Chiral symmetry restoration for helical magnetic fields in holography

We study the chiral symmetry breaking effects of helical magnetic fields in a simple bottom up AdS/CFT model. We explore the instability of the chirally symmetric solution in the presence of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>B</a:mi> </a:math> field and see how it switches off as the wave vector of the helix, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>k</c:mi> </c:math> , rises, resulting in a first order transition. At low energies the model averages over the helix and the magnetic field is not seen. We show that other sources of chiral symmetry breaking are not directly affected by the helical <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>B</e:mi> </e:math> field. We provide examples of both magnetic catalysis and inverse magnetic catalysis which switch off at large <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>k</g:mi> </g:math> .