The Lorentz-invariant boundary action of the confining string and its universal contribution to the inter-quark potential

Billó, Marco; Caselle, Michele; Gliozzi, F.; Meineri, Marco; Pellegrini, Roberto

doi:10.1007/jhep05(2012)130

Cited by 46 publications

(69 citation statements)

References 42 publications

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“…Imposing Lorentz invariance one can show that b 1 = 0 [1,10] and that the term having b 2 as its coefficient is nothing but the first contribution arising from the Lorentz-invariant combination [39] …”

Section: Effective String Action and Extrinsic Curvaturementioning

confidence: 99%

See 1 more Smart Citation

A different kind of string

Caselle

Panero

Pellegrini

et al. 2015

J. High Energ. Phys.

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In U(1) lattice gauge theory in three spacetime dimensions, the problem of confinement can be studied analytically in a semi-classical approach, in terms of a gas of monopoles with Coulomb-like interactions. In addition, this theory can be mapped to a spin model via an exact duality transformation, which allows one to perform highprecision numerical studies of the confining potential. Taking advantage of these properties, we carried out an accurate investigation of the effective string describing the low-energy properties of flux tubes in this confining gauge theory. We found striking deviations from the expected Nambu-Goto-like behavior, and, for the first time, evidence for contributions that can be described by a term proportional to the extrinsic curvature of the effective string worldsheet. Such term is allowed by Lorentz invariance, and its presence in the infrared regime of the U(1) model was indeed predicted by Polyakov several years ago. Our results show that this term scales as expected according to Polyakov's solution, and becomes the dominant contribution to the effective string action in the continuum limit. We also demonstrate analytically that the corrections to the confining potential induced by the extrinsic curvature term can be related to the partition function of the massive perturbation of a c = 1 bosonic conformal field theory. The implications of our results for SU(N ) Yang-Mills theories in three and in four spacetime dimensions are discussed.

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Section: Effective String Action and Extrinsic Curvaturementioning

confidence: 99%

“…For the boundary term, the extrinsic-curvature term leads to contributions beyond our resolution, hence we are left with the standard free bosonic result derived in refs. [10,39]. Its contribution to the interquark potential in the large-N t limit is…”

Section: Higher-order Correctionsmentioning

confidence: 99%

A different kind of string

Caselle

Panero

Pellegrini

et al. 2015

J. High Energ. Phys.

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show abstract

“…It was later observed in [5] that also b 3 = 0 and only the b 2 term is compatible with Lorentz invariance. In [23] we completed the analysis by solving the recursion relations dictated by the requirement of Lorentz invariance. The resulting expansion can be written in the closed form…”

Section: Example: the Boundary Termmentioning

confidence: 99%

“…The results for the three different values of β that we simulated in [23] Looking at the third column we see that the data show a rather good scaling behaviour and allow us to propose as a final estimate for the b 2 parameter in the 3D gauge Ising model the value: b 2 √ σ 3 ∼ 0.032 (2). It is interesting to notice that this result is of the same order of magnitude (but opposite in sign) of the value of b 2 measured in the 3D SU(2) gauge model in [24].…”

Section: Pos(lattice 2013)372mentioning

confidence: 99%

Recent progress in the effective string theory description of LGTs.

Caselle¹,

Pellegrini²,

Gliozzi³

et al. 2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

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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 TT , built with the chiral components, T andT , 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.

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“…This difference is called scaling and the expression (1.16) just constructed is the only Lorentz invariant of scaling 2. It is possible to show that there are no invariant of odd scaling [18]. It is easy to construct in this way boundary terms of higher scaling.…”

Section: The Effective String Picture Of the Confining Flux Tubementioning

confidence: 99%

The boundary action of the confining string and its universal contribution to the interquark potential

Gliozzi¹

2013

Proceedings of XTH Quark Confinement and the Hadron Spectrum — PoS(Confinement X)

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The request of Lorentz invariance of the effective string action describing the confining flux tube connecting a pair of static quarks implies that the first few terms in the expansion in the number of derivatives coincide with the Nambu-Goto action. The leading deviation from this action is a boundary term whose form is again determined by Lorentz invariance. Numerical simulations on 3D Z 2 gauge model allow to estimate and test this contribution.Xth Quark Confinement and the Hadron Spectrum,

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The Lorentz-invariant boundary action of the confining string and its universal contribution to the inter-quark potential

Cited by 46 publications

References 42 publications

A different kind of string

A different kind of string

Recent progress in the effective string theory description of LGTs.

The boundary action of the confining string and its universal contribution to the interquark potential

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