Fermions on replica geometries and the Θ - θ relation

TY - JOUR

T1 - Fermions on replica geometries and the Θ - θ relation

AU - Mukhi, Sunil

AU - Murthy, Sameer

PY - 2019/4/29

Y1 - 2019/4/29

N2 - 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.

AB - 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.

KW - Conformal field theory

KW - Entanglement entropy

KW - Rényi entropy

UR - http://www.scopus.com/inward/record.url?scp=85066614892&partnerID=8YFLogxK

U2 - 10.4310/CNTP.2019.v13.n1.a8

DO - 10.4310/CNTP.2019.v13.n1.a8

M3 - Article

AN - SCOPUS:85066614892

SN - 1931-4523

VL - 13

SP - 225

EP - 251

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

IS - 1

ER -