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Thermal Chiral and Deconfining Transitions in the Presence of a Magnetic Background

  • Chapter
Strongly Interacting Matter in Magnetic Fields

Part of the book series: Lecture Notes in Physics ((LNP,volume 871))

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. 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. 2.

    Higher-order (loop) corrections need the full propagator, not only its poles.

  3. 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. 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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  1. Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil

    Eduardo S. Fraga

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  1. Eduardo S. Fraga
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Editors and Affiliations

  1. Department of Physics, Stony Brook University, Nicolls Rd 100, Stony Brook, 11794, New York, USA

    Dmitri Kharzeev

  2. Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Nicolas Cabrera 13-15, Madrid, 28049, Spain

    Karl Landsteiner

  3. Institut für Theoretische Physik, Technische Universität Wien, Wiedner Haupstr. 8, Wien, 1040, Austria

    Andreas Schmitt

  4. Physics Department (MC 273), University of Illinois at Chicago, West Taylor Street 845Rm 2236, Chicago, 60607, Illinois, USA

    Ho-Ung Yee

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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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