Interaction potential in compact three-dimensional QED with mixed action

Kovner, Alex; Svetitsky, Benjamin

doi:10.1103/physrevd.60.105032

Cited by 8 publications

(20 citation statements)

References 18 publications

(51 reference statements)

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“…Clearly, its meaning is precisely the same as of the classical soliton solution of the effective σ-model eq. (11). Also, the QCD instanton action and the σ-model soliton action have the same physical meaning.…”

Section: The Hamiltonian Portrait Of An Instantonmentioning

confidence: 98%

“…Below we show how the divergent terms cancel exactly, so that in the numerical calculations we only take into account finite terms in the limit Λ → ∞. We are searching for an instanton solution of topological charge one to the action (11). Such a solution should have the maximally symmetric "hedgehog" form,…”

Section: Small Size Instantonsmentioning

confidence: 99%

“…Nevertheless this variational approach captures many of the essential features of gluodynamics; mass generation, formation of the gluon condensate, [2], and asymptotic freedom, [7,8,10]. Possible appearance of the linear potential between static quarks in this approach has also been discussed [9][10][11]. In fact one of the nicer features of this approximation is that it exhibits nontrivial nonperturbative infrared physics (gluon condensate) along with correct weak coupling ultraviolet behavior (one loop Yang-Mills β function).…”

Section: Introductionmentioning

confidence: 99%

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Instantons and the QCD vacuum wave functional

et al. 1999

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We analyze the instanton transitions in the framework of the gauge invariant variational calculation in the pure Yang-Mills theory. Instantons are identified with the saddle points in the integration over the gauge group which projects the Gaussian wave functional onto the gauge invariant physical Hilbert space. We show that the dynamical mass present in the best variational state provides an infrared cutoff for the instanton sizes. The instantons of the size ρ < 1/M are suppressed and the large size instanton problem arising in the standard WKB calculation is completely avoided in the present variational framework.

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Section: The Hamiltonian Portrait Of An Instantonmentioning

confidence: 98%

Section: Small Size Instantonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Instantons and the QCD vacuum wave functional

et al. 1999

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“…Several cautionary lessons from 3-dimensional, compact electrodynamics can be found in Ref. [21]. (The behavior of the adjoint Wilson loop would be of interest as well.)…”

Section: F Further Physical Implications and Applicationsmentioning

confidence: 99%

“…The mechanism of dimensional transmutation becomes manifestly gauge-invariant and particularly transparent from this perspective [18], and the dynamical mass gap [19] emerges already from a minimal parametrization of the Gaussian "core" wave functional [17]. The projection onto the gauge-singlet component of this core functional may furthermore generate an area law for spacelike Wilson loops and thereby account for linear quark confinement [17,18,20], although experience from compact electrodynamics suggests that the vacuum wave functional will need non-minimal adjustments to describe the charged sector [21]. Another attractive feature of this approach is that it reexpresses the infrared dynamics in terms of gauge-invariant matrix fields (which subsume whole families of gauge-field orbits [22]) and that it preserves traceable links of heuristic value between these soft collective fields and the underlying Yang-Mills fields.…”

Section: Introductionmentioning

confidence: 99%

Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional

Forkel

2010

Phys. Rev. D

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We study a gauge-invariant variational framework for the Yang-Mills vacuum wave functional. Our approach is built on gauge-averaged Gaussian trial functionals which substantially extend previously used trial bases in the infrared by implementing a general low-momentum expansion for the vacuum field dispersion (which is taken to be analytic at zero momentum). When completed by the perturbative Yang-Mills dispersion at high momenta, this results in a significantly enlarged trial functional space which incorporates both dynamical mass generation and asymptotic freedom. After casting the dynamics associated with these wave functionals into an effective action for collections of soft vacuum-field orbits, the leading infrared improvements manifest themselves as four-gradient interactions. Those turn out to significantly lower the minimal vacuum energy density, thus indicating a clear overall improvement of the vacuum description. The dimensional transmutation mechanism and the dynamically generated mass scale remain almost quantitatively robust, however, which ensures that our prediction for the gluon condensate is consistent with standard values. Further results include a finite group velocity for the soft gluonic modes due to the higher-gradient corrections and indications for a negative differential color resistance of the Yang-Mills vacuum.

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Conformal field theory and the hot phase of three-dimensional U(1) gauge theory

Caselle

Nada

Panero

et al. 2019

J. High Energ. Phys.

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We study the high-temperature phase of compact U(1) gauge theory in 2 + 1 dimensions, comparing the results of lattice calculations with analytical predictions from the conformalfield-theory description of the low-temperature phase of the bidimensional XY model. We focus on the two-point correlation functions of probe charges and the field-strength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory. arXiv:1903.00491v2 [cond-mat.str-el] 13 May 2019Polyakov loop can be directly related to the free energy associated with a chromoelectric probe charge: in the thermodynamic limit P vanishes for T < T c (implying an infinite energy cost for the existence of an isolated fundamental color source in the confining phase, i.e. quark confinement), whereas it has a finite expectation value at T > T c . In contrast, the U(1) center symmetry of U(1) gauge theory in 2 + 1 dimensions remains unbroken, and, while in the high-temperature phase the theory does not have a dynamically generated, finite, characteristic length scale, the logarithmic Coulomb potential is still sufficient to confine static charges.As the finite-temperature transition in U(1) gauge theory in 2 + 1 dimensions is continuous, one expects that at T = T c the long-distance properties of the system are equivalent to those of a two-dimensional spin system with global U(1) symmetry [116], i.e. the classical XY model, that exhibits a Kosterlitz-Thouless transition [117] (see also refs. [118-121]). In the past, the validity of this conjecture has been investigated in various numerical studies [87,[101][102][103] and the most recent work gives conclusive evidence in support of it [104].As discussed in ref. [116], this correspondence relies on the continuous nature of the transition at T = T c . In turn, the existence of an infinite correlation length is also an essential necessary condition for scale and conformal invariance. In the two-dimensional XY model, this condition is realized in a peculiar way: even though the system can never have spontaneous magnetization [122], at low temperatures the model is in a phase characterized by "topological" order [117], with two-point spin correlation functions decaying only with inverse powers of the spatial separation r between the spins [123,124]. The fact that the whole low-temperature phase of the two-dimensional XY model is gapless and admits a conformal-field-theory description raises the question, what happens in the corresponding phase of the three-dimensional gauge theory, i.e. the high-temperature phase? To answer this question, in this work we carry out a systematic study of compact U(1) lattice gauge theory at T > T c , and compare a large set of novel numerical results, obtained by Monte Carlo simulations, with analytical predictions derived from conformal field theory. Specifically, we focus our attention on correlation functions of plaquette operators, Polyakov loops, and on the profile of the flux tube ind...

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Interaction potential in compact three-dimensional QED with mixed action

Cited by 8 publications

References 18 publications

Instantons and the QCD vacuum wave functional

Instantons and the QCD vacuum wave functional

Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional

Conformal field theory and the hot phase of three-dimensional U(1) gauge theory

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