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2-group global symmetries, hydrodynamics and holography
by Nabil Iqbal, Napat Poovuttikul
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|Authors (as registered SciPost users):
|Nabil Iqbal · Nick Poovuttikul
We construct a theory of hydrodynamics describing the finite-temperature realization of a 2-group global symmetry composed out of $U(1)$ zero-form and $U(1)$ one-form symmetries. We study aspects of the thermodynamics from a Euclidean partition function and derive constitutive relations for ideal hydrodynamics from various points of view. Novel features of the resulting theory include an analogue of the chiral magnetic effect and a chiral sound mode propagating along magnetic field lines. We also discuss a minimalist holographic description of a theory dual to 2-group global symmetry and verify predictions of the hydrodynamic description.Along the way we clarify some aspects of symmetry breaking in higher-form theories at finite temperature.
Published as SciPost Phys. 15, 063 (2023)
List of changes
We would like to thank the referee for their comments and encouraging message, and we apologize for the long delay in our response. Regarding the comments requested by Referee 2, we have adjusted the manuscript as follows
1. We agree with the referee that the existence of a charged current even in equilibrium is an interesting phenomenon: we have added some further clarifying words about this on page 7, explaining further their microscopic origin and giving some other examples from elementary physics. At some level the microscopic origin is precisely the same as in the regular chiral magnetic effect – the key difference is just that the magnetic field itself is now a 0th order hydrodynamics degree of freedom, as we discuss further in the paper.
2. Below Eq. (4.14), we add a quick explanation of the limit in the dual QFT in which the backreaction is negligible and comments on the limitation of the presented background solution. We are not aware of the fully backreacted black brane solution but it is likely that it has to be obtained numerically (similar to those with finite 1-form charge density).
3. We have corrected the typos pointed out by the referee as well as a few other grammatical and spelling mistakes.
We hope that with these additions and corrections, the manuscript now meets the standard of SciPost.
Submission & Refereeing History
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