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Modularity in $d > 2$ free conformal field theory
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abstract
We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions.
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Critical dimensions and small cycle dominance from all-orders asymptotics of $d$-matrix theory
The weighted partition numbers of d-matrix theory admit an all-orders asymptotic expansion that switches from divergent to convergent at d=13 (bosonic) or 7 (fermionic).
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