Quantum fluctuations of k-strings: A case study.

K strings in Yang-Mills theory can be considered as bound states of k elementary confining strings carrying one unit of colour flux. Current estimates of k-stri ng tension σk are very sensitive to the leading corrections due to quantum fluctuations of the st ring. In this study we address this problem by comparing Polyakov-Polyakov correlators in the fundamental representation (k = 1) with the corresponding ones with k = 2 in the confining phase of a Z4 gauge theory in three dimensions. Highly efficient simulation techniques are ava ilable in this case. Although the k = 1 Polyakov-Polyakov correlator matches nicely with the expected bosonic string effects up to the Next-to-Leading-Order, the k = 2 Polyakov-Polyakov correlators show large deviations. This is an important source of potential systematic errors in the cu rrent estimates of σk.