θ dependence of SU(N) gauge theories in the presence of a topological term

Vicari, Ettore; Panagopoulos, H.

doi:10.1016/j.physrep.2008.10.001

Cited by 223 publications

(343 citation statements)

References 597 publications

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“…This is the reason why on the Lattice one can extract results only up to few terms in the expansion around θ = 0, either analytically continuing from imaginary θ values or computing certain correlators at θ = 0. See [1] for an excellent review on the subject.…”

Section: Introductionmentioning

confidence: 99%

Theta Dependence in Yang-Mills from Holography

2016

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Abstract. In this contribution we review how holographic tools can be used to study the dependence on the CP-breaking θ parameter of various observables in a large N c Yang-Mills model. Relevant examples are the ground-state energy density, the string tension, the glueball mass spectrum and the critical temperature for deconfinement. These observables have been also studied, in the small θ regime and up to very few powers of θ 2 , in pure Yang-Mills on the Lattice. The holographic results qualitatively agree with available Lattice data and, being exact in θ, provide benchmarks for higher order corrections.

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Section: Introductionmentioning

confidence: 99%

Theta Dependence in Yang-Mills from Holography

2016

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“…In that case, a possible partial solution is to study the theory at imaginary µ B , where the sign problem disappears, and then make use of analytic continuation to infer the dependence at real µ B , at least for small values of µ B /T [4]. An analogous approach has been proposed for exploring a non-zero θ [5-8]; as for µ B = 0, also in this case one assumes that the theory is analytic around θ = 0, a fact supported by our present knowledge about free energy derivatives at θ = 0 [9,10].Various studies have shown that the dependence of the critical temperature on the baryon chemical potential, T c (µ B ), can be determined reliably up to the quadratic order in µ B , while ambiguities related to the procedure of analytic continuation may affect higher order terms [11]. It is natural to assume that a similar scenario takes place for analytic continuation from an imaginary θ ≡ iθ I term, i.e.…”

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confidence: 99%

θDependence of the Deconfinement Temperature in Yang-Mills Theories

D’Elia

Negro

2012

Phys. Rev. Lett.

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We determine the θ dependence of the deconfinement temperature of SU(3) pure gauge theory, finding that it decreases in presence of a topological θ term. We do that by performing lattice simulations at imaginary θ, then exploiting analytic continuation. We also give an estimate of such dependence in the limit of a large number of colors N , and compare it with our numerical results.PACS numbers: 12.38. Aw, 11.15.Ha,12.38.Gc The possible effects of a CP violating term in Quantum ChromoDynamics (QCD) have been studied since long. Such term enters the Euclidean lagrangian as follows:where q(x) is the topological charge density. Experimental upper bounds on θ are quite stringent (|θ| 10 −10 ), suggesting that such term may be forbidden by some mechanism. Nevertheless, the dependence of QCD and of SU (N ) gauge theories on θ is of great theoretical and phenomenological interest. θ derivatives of the vacuum free energy, computed at θ = 0, enter various aspects of hadron phenomenology; an example is the topological susceptibility χ ≡ Q 2 /V (Q ≡ d 4 x q(x) and V is the space-time volume) which enters the solution of the so-called U (1) A problem [1,2]. Moreover it has been proposed [3] that topological charge fluctuations may play an important role at finite temperature T , especially around the deconfinement transition, where local effective variations of θ may be detectable as event by event P and CP violations in heavy ion collisions.In the present work we study the effect of a non-zero θ on the critical deconfining temperature T c , considering the case of pure Yang-Mills theories. Due to the symmetry under CP at θ = 0, the critical temperature T c (θ) is expected, similarly to the free energy, to be an even function of θ. Therefore we parameterize T c (θ) as followsIn the following we shall determine R θ for the SU (3) pure gauge theory, obtaining R θ > 0, and compare it with a simple model computation valid in the large N limit, showing that R θ is expected to be O(1/N 2 ).The method -Effects related to the topological θ term are typically of non-perturbative nature, hence numerical simulations on a lattice represent the ideal tool to explore them. However, it is well known that the Euclidean path integral representation of the partition functionis not suitable for Monte-Carlo simulations because the measure is complex when θ = 0. S QCD = d 4 x L QCD and periodic boundary conditions are assumed over the compactified time dimension of extension 1/T ; f (θ) is the free energy density and V s is the spatial volume.A similar sign problem is met for QCD at finite baryon chemical potential µ B , where the fermion determinant becomes complex. In that case, a possible partial solution is to study the theory at imaginary µ B , where the sign problem disappears, and then make use of analytic continuation to infer the dependence at real µ B , at least for small values of µ B /T [4]. An analogous approach has been proposed for exploring a non-zero θ [5-8]; as for µ B = 0, also in this case one assumes that the theory is a...

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“…After 10-15 years of exploratory computations with cooling techniques, well summarized in Ref. [25], a theoretically well defined definition of the cumulants of the topological charge was found [26,27,28,29,30,31]. The value of the topological susceptibility obtained with the Neuberger definition of the charge [32] indeed supports the Witten-Veneziano explanation for the large experimental value of the η ′ mass.…”

Section: Introductionmentioning

confidence: 53%