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.
Universality of Sparse $d>2$ Conformal Field Theory at Large $N$
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We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two dimensions and must be satisfied by any conformal field theory dual to Einstein gravity. We construct and analyze symmetric product orbifold theories on $\mathbb{T}^d$ and show that they only realize the necessary phase structure and extended range of validity if the seed theory is assumed to have a universal vacuum energy.
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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.