AdS Q-soliton and inhomogeneously mass-deformed ABJM model

Abstract

We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function m(x) = m 0 sin kx and its derivative m (x). As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons has lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.

Thermodynamics of inhomogeneously mass-deformed ABJM model and pressure anisotropy

“…The neutral solution corresponds to the marginal deformation in the dual conformal field theory(CFT) [28]. The other charged solution, which was recently found in [9], is dual to a mass-deformed ABJM theory which is generated by spatially dependent source functions. It can also be regarded as dual to the 3-dimensional CFT in the background of non-trivial charge distribution and corresponding chemical potential.…”

“…The mass of the complex scalar field z = X + iY is given by m 2 = −2 and thus in the hairy solutions the scalar field can have two normalizable complex modes at the boundary, one of which is interpreted as the source of the dual boundary operator and the other its expectation value. In [9], the numerical black brane solutions were found in which the complex scalar field z is found to be in the Q-lattice configuration as…”

“…The behavior of these functions on the radial coordinate r is plotted in Figure 1 for a numerical solution. For more numerical results on this black branes solution, see [9]. The temperature and the entropy density of this charged black brane are computed as…”

“…We show this structure by a field redefinition of the complex scalar field in the action (1). Although we focused on the AdS Q-soliton with a complex scalar hair, a part of study on the black branes has been done recently without introduction of the brane charge in [9].…”

“…ImABJM model with a relevant deformation related to mass function,m(x) =m 0 sin kx. This is the first study of the ImABJM model at finite temperature accompanied by our preliminary study for the Q-lattice black brane [9]. This paper is organized as follows.…”