arXiv subjects

Marina Huerta

Publications and source records attributed to Marina Huerta.

25 records · Page 2Linked to original sources

arXiv2012

Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.

hep-th↗

arXiv2012

On the RG running of the entanglement entropy of a circle

We show, using strong subadditivity and Lorentz covariance, that in three dimensional space-time the entanglement entropy of a circle is a concave function. This implies the decrease of the coefficient of the area term and the increase of the constant term in the entropy between the ultraviolet and infrared fixed points. This is in accordance with recent holographic c-theorems and with conjectures about the renormalization group flow of the partition function of a three sphere (F-theorem). The irreversibility of the renormalization group flow in three dimensions would follow from the argument provided there is an intrinsic definition for the constant term in the entropy at fixed points. We discuss the difficulties in generalizing this result for spheres in higher dimensions.

hep-th↗

arXiv2012

Numerical determination of the entanglement entropy for free fields in the cylinder

We calculate numerically the logarithmic contribution to the entanglement entropy of a cylindrical region in three spatial dimensions for both, free scalar and Dirac fields. The coefficient is universal and proportional to the type $c$ conformal anomaly in agreement with recent analytical predictions. We also calculate the mass corrections to the entanglement entropy for scalar and Dirac fields in a disk. These apparently unrelated problems make contact through the dimensional reduction procedure valid for free fields whereby the entanglement entropy for the cylinder can be calculated as an integral over masses of the disk entanglement entropies. Coming from the same numerical evaluation in the lattice, each coefficient is cross checked by the other, testing in this way the two results simultaneously.

hep-th↗

arXiv2011

Towards a derivation of holographic entanglement entropy

We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.

hep-th↗

arXiv2001

Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States

Chiral conformal field theories are characterized by a ground-state current at finite temperature, that could be observed, e.g. in the edge excitations of the quantum Hall effect. We show that the corresponding thermal conductance is directly proportional to the gravitational anomaly of the conformal theory, upon extending the well-known relation between specific heat and conformal anomaly. The thermal current could signal the elusive neutral edge modes that are expected in the hierarchical Hall states. We then compute the thermal conductance for the Abelian multi-component theory and the W-infinity minimal model, two conformal theories that are good candidates for describing the hierarchical states. Their conductances agree to leading order but differ in the first, universal finite-size correction, that could be used as a selective experimental signature.

cond-mat.mes-hall↗

arXiv2000

Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories

We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the electromagnetically charged and neutral sectors of these models, respectively. The charged sector is the usual Abelian Chern-Simons theory that successfully describes Laughlin-type incompressible fluids. The neutral sector is a 2+1-dimensional theory analogous to the 1+1-dimensional orbifold conformal field theories. It is based on the gauge group O(2) which contains a ${\bf Z}_2$ disconnected group manifold, which is the salient feature of this theory. At level q, the Abelian theory of the neutral sector gives rise to a ${\bf Z}_{2q}$ symmetry, which is further reduced by imposing the ${\bf Z}_2$ symmetry of charge-conjugation invariance. The remaining ${\bf Z}_q$ symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-Pfaffian states.

cond-mat.mes-hall↗

arXiv1999

U(1)xSU(m)_1 Theory and c=m W_{1+\infty} Minimal Models in the Hierarchical Quantum Hall Effect

Two classes of Conformal Field Theories have been proposed to describe the Hierarchical Quantum Hall Effect:the multi-component bosonic theory, characterized by the symmetry U(1)xSU(m)_1 and the W_{1+\infty} minimal models with central charge c=m. In spite of having the same spectrum of edge excitations, they manifest differences in the degeneracy of the states and in the quantum statistics, which call for a more detailed comparison between them. Here, we describe their detailed relation for the general case, c=m and extend the methods previously published for c < 4. Specifically, we obtain the reduction in the number of degrees of freedom from the multi-component Abelian theory to the minimal models by decomposing the characters of the U(1)xSU(m)_1 representations into those of the c=m W_{1+\infty} minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W_{1+\infty} minimal models as infra-red fixed point.

hep-th↗