Comparing the excitations of the periodic flux tube with effective string models.

Abstract

The spectrum of a periodic flux tube in pure SU(3) Yang-Mills theory is evaluated non-perturbatively through computations on the lattice in the region from intermediate to long distances (1.5 < L < 4 fm ). For these flux lengths our results are compared with the predictions of a bosonic effective string theory, finding a surprising good agreement. The main object of the first part of this work is the description of the lattice technology and methodology used to evaluate the spectrum of a periodic flux tube. We give details of the improved anisotropic lattice action we used in our calculations and of the methodology we adopted in order to identify the symmetries of a periodic flux tube that winds around one direction. A large number of torelon operators are then systematically constructed and details on the implementation and on the form of these operators are also given. We perform several long numerical Monte Carlo simulations for different flux lengths and with different volumes and different values of β. The second part of this work is dedicated to the description of an effective string theory with central charge not equal to the dimension d and the resulting covariant quantization with d - 2 oscillators presented by Polchinski and Strominger in 1991. However, as it is also clear from their article, the spectrum derived from it does not deviate from the Nambu-G oto spectrum at least for the corrections they introduced. We then proceed to compare the spectrum of the QCD periodic flux tube with the string expectations. Our numerical results confirm the string-like flux formation and details are given regarding the Luscher term in the ground state, the level ordering, degeneracy and energy gaps between levels. The agreement with a string theory is striking in the presence of the Luscher term , in the level ordering and in the degeneracy of all of the fourteen states we considered (apart from the A2u(0) state that reaches a perfect degeneracy only at L > 2.5 fm and the problematic A2(1) state which seems to show a string-like behavior for bigger L). The deviations from the string energy gap for lengths L > 2.5 fm is problematic and already seen in the spectrum of a quark-antiquark system . Further studies are required in order to settle this issue.