Small-ν correction to the AdS Hagedorn temperature

Determine the leading ν-dependent correction to the Hagedorn temperature R_H(ν) for rotating thermal AdS backgrounds in type II string theory in the limit ν ≪ l_s/l_ads, i.e., compute R_H(ν) when ν acts as a perturbation at finite l_s/l_ads beyond the ν-independent strong-coupling expansion.

Background

The authors compute the leading behavior of the AdS Hagedorn temperature as a function of angular velocity Ω and, for imaginary angular velocity βΩ = i2πν, derive R_H(ν) to first order in l_s/l_ads under specific scaling limits. They obtain controlled results for fixed Ω and for fixed ν with l_s/l_ads ≪ ν < 1, but note a regime where ν is much smaller than l_s/l_ads.

When ν ≪ l_s/l_ads, ν is a perturbation of the full AdS computation. The authors state that due to lack of control over the ν = 0 behavior at finite l_s/l_ads, they cannot presently analyze the leading ν correction, leaving the small-ν expansion of R_H(ν) in AdS unresolved.