Abstract
We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents mathcal{N} = 4 supersymmetric Yang-Mills theory coupled to mathcal{N} = 2 flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes show a diffusive behavior in the dispersion relation, which agrees with that found with the effective field theory approach. We also study a non-equilibrium steady state which has a constant current flow in the presence of an external electric field. In a non-equilibrium steady state, we find that the Nambu-Goldstone modes show a linear dispersion in the real part of the frequency in addition to the diffusive behavior. Moreover, we analyze the linear dispersion of the Nambu-Goldstone modes in the hydrodynamic approximation. As a result, we find that the linear dispersion can be written as the analytic functions of quantities in the dual field theory. Our results imply that such a linear dispersion is a characteristic behavior of Nambu-Goldstone modes in a non-equilibrium steady state.
Highlights
We assume that the bulk geometry is given by a five-dimensional AdS-Schwarzschild black hole (AdS-BH) and an S5: ds2 = 1 u2− f (u)dt2 + dx2 + du2 f (u) + dΩ25, (2.1)where u4 f (u) = 1 − u4H . (2.2)Here, (t, x) = (t, x, y, z) is the coordinate of the dual gauge theory in the (3+1)-dimensional spacetime and u is the radial coordinate
We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence
We study the dispersion relation of the NG mode which appears in the dissipative system
Summary
The system consists of a stack of Nc D3-branes and Nf D7-branes. If we take the limit of Nf Nc and large ’t Hooft coupling λ = gY2 MNc with Nf fixed, the D7-branes can be regarded as probes in the black D3-brane geometry. The dual field theory of the D3/D7 model is N = 4 SU(Nc) supersymmetric Yang-Mills theory coupled to flavor fields preserving N = 2 supersymmetry. We briefly review the spontaneous symmetry breaking of the U(1) chiral symmetry induced by the magnetic field in the D3/D7 model
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