On the effective string spectrum of the tridimensional Bbb Z₂gauge model

Abstract

We study the Z 2 lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance r ≈ 10/ √ σ. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.

gauge theories at large

“…Inspection of the numerical results for V (r) at intermediate distances reveals that the potential also includes a 1/r contribution, with a coefficient that is compatible with the Lüscher term prediction: this means that, similarly to what happens in 4D, also in 3D the low-energy dynamics of confining flux tubes can be described in terms of (massless) fluctuations of a bosonic string [825,830,966,[977][978][979][980][981][982]. Again, this is not specific of the large-N limit only, but rather appears as a generic feature of all confining models in 3D: the Lüscher term (or the broadening of confining flux tubes with their length [983][984][985][986][987][988][989], which is a related implication of the same effective picture) is also observed in high-precision studies of SU(2) Yang-Mills theory [982,[990][991][992][993][994][995], of 3D lattice models with local invariance under a discrete gauge group [982,992,[996][997][998][999][1000][1001][1002][1003][1004][1005][1006] and even in random percolation models (with an appropriate, topological definition of Wilson loop operators) [1007,1008].…”

Jarzynski’s theorem for lattice gauge theory

“…[60] and references therein). For each set at fixed L 2 > 32a, these data can be successfully fitted to the form expected for the leading and next-to-leading corrections to the Nambu-Gotō model, which, according to the discussion in ref.…”

Logarithmic finite-size effects on interfacial free energies: Phenomenological theory and Monte Carlo studies

“…In both these methods the error estimation is a very subtle problem. Alternative algorithms due to Mon [42] and Caselle et al [50,60,61] which are particularly valuable to study the interfacial tension near the bulk critical point, have also been out of our consideration.…”