2830444
Thermodynamical property of entanglement entropy for excited states.
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two-dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.
119216245
Holographic local quenches and entanglement density
A bstractWe propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.
33013781
Holographic geometry of cMERA for quantum quenches and finite temperature
A bstractWe study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
92986310
Entanglement of local operators in large-N conformal field theories
We study Renyi and von-Neumann entanglement entropy of excited states created by local operators in large N (or large central charge) CFTs. First we point that a naive large N expansion can break down for the von-Neumann entanglement entropy, while it does not for the Renyi entanglement entropy. This happens even for the excited states in free Yang-Mills theories. Next, we analyze strongly coupled large N CFTs from both field theoretic and holographic viewpoints. We find that the Renyi entanglement entropy of the excited state produced by a local operator, grows logarithmically under its time evolution and its coefficient is proportional to the conformal dimension of the local operator.
23166563
Notes on quantum entanglement of local operators
A bstractThis is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.
118536853
Central charges for BCFTs and holography
A bstractIn this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing functions under the RG flows. We present a few supporting evidences from field theory calculations. In two dimensions, we give a holographic construction (AdS/BCFT) for an arbitrary shape of boundary and calculate its logarithmic term as well as boundary energy momentum tensors, confirming its consistency with the Weyl anomaly. Moreover, we give perturbative solutions of gravity duals for the three dimensional BCFTs with any shapes of boundaries. We find that the standard Fefferman-Graham expansion breaks down for generic choices of BCFT boundaries.
118695956
Spherical D2-brane from multiple D0-branes
We show that the spherical D2-brane in SU(2) WZW model can be well described as the “fuzzy sphere” configuration of D0-branes. We further investigate the stability of some configurations of D0-branes in NS5 background.
17506465
Singular Calabi-Yau manifolds and ADE classification of CFTS
Abstract We study superstring propagations on the Calabi–Yau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N=2 Landau–Ginzburg theory and Liouville theory. If the Landau–Ginzburg description precisely reflects the information of ADE singularity, the Landau–Ginzburg model of D 4 ,E 6 ,E 8 and Gepner model of A 2 ⊗A 2 ,A 2 ⊗A 3 ,A 2 ⊗A 4 should give the same result. We compute the elements of D 4 ,E 6 ,E 8 modular invariants for the singular Calabi–Yau compactification in terms of the spectral flow invariant orbits of the tensor product theories with the theta function which encodes the momentum mode of the Liouville theory. Furthermore we find the interesting identity among characters in minimal models at different levels. We give the complete proof for the identity.
16198184
Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories
We study D-branes in Kazama-Suzuki models by means of the boundary state description. We can identify the boundary states of Kazama-Suzuki models with the solitons in = 2 Landau-Ginzburg theories. We also propose a geometrical interpretation of the boundary states in Kazama-Suzuki models.
119541412
Boundary states in Gepner models
We extend the construction of the boundary states in Gepner models to the non-diagonal modular invariant theories, and derive the same supersymmetric conditions as the diagonal theories. We also investigate the relation between the microscopic charges of the boundary states and Ramond charges of the B-type D-branes on the Calabi-Yau threefolds with one Kahler modulus in the large volume limit.