 3 and its extensions for N ≥ 3. We find that the interaction potential has qualitatively the same asymptotic behavior and N -dependence as those of bions for Z N twisted boundary conditions.

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Polyakov loops and the Hosotani mechanism on the lattice

Cited by 51 publications

References 56 publications

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model

QCD on a small circle

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

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