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Register a new userHolographic Entanglement Entropy of Mass-deformed ABJM Theory
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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.
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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.
Recent work has shown that entanglement and the structure of spacetime are intimately related. One way to investigate this is to begin with an entanglement entropy in a conformal field theory (CFT) and use the AdS/CFT correspondence to calculate the bulk metric. We perform this calculation for ABJM, a particular 3-dimensional supersymmetric CFT (SCFT), in its ground state. In particular we are able to reconstruct the pure AdS4 metric from the holographic entanglement entropy of the boundary ABJM theory in its ground state. Moreover, we are able to predict the correct AdS radius purely from entanglement. We also address the general philosophy of relating entanglement and spacetime through the Holographic Principle, as well as some of the philosophy behind our calculations.
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.
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 review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newtons constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.
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