String Theory in Polar Coordinates and the Vanishing of the One-Loop Rindler Entropy

Abstract

We analyze the string spectrum of flat space in polar coordinates, following the small curvature limit of the $SL(2,\mathbb{R})/U(1)$ cigar CFT. We first analyze the partition function of the cigar itself, making some clarifications of the structure of the spectrum that have escaped attention up to this point. The superstring spectrum (type 0 and type II) is shown to exhibit an involution symmetry, that survives the small curvature limit. We classify all marginal states in polar coordinates for type II superstrings, with emphasis on their links and their superconformal structure. This classification is confirmed by an explicit large ${\tau }_2$ analysis of the partition function. Next we compare three approaches towards the type II genus one entropy in Rindler space: using a sum-over-fields strategy, using a Melvin model approach and finally using a saddle point method on the cigar partition function. In each case we highlight possible obstructions and motivate that the correct procedures yield a vanishing result: $S=0$. We finally discuss how the QFT UV divergences of the fields in the spectrum disappear when computing the free energy and entropy using Euclidean techniques.

58 pages + appendices, v2: typos corrected, matches published version

References in corpus (4)

• Perturbative String Thermodynamics near Black Hole Horizons
• On the Relevance of the Thermal Scalar
• Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples
• Compact Formulas for the Completed Mock Modular Forms

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• Stringy Horizons II
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• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Dynamical Edge Modes in $p$-form Gauge Theories
• Fiducial observers and the thermal atmosphere in the black hole quantum throat