Holographic Description of Chiral Symmetry Breaking in a Magnetic Field in 2+1 Dimensions with an Improved Dilaton

Understand

We consider a holographic description of the chiral symmetry breaking in an external magnetic field in $ (2+1) $-dimensional gauge theories from the softwall model using an improved dilaton field profile given by $\Phi(z) = - kz^2 + (k+k_1)z^2\tanh (k_{2}z^2)$.

• We find inverse magnetic catalysis for $B<B_c$ and magnetic catalysis for $B>B_c$, where $B_c$ is the pseudocritical magnetic field.
• The transition between these two regimes is a crossover and occurs at $B=B_c$, which depends on the fermion mass and temperature.
• We also find spontaneous chiral symmetry breaking (the chiral condensate $\sigma \not=0$) at $T=0$ in the chiral limit ($m_q\to 0$) and chiral symmetry restoration for finite temperatures.