Abstract
We assume that QCD can be effectively described with stringlike variables and that this string is approximately represented by a Nambu–Goto or Polyakov string in some energy region. But to overcome the long-standing problems with the behavior of hadronic string amplitudes at low energies, the string is built over the correct (chirally noninvariant) QCD vacuum using a boundary interaction with background chiral fields associated with pions. Making this interaction compatible with the conformal symmetry of the string and with the unitarity constraint on chiral fields, we reconstruct the equations of motion for the latter and, furthermore, recover the Lagrangian of a nonlinear sigma model of pion interactions. We obtain the chiral structural constants of Gasser and Leutwyler in the next-to-leading order in the derivative expansion. The estimated coefficients fit the phenomenological values well.
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Andrianov, A.A., Espriu, D. Strings and Pions. Theoretical and Mathematical Physics 135, 745–756 (2003). https://doi.org/10.1023/A:1024045917981
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DOI: https://doi.org/10.1023/A:1024045917981