Journal of High Energy Physics

, 2017:66 | Cite as

Boundary conformal anomalies on hyperbolic spaces and Euclidean balls

  • Diego Rodriguez-Gomez
  • Jorge G. RussoEmail author
Open Access
Regular Article - Theoretical Physics


We compute conformal anomalies for conformal field theories with free conformal scalars and massless spin 1/2 fields in hyperbolic space ℍ d and in the ball \( {\mathbb{B}}^d \), for 2≤d≤7. These spaces are related by a conformal transformation. In even dimensional spaces, the conformal anomalies on ℍ2n and \( {\mathbb{B}}^{2n} \) are shown to be identical. In odd dimensional spaces, the conformal anomaly on \( {\mathbb{B}}^{2n+1} \) comes from a boundary contribution, which exactly coincides with that of ℍ2n + 1 provided one identifies the UV short-distance cutoff on \( {\mathbb{B}}^{2n+1} \) with the inverse large distance IR cutoff on ℍ2n + 1, just as prescribed by the conformal map. As an application, we determine, for the first time, the conformal anomaly coefficients multiplying the Euler characteristic of the boundary for scalars and half-spin fields with various boundary conditions in d = 5 and d = 7.


Conformal Field Theory Anomalies in Field and String Theories 


Open Access

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© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversidad de OviedoOviedoSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  3. 3.Departament de F ısica Cuántica i Astrofísica and Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain

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