153 research outputs found
Action principle for OPE
We formulate an "action principle" for the operator product expansion (OPE)
describing how a given OPE coefficient changes under a deformation induced by a
marginal or relevant operator. Our action principle involves no ad-hoc
regulator or renormalization and applies to general (Euclidean) quantum field
theories. It implies a natural definition of the renormalization group flow for
the OPE coefficients and of coupling constants. When applied to the case of
conformal theories, the action principle gives a system of coupled dynamical
equations for the conformal data. The last result has also recently been
derived (without considering tensor structures) independently by Behan
(arXiv:1709.03967) using a different argument. Our results were previously
announced and outlined at the meetings "In memoriam Rudolf Haag" in September
2016 and the "Wolfhart Zimmermann memorial symposium" in May 2017.Comment: 29 pages, 5 figures, based on conference talks at the meetings "In
memoriam Rudolf Haag" in September 2016 and the "Wolfhart Zimmermann memorial
symposium" in May 2017; v2: details added concerning geometry of field
redefinitions, discussion of degeneracies and normalization issues,
references edited, other minor editorial changes, v3: edited para on
invariant 2-point tensor structure
Relative entropy for coherent states in chiral CFT
We consider the relative entropy between the vacuum state and a state
obtained by applying an exponentiated stress tensor to the vacuum of a chiral
conformal field theory on the lightray. The smearing function of the stress
tensor can be viewed as a vector field on the real line generating a
diffeomorphism. We show that the relative entropy is equal to times the
so-called Schwarzian action of the diffeomorphism. As an application of this
result, we obtain a formula for the relative entropy between the vacuum and a
solitonic state.Comment: v2: 19pp, no figures. Extended more detailed version of v1, stronger
results, refs. edited, minor presentation change
Non-Equilibrium Thermodynamics and Conformal Field Theory
We present a model independent, operator algebraic approach to
non-equilibrium quantum thermodynamics within the framework of two-dimensional
Conformal Field Theory. Two infinite reservoirs in equilibrium at their own
temperatures and chemical potentials are put in contact through a defect line,
possibly by inserting a probe. As time evolves, the composite system then
approaches a non-equilibrium steady state that we describe. In particular, we
re-obtain recent formulas of Bernard and Doyon.Comment: 19 pages, 3 figure
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