Fermions on replica geometries and the Θ - θ relation

Sunil Mukhi, Sameer Murthy

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In arXiv:1706.09426 we conjectured and provided evidence for an identity between Siegel Θ-constants for special Riemann surfaces of genus n and products of Jacobi θ-functions. This arises by comparing two different ways of computing the nth Rényi entropy of free fermions at finite temperature. Here we show that for n = 2 the identity is a consequence of an old result due to Fay for doubly branched Riemann surfaces. For n > 2 we provide a detailed matching of certain zeros on both sides of the identity. This amounts to an elementary proof of the identity for n = 2, while for n ≥ 3 it gives new evidence for it. We explain why the existence of additional zeros renders the general proof difficult.

Original languageEnglish
Pages (from-to)225-251
Number of pages27
JournalCommunications in Number Theory and Physics
Issue number1
Early online date29 Apr 2019
Publication statusPublished - 29 Apr 2019


  • Conformal field theory
  • Entanglement entropy
  • Rényi entropy


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