In this paper, we study the influence of an external magnetic field in holographic QCD models where the backreaction is modeled in via an appropriate choice of the background metric. We add a phenomenological soft wall dilaton to incorporate better IR behavior (confinement). Elaborating on previous studies conducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Page transition, the dual of the deconfinement transition, as a function of the magnetic field. We confirm that the critical deconfinement temperature can drop with the magnetic field. Secondly, we study the quark condensate holographically as a function of the applied magnetic field and demonstrate that this model does not exhibit inverse magnetic catalysis at the level of the chiral transition. The quest for a holographic QCD model that qualitatively describes the inverse magnetic catalysis at finite temperature is thus still open. Throughout this work, we pay special attention to the different holographic parameters and we attempt to fix them by making the link to genuine QCD as close as possible. This leads to several unanticipated and so far overlooked complications (such as the relevance of an additional length scale in the confined geometry) that we discuss in detail.Comment: 48 pages. v2: corrected typos, added references and improved discussion, in particular on the role of an extra relevant length scale and on the magnetized background itself. v3: minor edits, version accepted for publication in PhysRev

The renormalization of N = 1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The nonrenormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N = 1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three loop calculation. *

In this work we investigate the description of superconducting systems with multiple Fermi surfaces. For the case of one Fermi surface we re-obtain the result that the superconductor is more precisely described as a topological state of matter. Studying the case of more than one Fermi surface, we obtain the effective theory describing a time reversal symmetric topological superconductor. These results are obtained by employing a general procedure to construct effective low energy actions describing states of electromagnetic systems interacting with charges and defects. The procedure consists in taking into account the proliferation or dilution of these charges and defects and its consequences for the low energy description of the electromagnetic response of the system. We find that the main ingredient entering the low energy characterization of the system with more the one Fermi surface is a non-conservation of the canonical supercurrent triggered by particular vortex configurations.This present work was mainly motivated by the illuminating study developed in [1], where the authors centered the analysis of a superconductor state on the proper identification of its low energy degrees of freedom. This lead to the conclusion that the effective low energy theory of a superconductor, usually described by Ginzburg-Landau theory, is more appropriately described by a topological BF theory encoding the topological interactions of vortices and charges in the system. This strategy led us to consider the use of a procedure, known as the Julia-Toulouse approach (JTA) [11], which naturally accommodates such a focus on the behavior of the degrees of freedom. The JTA has the aim of constructing an effective field theory for gauge fields from semi-classical considerations about the collective dynamics of charged particles and defects in the system. The procedure is throughly reviewed in [12] and has already been employed for the study of superconducting systems in relation to confinement [13], see also [14,15] for related work.Another motivation for the present work comes from the recent studies of Qi, Witten and Zhang [2]. These authors proposed an effective theory for a time reversal invariant topological superconductor in three spatial dimensions, (3 + 1)D (for a review of topological materials see [3]). Their construction involves consideration of a time reversal topological insulator in (4 + 1)D sandwiched between two boundaries, where each boundary sustain a (3+1)D s-wave superconductor. This construction leads, upon dimensional reduction, to an effective description of topological superconductor characterized by a topological term describing a coupling between the electromagnetic field and the superconducting phase fluctuation. Such a coupling is mathematically the same as the one between an Abelian gauge field and an axion. One of the main results presented in their work is the realization of the phenomenon of anomaly inflow [7] due to the contribution of so called "chiral vortices".