A Farey Tail

A Black Hole Farey Tail

We derive an exact expression for the Fourier coefficients of elliptic genera on Calabi-Yau manifolds which is well-suited to studying the AdS/CFT correspondence on AdS3 × S. The expression also elucidates an SL(2,ZZ) invariant phase diagram for the D1/D5 system involving deconfining transitions in the k → ∞ limit.

A Farey Fraction Spin Chain

We introduce a new number–theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation–invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and exhibits a unique phase transition at inverse temperature β = 2. The free energy i...

Farey Curves

^nr", Hn , INTRODUCTION 4. Observations and Questions References Consider the family of quadratic polynomials PA : C —> C, where A is a complex number with |A| < 1, defined by Px(z) = Xz + z. We will examine this polynomial from a dynamical point of view; that is, we will be interested in its behaviour under iteration. The first observation is that the polynomial Px has a fixed point at zero: P...

Products of Farey Fractions

A Farey tale for N = 4 dyons

We study exponentially suppressed contributions to the degeneracies of extremal black holes. Within Sen’s quantum entropy function framework and focusing on extremal black holes with an intermediate AdS3 region, we identify an infinite family of semi-classical AdS2 geometries which can contribute effects of order exp(S0/c), where S0 is the Bekenstein-Hawking-Wald entropy and c is an integer gre...