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In this short note we begin the analysis of deformed integrable Chern-Simons theories. We construct the two loop dilatation operator for the scalar sector of the ABJM theory with $k1 eq -k2$ and we compute the anomalous dimension of some operators.
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We investigate the effect of supersymmetry preserving mass deformation near the UV fixed point represented by the ${cal N}=6$ ABJM theory. In the context of the gauge/gravity duality, we analytically calculate the leading small mass effect on the renormalized entanglement entropy (REE) for the most general Lin-Lunin-Maldacena (LLM) geometries in the cases of the strip and disk shaped entangling surfaces. Our result shows that the properties of the REE in (2+1)-dimensions are consistent with those of the $c$-function in (1+1)-dimensions. We also discuss the validity of our computations in terms of the curvature behavior of the LLM geometry in the large $N$ limit and the relation between the correlation length and the mass parameter for a special LLM solution.
We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in (2+1)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena (LLM) geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in (2+1)-dimensions are consistent with the Zamolodchikov $c$-function proposed in (1+1)-dimensional conformal field theory.
We consider real mass and FI deformations of ABJM theory preserving supersymmetry in the large $N$ limit, and compare with holographic results. On the field theory side, the problems amounts to a spectral problem of a non-Hermitian Hamiltonian. For certain values of the deformation parameters this is invariant under an antiunitary operator (generalised $mathcal{PT}$ symmetry), which ensures the partition function remains real and allows us to calculate the free energy using tools from statistical physics. The results obtained are compatible with previous work, the important new feature being that these are obtained directly from the real deformations, without analytic continuation.
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 $m(x)= m_0 sin k x$ 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 have 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.
In this paper we study the thermodynamics of black branes with a modulated complex scalar in the context of bulk and boundary theories. The modulation induces inhomogeneity to the dual field theory, anisotropic pressure, and brane charge to the bulk geometry. The first law of thermodynamics and the Smarr relation are obtained using the off-shell ADT and the reduced action formalisms. We discuss the prescription for the mass of black branes, which relies on relevant and marginal deformations in the dual field theory. One of the cases is the gravity dual to a ABJM model with a sinusoidal mass function depending on a spatial coordinate. This is the first study of the deformed ABJM model at finite temperature including bulk thermodynamics.
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