Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation

Abstract

We carry out a systematic study of the effective bosonic string describing confining flux tubes in $\mathrm{SU}(N)$ Yang--Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu--Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with $N=3$ and $6$ color charges, and report an improved estimate for the $N=2$ case, discussing the approach to the large-$N$ limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky--Yaffe conjecture for the $\mathrm{SU}(3)$ theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky--Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

35 pages, 14 figures, 17 tables

References in corpus (20)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• SU(N) gauge theories at large N
• Effective String Theory Revisited
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Flux Tube Spectra from Approximate Integrability at Low Energies
• Conformal perturbation theory beyond the leading order
• A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions
• Closed k-strings in SU(N) gauge theories : 2+1 dimensions
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions
• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• Poincare invariance in effective string theories
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions I - The confining phase
• On the Glueball Spectrum of Pure Yang-Mills Theory in 2+1 Dimensions
• Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane-world scenarios
• Revisiting the deconfinement phase transition in SU(4) Yang-Mills theory in 2+1 dimensions
• On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories
• The unreasonable effectiveness of effective string theory: the case of the 3d SU(2) Higgs model