From Effective Strings to the Simplest theory of Quantum Gravity

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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, but for QCD flux tubes
numerical calculations of the energy levels of these objects have become so
accurate that a systematic understanding of corrections to this simple
description is desirable.

In the first part of my talk, I discuss an effective
field theory describing long relativistic strings. The construction parallels
that of the chiral Lagrangian in that it is based on the pattern of symmetry
breaking. To compare with previous works, 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 the worldsheet S-matrix in
this case 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,
the Hagedorn behavior of strings, and argue that the theory on the string
worldsheet behaves like a 1+1 dimensional theory of quantum gravity rather than
a field theory.

If time permits, I will return to the task of computing
the energy levels of flux-tubes using lessons learned from the second part of
my talk.