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, Mohamed M.; Poppitz, Erich

doi:10.1007/jhep10(2015)051

Cited by 35 publications

(63 citation statements)

References 55 publications

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“…However, that result is not conclusive because the theory with n f ¼ 4 may have a conformal fixed point [9,11,12]. Results in a sequence of semiclassical studies of adjoint QCD, e.g., [13][14][15][16][17][18][19], are consistent with our constraints.…”

Section: Inequality For T Deconf and T Chiralsupporting

confidence: 75%

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Anomaly constraints on deconfinement and chiral phase transition

Shimizu

Yonekura²

2018

Phys. Rev. D

111

109

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We study the constraints on thermal phase transitions of SUðN c Þ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions and (ii) N f flavors of fundamental fermions with a nontrivial greatest common divisor, gcdðN c ; N f Þ ≠ 1. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version of the center symmetry, which we call centerflavor symmetry, and draw similar conclusions under a certain definition of confinement. Moreover, at zero temperature, our results give a partial explanation of the appearance of dual magnetic gauge groups in (supersymmetric) QCD when gcdðN c ; N f Þ ≠ 1.

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Section: Inequality For T Deconf and T Chiralsupporting

confidence: 75%

“…Because of the anomaly (19), there are constraints on phase transitions. First, let us discuss the case of a specific value of μ B .…”

Section: Thermal Phase Transitionmentioning

confidence: 99%

Anomaly constraints on deconfinement and chiral phase transition

Shimizu

Yonekura²

2018

Phys. Rev. D

111

109

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“…As emphasized, dYM has intrinsically 4d aspects not present in the 3d Polyakov model. There are a number of interesting recent works studying dYM, for example, [62][63][64][65][66], and [67][68][69], and see [70,71] for initial lattice studies.…”

Section: Deformed Yang-mills and Adiabatic Continuitymentioning

confidence: 99%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-N orbifold-orientifold equivalence connects a natural large-N limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-N volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at N = ∞ exhibit adiabatic continuity at finite-N , and also become semi-classically calculable on small R 3 × S 1 . We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.Keywords: large-N orbifold and orientifold equivalence, volume independence, double-trace deformations, adiabatic continuity, semi-classical calculability, magnetic and neutral bions, Picard-Lefschetz theory of path integration, and resurgence arXiv:1601.03414v1 [hep-th]

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“…33 Plugging the expansion (A.1) into the Yang-Mills Lagrangian one obtains, up 33 Here, ρ a = 1 2 (N +1) − a are the components of the Weyl vector in our basis. The expectation value A awhere ω k ≡ √ k 2 + M 2 and ( k) i ≡ ij (k) j (we use i, j = 1, 2 to denote spatial indices and take 12 = − 21 = 1).…”

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

Cited by 35 publications

References 55 publications

Anomaly constraints on deconfinement and chiral phase transition

Anomaly constraints on deconfinement and chiral phase transition

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

QCD on a small circle

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