Probing boundary-corrections to Nambu-Goto open string energy levels in 3d SU(2) gauge theory

Abstract

We measure the energy levels of the excitations of the flux tube between static quark and antiquark in three-dimensional SU(2) gauge theory. Combining exponential error reduction techniques and a variational method we are able to reduce the errors for the excited states significantly and to extract excited states in distinct parity and charge conjugation channels. It is conjectured that the infrared behavior (at large q\bar{q} separation R) of the flux tube is governed by an effective string theory. Indeed previous simulations show good agreement between lattice data and predictions from Nambu-Goto string theory. Recently, new results on the effective string theory obtained corrections to the Nambu-Goto predictions and showed that for the open string in three dimensions first corrections should appears at order 1/R^4. They correspond to boundary terms in the worldsheet field theory. These corrections are presumably small for the ground state, but significantly larger for the excited states and lift the degeneracies of the free theory. Assuming this functional form of the correction, we obtain for the coefficient b_2=-0.5(2)(2).

arXiv comment20 pages, 7 figures; v2: Style changed to JHEP. Typos corrected and minor changes in the conclusions and the final results. Revised version to match published version

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• The Lorentz-invariant boundary action of the confining string and its universal contribution to the inter-quark potential
• A different kind of string
• Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N=2,3)
• Universal signatures of the effective string in finite temperature lattice gauge theories
• New numerical results and novel effective string predictions for Wilson loops
• The static quark potential from a multilevel algorithm for the improved gauge action
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• Boundary Operators in Effective String Theory
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• Heavy Quark Potential from Gauge/Gravity Duality: A Large D Analysis
• Can holography reproduce the QCD Wilson line?
• Ising string beyond Nambu-Goto
• Effective long distance $q\bar{q}$ potential in holographic RG flows
• Perturbative width of open rigid strings
• Induced QCD II: Numerical results
• The finite temperature ground state energy of the confining string in three-dimensional U(1) gauge theory