Abstract
We study the deconfinement phase transition in $ (2+1) $-dimensional holographic $ SU(N) $ gauge theories in the presence of an external magnetic field from the holographic hard and soft wall models. We obtain exact solutions for the critical temperature of the deconfinement transition for any range of magnetic field. As a consequence, we find a critical magnetic field $(B_c)$, in which the critical temperature $(T_c)$ vanishes; for $B<B_c$ we have an inverse magnetic catalysis and for $ B>B_c $ we have a magnetic catalysis.
Highlights
The understanding of nonperturbative physics of Yang-Mills theory, especially QCD, remains an outstanding problem in modern theoretical physics
This is in contrast with what would be expected: a magnetic catalysis (MC), meaning the increasing of the critical temperature with increasing magnetic field [22]
We studied the problem of the deconfinement phase transition in the presence of an external magnetic field in SUðNÞ gauge theories in (2 þ 1) dimensions using two different holographic models
Summary
The understanding of nonperturbative physics of Yang-Mills theory, especially QCD, remains an outstanding problem in modern theoretical physics. Both solutions are in the presence of an external background magnetic field B and satisfy the differential equations (13) and (14). From the point of view of the boundary gauge theory, according to the holographic dictionary [27,28], the above solutions correspond to the gauge theory at zero and finite-temperature, respectively, both in the presence of an external magnetic field, and have been found by the present authors recently in [46]. It is important to mention that these solutions are exact in the magnetic field B while in other references the corresponding solutions are perturbative in B, as one can see in [15,16,17]
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