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String-like objects arise in many quantum field theories. Well known
examples include flux tubes in QCD and cosmic strings. To a first
approximation, their dynamics is governed by the Nambu-Goto action.
For QCD flux tubes numerical calculations of their energy levels have
become so accurate that a systematic understanding of the corrections
to this action is desirable. In the first part of my talk, I discuss
an effective field theory describing these long relativistic strings
in static gauge. At first sight in this way of quantizing the string
nothing seems special about D=26. To recover the critical number of
dimensions, and to understand its physical meaning, I will present the
results of the calculation of the S-matrix describing the scattering
of excitations on the string worldsheet.
In the second part of my talk, I will discuss critical strings from
the same point of view and show that their worldsheet S-matrix is
non-trivial but can be calculated exactly. I will show that it encodes
the familiar square-root formula for the energy levels
of the string. This S-matrix also implies that the theory on the
string worldsheet in several ways does not behave like a conventional
1+1 dimensional quantum field theory but instead displays features that are
usually associated with gravitational theories.
In the last part of the talk, I will return to the task of computing
the energy levels of flux-tubes. Rather surprisingly, using lessons
learned from the second part of my talk will allow us to significantly
improve on previous results. The improved analytic control makes it
manifest that existing lattice data provides strong evidence for the
existence of a massive pseudoscalar on the worldsheet of QCD