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We calculate log corrections to the entropy of three-dimensional black holeswith "soft hairy" boundary conditions. Their thermodynamics possesses somespecial features that preclude a naive direct evaluation of these corrections,so we follow two different approaches. The first one exploits that the BTZblack hole belongs to the spectrum of Brown-Henneaux as well as soft hairyboundary conditions, so that the respective log corrections are related througha suitable change of the thermodynamic ensemble. In the second approach theanalogue of modular invariance is considered for dual theories with anisotropicscaling of Lifshitz type with dynamical exponent z at the boundary. On thegravity side such scalings arise for KdV-type boundary conditions, whichprovide a specific 1-parameter family of multi-trace deformations of the usualAdS3/CFT2 setup, with Brown-Henneaux corresponding to z=1 and soft hairyboundary conditions to the limiting case z=0. Both approaches agree in the caseof BTZ black holes for any non-negative z. Finally, for soft hairy boundaryconditions we show that not only the leading term, but also the log correctionsto the entropy of black flowers endowed with affine u(1) soft hair chargesexclusively depend on the zero modes and hence coincide with the ones for BTZblack holes.

Log corrections to entropy of three dimensional black holes with soft hair