arXiv subjects

Jia-ju Zhang

Publications and source records attributed to Jia-ju Zhang.

At least 19 recordsLinked to original sources

arXiv2017

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length $\ell$ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the Rényi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of $\ell^9$ for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

hep-th↗

arXiv2017

New BPS Wilson loops in $\mathcal N \textbf{= 4}$ circular quiver Chern-Simons-matter theories

We construct new families of 1/4 BPS Wilson loops in circular quiver $\mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops. The new operators are cohomologically equivalent to bosonic 1/4 BPS Wilson loops and are then amenable of exact evaluation via localization techniques. Moreover, in the case of orbifold ABJM theory we identify the corresponding gravity duals for some of the 1/4 and 1/2 BPS Wilson loops.

hep-th↗

arXiv2017

Corrections to holographic entanglement plateau

We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that $ΔS=S(L)-|S(L-\ell)-S(\ell)|$ is nonnegative, where $S(L)$ is the thermal entropy and $S(L-\ell)$, $S(\ell)$ are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when $\ell \leq \ell_c$ the inequality saturates $ΔS=0$. In thermal AdS background, the holographic entanglement entropy leads to $ΔS=0$ for arbitrary $\ell$. We compute the next-to-leading order contributions to $ΔS$ in the large central charge CFT at both high and low temperatures. In both cases we show that $ΔS$ is strictly positive except for $\ell = 0$ or $\ell = L$. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.

hep-th↗

arXiv2017

Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval Rényi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of Rényi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.

hep-th↗

arXiv2017

String theory duals of Wilson loops from Higgsing

For three-dimensional ABJ(M) theories and $\mathcal N=4$ Chern-Simons-matter quiver theories, we construct two sets of 1/2 BPS Wilson loop operators by applying the Higgsing procedure along independent directions of the moduli space, and choosing different massive modes. For theories whose dual M-theory description is known, we also determine the corresponding spectrum of 1/2 BPS M2-brane solutions. We identify the supercharges in M-theory and field theory, as well as the supercharges preserved by M2-/anti-M2-branes and 1/2 BPS Wilson loops. In particular, in $\mathcal N=4$ orbifold ABJM theory we find pairs of different 1/2 BPS Wilson loops that preserve exactly the same set of supercharges. In field theory they arise by Higgsing with the choice of either particles or antiparticles, whereas in the dual description they correspond to a pair of M2-/anti-M2-branes localized at different positions in the compact space. This result enlightens the origin of classical Wilson loop degeneracy in these theories, already discussed in arXiv:1506.07614. A discussion on possible scenarios that emerge by comparison with localization results is included.

hep-th↗

arXiv2017

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by $Δ$. For the case of two short intervals on complex plane, we expand the Rényi mutual information by the cross ratio $x$ to order $x^{2Δ+2}$. For the case of one interval on torus with the temperature being low, we expand the Rényi entropy by $q=\exp(-2πβ/L)$, with $β$ being the inverse temperature and $L$ being the spatial period, to order $q^{Δ+2}$. To make the result meaningful, we require that the scaling dimension $Δ$ cannot be too small. For two intervals on complex plane we need $Δ>1$, and for one interval on torus we need $Δ>2$. We work in small Newton constant limit in gravity side and so large central charge limit in CFT side, and find matches of gravity and CFT results.

hep-th↗

arXiv2016

Thermality and excited state Rényi entropy in two-dimensional CFT

We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.

hep-th↗

arXiv2016

Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory

We investigate the holographic Rényi entropy for two-dimensional $\mathcal N=(2,2)$ superconformal field theory (SCFT), which is dual to $\mathcal N=2$ supergravity in AdS$_3$ background. In SCFT we have the stress tensor, current, and their supersymmetric partners, and in supergravity we have the graviton, vector field, and two gravitinos. We get the Rényi mutual information of two short intervals on complex plane in expansion by the cross ratio $x$ to order $x^4$, and Rényi entropy of one interval on torus in expansion by $q=\exp(-2πβ/L)$, with $β$ being the inverse temperature and $L$ being the spatial period, to order $q^2$. We calculate in both the supergravity and SCFT sides, and find matches of the results.

