Abstract
We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed position in space.
Highlights
One of the main goals of the high-energy physics community is to determine the properties of hadronic matter at extremes of temperature and baryonic densities
The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number
We have determined an inhomogeneous solution of a system of pions at non-vanishing isospin chemical potential
Summary
One of the main goals of the high-energy physics community is to determine the properties of hadronic matter at extremes of temperature and baryonic densities. In terrestrial relativistic heavy-ion colliders, as well as in compact stellar objects, the energy scale is not sufficiently large to ensure that perturbative methods are under control This means that di↵erent phenomenological methods should be used to infer the properties of hadronic matter. Lattice QCD simulations at non-vanishing μB are hampered by the so-called sign problem, they are feasible at non-vanishing isospin chemical potential [2] This o↵ers the opportunity to study deconfinement as a function of μI and to compare the results with the outcome of e↵ective field theories, in particular with the results of chiral perturbation theory (χPT), see [3,4,5,6,7,8,9,10,11], which is a low-energy realization of hadronic matter having the same global symmetries of QCD. Since the obtained set of di↵erential equations is quite difficult to solve, we have used a number of simplifying assumptions that make the problem almost analytically tractable
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