Sign confusions on CFT (yellow book) Page 29

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SUMMARY

The discussion centers on a sign discrepancy in the derivation of the propagator kernel K(δt, ξ, ξ') on page 29 of the book "Conformal Field Theory" by Francesco, Mathieu, and Senechal. Specifically, the first line presents the expression -ξ⁺ T ξ' - {ξ'}⁺ T ξ', while the second line simplifies to ξ⁺ T ξ' - {ξ'}⁺ T ξ', leading to confusion regarding the correct sign. The author seeks clarification on whether a negative sign should indeed be present in the exponent of equation (2.69c) and notes that this issue is not addressed in the book's errata.

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On the book Conformal Field Theory by Francesco, Mathieu and Senechal (the yellow book), in the derivation of the propagator kernel K(\delta t,\xi,\xi') on (2.73), the signs on the first and second line just doesn't match.

On first line it has -\xi^+ T \xi'-{\xi'}^+ T \xi' while the second line, after simplifying, has \xi^+ T \xi'-{\xi'}^+ T \xi', which is necessary to identify the term with the derivatives.

However, tracing back up to the definition of the properties of the coherent states, I cannot find any way to fix this sign. Does anyone has encounter this part and have a solution?

(For those without the book, the page is attached)
 

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It is not mentioned in the errata (for future reference, it is found at http://www.physique.usherbrooke.ca/pages/senechal/cft ), however I wonder if there really should be a negative sign in the exponent in eq. (2.69c). I don't have time to check it carefully now, but compare, for example, Fradkin's notes: http://webusers.physics.illinois.edu/~efradkin/phys582/582-chapter8.pdf
 
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