Abstract
Using recent lattice data on the thermodynamics of QCD in the presence of a background magnetic field, we show that the ratio of transverse to longitudinal pressure exhibits, to good accuracy, a simple scaling behavior over a wide range of temperature and magnetic field, essentially depending only on the ratio T/sqrt{B} . We compare this QCD response to the corresponding magnetoresponse in maximally supersymmetric Yang Mills theory. Given suitable calibrations defining the comparison, we find excellent agreement. This may be viewed as a further test of the applicability of holographic models for hot QCD.
Highlights
Are modest [12, 13], and that Nc dependence is essentially trivial, with extensive quantities scaling with the number of gauge fields [14, 15]
To investigate whether a similar robustness exists with respect to conformal symmetry it is natural to examine the effects of deformations which explicitly break conformal symmetry
The underlying lattice QCD data is discussed in more detail in section 3, (Deviations from this scaling behavior appear to be present at the lowest temperatures and highest magnetic fields, but the growth of the error bars precludes making any definitive statement about this region.)
Summary
Consider a quantum field theory (QFT) minimally coupled to an external electromagnetic. We choose to scale the external gauge field Aeμxt so that the electromagnetic coupling e does not appear in covariant derivatives, but instead e2 is an inverse factor in the Maxwell action. With V = LxLyLz the spatial volume This separation, by definition, places all the response to the applied magnetic field in the QFT contribution to the free energy. The microscopic definition (2.4) of pressures as stress-energy eigenvalues corresponds to a thermodynamic definition in which the effect of compression is evaluated at a fixed magnetic flux Φ = B LxLy.. For an asymptotically free theory like QCD, the stress-energy trace has an intrinsic contribution from the running of the coupling (and quark masses terms), plus the additional contribution from the external magnetic field.
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