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

The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes

We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson-Walker spacetimes in any even dimension. Using this characterisation, we construct adiabatic vacuum states of order $n$ corresponding to some Cauchy surface. We then show that any two such states (of sufficiently high order) are locally quasi-equivalent. We propose a microlocal version of the Hadamard condition for spinor fields on arbitrary spacetimes, which is shown to entail the usual short distance behaviour of the twopoint function. The polarisation set of these twopoint functions is determined from the Dencker connection of the spinorial Klein-Gordon operator which we show to equal the (pull-back) of the spin connection. Finally it is demonstrated that adiabatic states of infinite order are Hadamard, and that those of order $n$ correspond, in some sense, to a truncated Hadamard series and will therefore allow for a point splitting renormalisation of the expected stress-energy tensor.Comment: 29 pages, Latex, no figures. v2: corrections in the proof of Thm. IV.1. v3: published versio

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 $c$ 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