Abstract
We review the influence of a magnetic background on the phase diagram of strong interactions and how the chiral and deconfining transitions can be affected. First we summarize results for both transitions obtained in the framework of the linear sigma model coupled to quarks and to the Polyakov loop, and how they compare to other effective model approaches and to lattice QCD. Then we discuss the outcome of the magnetic MIT bag model that yields a behavior for the critical deconfining temperature which is compatible with recent lattice results and magnetic catalysis. The qualitative success of the magnetic MIT bag model hints to T c being a confinement-driven quantity, and leads us to the discussion of its behavior as predicted within the large-N c limit of QCD, which is also in line with the most recent lattice QCD results provided that quarks behave paramagnetically.
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Notes
- 1.
Contrastingly, a significant decrease in the critical temperature as a function of B, vanishing at \(eB_{c}\sim25m_{\pi}^{2}\), was found in Ref. [43], featuring the disappearance of the confined phase at large magnetic fields. This phenomenon that was not reproduced by any other effective model nor observed on the lattice (even for much larger fields).
- 2.
Higher-order (loop) corrections need the full propagator, not only its poles.
- 3.
This will be a key feature in the discussion of recent results for the critical temperature, since T c seems to be a confinement-driven observable for both QCD transitions.
- 4.
Of course, our description necessarily predicts a first-order transition, as usual with the MIT bag model, and our numbers should be taken as rough estimates, as is always the case in effective models.
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Acknowledgements
It is a pleasure to thank the editors of this volume of Lecture Notes in Physics for the invitation to contribute to this special edition. The discussion presented here in part summarizes work done in collaboration with M.N. Chernodub, A.J. Mizher, J. Noronha and L.F. Palhares to whom I am deeply grateful. I am especially indebted to my former students A.J. Mizher and L.F. Palhares, from whom I have learnt so much over several years. I also thank J.-P. Blaizot, M. D’Elia and G. Endrodi for fruitful discussions.
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Fraga, E.S. (2013). Thermal Chiral and Deconfining Transitions in the Presence of a Magnetic Background. In: Kharzeev, D., Landsteiner, K., Schmitt, A., Yee, HU. (eds) Strongly Interacting Matter in Magnetic Fields. Lecture Notes in Physics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37305-3_5
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