arXiv subjects

Arnav Advant

Publications and source records attributed to Arnav Advant.

2 recordsLinked to original sources

arXiv2026

From Z to all: cyclic sum rules for thermal CFT partition functions

The high-temperature expansion of twisted $S^{d-1}\times S^1$ partition functions of CFT$_d$, $d = 2κ$, has recently been shown to obey an infinite tower of universal constraints. We determine these constraints explicitly and demonstrate that they can be packaged into a single equation involving a large conformal diffeomorphism isomorphic to $\mathbb{Z}_{κ+1}$, which cyclically permutes the thermal circle and the rotation angles. Our equation asserts that the $\mathbb{Z}_{κ+1}$-invariant part of $\ln Z/β$ is a constant fixed by the a-anomaly. Our derivation assumes CP-invariance and locality of the thermal effective action, whose structure we constrain using an algebraic formalism starting from embedding space.

hep-th↗

arXiv2026

From $Z$ to $a$: High-temperature relations, subleading semi-universality, and conformal anomalies

The free energy of any CFT, $ \ln Z(β; ω_i)$, admits two expansions: high temperature ($β\rightarrow 0$) and fast rotation ($ω_i \rightarrow 1$). We demonstrate that in $4d$, locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $β^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $β$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.

hep-th↗