One-point thermal conformal blocks from four-point conformal integrals · arXivDesk
2407.01741Jul 1, 202418 pp, v2: misprints corrected, extended discussion in Section 2, more clarifying comments, references added; v3: extended discussion of the thermal conformal block in the high-temperature regime as well as at self-dual conformal dimensions; more detail on non-parametric conformal and thermal integrals and their relation to the Bloch-Wigner function in a new appendix A; refs added, journal version
One-point thermal conformal blocks from four-point conformal integrals
We develop the thermal shadow formalism to study the conformal blocks decomposition in D-dimensional conformal field theory on Sβ1×SD−1, where the temperature is T=β−1
Nearby in the stack
. It is demonstrated that both the 1-point thermal (
T=0
) conformal blocks and the 4-point plane (
T=0
) conformal blocks are defined by the same 4-point conformal integral. It is shown that up to power prefactors the 1-point thermal conformal block is given by the fourth Appell function.