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Thermal One-point Functions and Their Partial Wave Decomposition
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abstract
In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposition of one-point functions of the scalar $\phi^2$ and the stress tensor $T$ for a three-dimensional free scalar field $\phi$. We are able to read off averaged OPE coefficients into exchanged fields of high weight and spin for a complete set of tensor structures. We also extract an asymptotic behaviour of conformal blocks and use it to analyse the density of heavy-heavy-light OPE coefficients for spinning operators, comparing it with semi-classical predictions, such as the dimensions of operators at large charge.
Forward citations
Cited by 7 Pith papers
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KMS-symmetric thermal Polyakov blocks Fourier-transform into asymptotic retarded correlators, yielding inversion formulae that express thermal OPE coefficients in terms of quasinormal-mode frequencies under meromorphicity.
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Thermal double-twist OPE coefficients in a 4d holographic CFT are obtained individually as regulated momentum-space integrals of the AdS5 black-brane scalar response function, yielding new spin-resolved data at Δ=3/2.
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Heavy-Heavy-Light Asymptotics from Thermal Correlators
The authors derive and test systematic large-dimension asymptotics for heavy-heavy-light OPE coefficients in 3D CFTs from thermal one-point functions on S1 x S2.
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Universal dispersion-based formulae for thermal two-point functions of scalars that satisfy bootstrap axioms except clustering at infinite distance.
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Spin-resolved double-trace thermal coefficients in holography
Zero-frequency bulk Heun solutions fix the residual spatial ambiguity left by KMS, yielding spin-resolved holographic double-trace thermal coefficients and canceling complex bulk-cone singularities.
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An equal-weight superposition of all non-crossing singlet pairings in a Heisenberg chain shows logarithmic entanglement growth (c≈5.2) and near-infinite-temperature thermalization.
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Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations
New analytic formulas for four-dimensional thermal n-point conformal blocks are derived from oscillator representations, with a correct low-temperature limit to vacuum comb-channel blocks.
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