Revisiting noninteracting string partition functions in Rindler space

Abstract

We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way in a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal. A possible link with the firewall paradox is apparent.

33 pages, v2: added several clarifications including a section on the difference between closed strings and the sum-of-fields approach, matches published version

References in corpus (17)

• Complexity and Shock Wave Geometries
• Aspects of Entanglement Entropy for Gauge Theories
• Chaos in the black hole S-matrix
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Notes on Entanglement in Abelian Gauge Theories
• Perturbative String Thermodynamics near Black Hole Horizons
• Revisiting Entanglement Entropy of Lattice Gauge Theories
• Newton constant, contact terms and entropy
• On the Relevance of the Thermal Scalar
• Strings in Horizons, Dissipation and a Possible Interpretation of the Hagedorn Temperature
• Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples
• Black Holes as Conformal Field Theories on Horizons
• Longitudinal nonlocality in the string S-matrix
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• On the Stringy Hartle-Hawking State
• Stringy Horizons
• Lecture notes on thermodynamics of ideal string gases and its application in cosmology

Cited by in corpus (9)

• Entanglement entropy and $T\overline{T}$ deformation
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
• Comments on Entanglement Entropy in String Theory
• Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers
• Recovering Infalling Information via String Spreading
• Dynamical Edge Modes in $p$-form Gauge Theories
• Unruh Duality and Maximum Acceleration in String Theory
• Non-Gaussian Saha's ionization in Rindler spacetime and the equivalence principle