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Register a new userSpectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N=2,3)
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Bastian B. Brandt
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We perform a high precision measurement of the static $qbar{q}$ potential in three-dimensional SU($N$) gauge theory with $N=2,3$ and compare the results to the potential obtained from the effective string theory. In particular, we show that the exponent of the leading order correction in $1/R$ is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficient $bar{b}_2$, including an extensive analysis of all types of systematic uncertainties. We find that the magnitude of $bar{b}_2$ decreases with increasing $N$, leading to the possibility of a vanishing $bar{b}_2$ in the large $N$ limit. In the standard form of the effective string theory possible massive modes and the presence of a rigidity term are usually not considered, even though they might give a contribution to the energy levels. To investigate the effect of these terms, we perform a second analysis, including these contributions. We find that the associated expression for the potential also provides a good description of the data. The resulting continuum values for $bar{b}_2$ are about a factor of 2 smaller than in the standard analysis, due to contaminations from an additional $1/R^4$ term. However, $bar{b}_2$ shows a similar decrease in magnitude with increasing $N$. In the course of this extended analysis we also obtain continuum results for the masses appearing in the additional terms and we find that they are around twice as large as the square root of the string tension in the continuum and compatible between SU(2) and SU(3) gauge theory. In the follow up papers we will extend our investigations to the large $N$ limit and excited states of the open flux tube.
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I perform a high precision measurement of the static quark-antiquark potential in three-dimensional ${rm SU}(N)$ gauge theory with $N=2$ to 6. The results are compared to the effective string theory for the QCD flux tube and I obtain continuum limit results for the string tension and the non-universal leading order boundary coefficient, including an extensive analysis of all types of systematic uncertainties. The magnitude of the boundary coefficient decreases with increasing $N$, but remains non-vanishing in the large-$N$ limit. I also test for the presence of possible contributions from rigidity or massive modes and compare the results for the string theory parameters to data for the excited states.
We perform a high precision measurement of the spectrum of the QCD flux tube in three-dimensional $SU(2)$ gauge theory at multiple lattice spacings. We compare the results at large $qbar{q}$ separations $R$ to the spectrum predicted by the effective string theory, including the leading order boundary term with a non-universal coefficient. We find qualitative agreement with the predictions from the leading order Nambu-Goto string theory down to small values of $R$, while, at the same time, observing the predicted splitting of the second excited state due to the boundary term. On fine lattices and at large $R$ we observe slight deviations from the EST predictions for the first excited state.
In presence of a static pair of sources, the spectrum of low-lying states of any confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. Recently two important advances improved our understanding of this effective theory. First, it was realized that the form of the effective action is strongly constrained by the requirement of the Lorentz invariance of the gauge theory, which is spontaneously broken by the formation of a long confining flux tube in the vacuum. This constraint is strong enough to fix uniquely the first few subleading terms of the action. Second, it has been realized that the first of these allowed terms - a quartic polynomial in the field derivatives - is exactly the composite field $Tbar{T}$, built with the chiral components, $T$ and $bar{T}$, of the energy-momentum tensor of the 2d QFT describing the infrared limit of the effective string. This irrelevant perturbation is quantum integrable and yields, through the thermodynamic Bethe Ansatz (TBA), the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. In this talk we first review the general implications of these two results and then, as a test of the power of these methods, use them to construct the first few boundary corrections to the effective string action.
We compute chromoelectric and chromomagnetic flux densities for hybrid static potentials in SU(2) and SU(3) lattice gauge theory. In addition to the ordinary static potential with quantum numbers $Lambda_eta^epsilon = Sigma_g^+$, we present numerical results for seven hybrid static potentials corresponding to $Lambda_eta^{(epsilon)} = Sigma_u^+, Sigma_g^-, Sigma_u^-, Pi_g, Pi_u, Delta_g, Delta_u$, where the flux densities of five of them are studied for the first time in this work. We observe hybrid static potential flux tubes, which are significantly different from that of the ordinary static potential. They are reminiscent of vibrating strings, with localized peaks in the flux densities that can be interpreted as valence gluons.
We review the current knowledge about the theoretical foundations of the effective string theory for confining flux tubes and the comparison of the predictions to pure gauge lattice data. A concise presentation of the effective string theory is provided, incorporating recent developments. We summarize the predictions for the spectrum and the profile/width of the flux tube and their comparison to lattice data. The review closes with a short summary of open questions for future research.
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