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Dietmar Ebert

Publications and source records attributed to Dietmar Ebert.

14 recordsLinked to original sources
arXiv2024

Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model

We study a generalized version of the Gross-Neveu model in 2+1 dimensions. The model is inspired from Graphene, which shows a linear dispersion relation near the Dirac points. The phase structure and the thermodynamic properties in the mean field approximation have been studied before. Here, we go beyond the mean field level by deriving a Beth-Uhlenbeck equation for Gaussian fluctuations formulated in phase shift solutions, which we explore numerically, for the first time including their momentum dependence. We discuss the excitonic mass, fluctuation pressure, and phase shifts. The inclusion of momentum dependence in the phase shift shows a significant difference from the Lorentz-boosted version of the phase shift previously used in the literature. We find resurrection of the pseudoscalar bound states at large momentum above Mott temperature and show that the presence of Landau modes significantly contributes to the fluctuation pressure.

cond-mat.mes-hall↗
arXiv2009

Gravitational Contributions to the Running Yang-Mills Coupling in Large Extra-Dimensional Brane Worlds

We study the question of a modification of the running gauge coupling of Yang-Mills theories due to quantum gravitational effects in a compact large extra dimensional brane world scenario with a low energy quantum gravity scale. The ADD scenario is applied for a D=d+δdimensional space-time in which gravitons freely propagate, whereas the non-abelian gauge fields are confined to a d-dimensional brane. The extra dimensions are taken to be toroidal and the transverse fluctuation modes (branons) of the brane are taken into account. On this basis we have calculated the one-loop corrections due to virtual Kaluza-Klein graviton and branon modes for the gluon two- and three-point functions in an effective field theory treatment. Applying momentum cut-off regularization we find that for a d=4 brane the leading gravitational divergencies cancel irrespective of the number of extra dimensions δ, generalizing previous results in the absence of extra-dimensions. Hence, again the Yang-Mills β-function receives no gravitational corrections at one-loop. This is no longer true in a `universal' extra dimensional scenario with a d>4 dimensional brane. Moreover, the subleading power-law gravitational divergencies induce higher-dimensional counterterms, which we establish in our scheme. Interestingly, for d=4 these gravitationally induced counterterms are of the form recently considered in non-abelian Lee-Wick extensions of the standard model -- now with a possible mass scale in the TeV range due to the presence of large extra dimensions.

hep-ph↗
arXiv2007

Absence of gravitational contributions to the running Yang-Mills coupling

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. The logarithmic divergencies give rise to an extended effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six. In the pure Yang-Mills sector this counterterm can be removed by a nonlinear field redefinition of the gauge potential, reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in the background field method with dimensional regularization.

hep-th↗
arXiv2004

k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

The k-string tensions are explored in the 4-d $[U(1)]^{N-1}$-invariant dual Abelian-Higgs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N-ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N-ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the non-diluteness of the monopole plasma in the 3-d SU(N) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.

hep-th↗
arXiv2004

Confinement in the Abelian-Higgs-type theories: string picture and field correlators

Field correlators and the string representation are used as two complementary approaches for the description of confinement in the SU(N)-inspired dual Abelian-Higgs-type model. In the London limit of the simplest, SU(2)-inspired, model, bilocal electric field-strength correlators have been derived with accounting for the contributions to these averages produced by closed dual strings. The Debye screening in the plasma of such strings yields a novel long-range interaction between points lying on the contour of the Wilson loop. This interaction generates a Luescher-type term, even when one restrics oneself to the minimal surface, as it is usually done in the bilocal approximation to the stochastic vacuum model. Beyond the London limit, it has been shown that a modified interaction appears, which becomes reduced to the standard Yukawa one in the London limit. Finally, a string representation of the SU(N)-inspired model with the theta-term, in the London limit, can be constructed.

hep-th↗
arXiv2002

String representation of the dual Ginzburg-Landau theory beyond the London limit

The effective string action of the color-electric flux tube in the dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. A modified Yukawa interaction appears as a boundary contribution and is reduced into the ordinary Yukawa interaction in the London Limit.

hep-ph↗
arXiv2002

Effective string action for the U(1)xU(1) dual Ginzburg-Landau theory beyond the London limit

The effective string action of the color-electric flux tube in the U(1) x U(1) dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into accountthe finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as s [U(1)]^{3} dual Abelian Higgs (DAH) model with a certain constraint in the Weyl symmetric formulation. This formulation allows us to adopt quite similar path-integral techniques as in the U(1) DAH model, and therefore, the resulting effective string action in the U(1) x U(1) DGL theory has also quite a similar structure except the number of color degrees of freedom. A modified Yukawa interaction appears as a boundary contribution, which is completely due to the finite thickness of the flux tube, and is reduced into the ordinary Yukawa interaction in the deep type-II (London) Limit.

hep-th↗
arXiv2002

Towards the String representation of the dual Abelian Higgs model beyond the London limit

We perform a path-integral analysis of the string representation of the dual Abelian Higgs (DAH) model beyond the London limit, where the string describing the vortex of a flux tube has a finite thickness. We show that besides an additional vortex core contribution to the string tension, a modified Yukawa interaction appears as a boundary contribution in the type-II dual superconducting vacuum. In the London limit, the modified Yukawa interaction is reduced to the Yukawa one.

hep-th↗
arXiv1999

Monopole-like Excitations as a Source of Confinement in the SU(2)-Gluodynamics

By making use of the Abelian projection method, a dual version of the SU(2)-gluodynamics with manifest monopole-like excitations, arising from the integration over singular gauge transformations, is formulated in the continuum limit. The resulting effective theory emerges due to the summation over the grand canonical ensemble of these excitations in the dilute gas approximation. As a result, the dual Abelian gauge boson acquires a nonvanishing (magnetic) mass due to the Debye screening effects in such a gas. The obtained theory is then used for the construction of the corresponding effective potential of monopole loop currents and the string representation. Finally, by virtue of this representation, confining properties of the SU(2)-gluodynamics are emphasized.

hep-th↗
arXiv1999

Confining Properties of Abelian-Projected Theories and Field Strength Correlators

We review the string representations of Abelian-projected SU(2)- and SU(3)-gauge theories and their application to the evaluation of bilocal field strength correlators. The large distance asymptotic behaviours of the latter ones are shown to be in agreement with the Stochastic Vacuum Model of QCD and existing lattice data.

hep-th↗
arXiv1998

Confining Properties of Abelian(-Projected) Theories

Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics in terms of the magnetic monopole currents are derived. Besides the quadratic part, the obtained effective actions contain interactions of these currents with the world-sheets of electric strings in 4D or electric vortex lines in 3D. Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3D Abelian Higgs model with external monopoles and give a physical interpretation to the confining string theory as the integral over the monopole densities. Finally, we derive the bilocal field strength correlator in the weak-field limit of 3D compact QED, which turns out to be in line with the one predicted by the Stochastic Vacuum Model.

hep-th↗
arXiv1998

String Representation of Field Correlators in the SU(3)-Gluodynamics

The string representation of the Abelian projected SU(3)-gluodynamics partition function is derived by using the path-integral duality transformation. On this basis, we also derive analogous representations for the generating functionals of correlators of gluonic field strength tensors and monopole currents, which are finally applied to the evaluation of the corresponding bilocal correlators. The large distance asymptotic behaviours of the latter turn out to be in a good agreement with existing lattice data and the Stochastic Model of the QCD vacuum.

hep-th↗
arXiv1998

String Representation of Field Correlators in the Dual Abelian Higgs Model

By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and with the Stochastic Model of the QCD vacuum.

hep-th↗