hep-th↗

arXiv2016

Holographic Description of 2D Conformal Block in Semi-classical Limit

In this paper, we study the holographic descriptions of the conformal block of heavy operators in two-dimensional large c conformal field theory. We consider the case that the operators are pairwise inserted such that the distance between the operators in a pair is much smaller than the others. In this case, each pair of heavy operators creates a conical defect in the bulk. We propose that the conformal block is dual to the on-shell action of three dimensional geometry with conical defects in the semi-classical limit. We show that the variation of the on-shell action with respect to the conical angle is equal to the length of the corresponding conical defect. We derive this differential relation on the conformal block in the field theory by introducing two extra light operators as both the probe and the perturbation. Our study also suggests that the area law of the holographic Renyi entropy must holds for a large class of states generated by a finite number of heavy operators insertion.

hep-th↗

arXiv2016

Short interval expansion of Rényi entropy on torus

We investigate the short interval expansion of the Rényi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval $\ell$ to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the Rényi entropy at any temperature. In particular, we pay special attention to the large $c$ CFTs dual to the AdS$_3$ gravity and its cousins. At both low and high temperature limits, we read the Rényi entropies to order $\ell^6$, and find good agreements with holographic results. Moreover, the expansion allows us to read $1/c$ contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well.

hep-th↗

arXiv2016

Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories

In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in $\mathcal N=2,3$ quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\mathcal N=4$ orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and $\mathcal N=4$ orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.

hep-th↗

arXiv2016

Exact results for Wilson loops in orbifold ABJM theory

We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the $d=3$ ${\mathcal N}=4$ super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the ${\mathcal N}=4$ orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results.

hep-th↗

arXiv2016

On one-loop entanglement entropy of two short intervals from OPE of twist operators

We investigate the one-loop entanglement entropy of two short intervals with small cross ratio $x$ on a complex plane in two-dimensional conformal field theory (CFT) using operator product expansion of twist operators. We focus on the one-loop entanglement entropy instead of the general order $n$ Rényi entropy, and this makes the calculation much easier. We consider the contributions of stress tensor to order $x^{10}$, contributions of $W_3$ operator to order $x^{12}$, and contributions of $W_4$ operator to order $x^{14}$. The CFT results agree with the ones in gravity.

hep-th↗

arXiv2016

Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories

We show that generic three-dimensional $\mathcal N=2$ quiver super Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.

hep-th↗

arXiv2015

BPS Wilson loops in Minkowski spacetime and Euclidean space

We give evidence that spacelike BPS Wilson loops do not exist in Minkowski spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot preserve any supersymmetries, in $d = 4$ $\mathcal N = 4$ super Yang-Mills theory, $d = 3$ $\mathcal N = 2$ super Chern-Simons-matter theory, and $d = 3$ $\mathcal N = 6$ Aharony-Bergman-Jafferis-Maldacena theory. We not only show this using infinite straight lines and circles as examples, but also we give proofs for general curves. We attribute this to the conflicts of reality conditions of the spinors. However, spacelike Wilson loops do exist in Euclidean space. There are both BPS Wilson loops along infinite straight lines and circular BPS Wilson loops. This is because the reality conditions of the spinors are lost after Wick rotation. The result is reasonable in view of the AdS/CFT correspondence.

hep-th↗

arXiv2015

Holographic Rényi entropy for two-dimensional N=(1,1) superconformal field theory

In this paper we investigate the holographic Rényi entropy in $\mathcal N=1$ supergravity (SUGRA) in AdS$_3$ spacetime, which is dual to the two-dimensional $\mathcal N=(1,1)$ superconformal field theory (SCFT). We consider both cases of two short intervals on a line with zero temperature and one interval on a circle with low temperature. In SUGRA side we consider contributions of both graviton and gravitino, and in SCFT side we consider contributions of both stress tensor $T$, $\bar T$ and their superpartners $G$, $\bar G$. We find matches between SUGRA and SCFT results.

hep-th↗

arXiv2015

Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory

We investigate the supersymmetric Wilson loops in $d=3$ $\mathcal{N}=4$ super Chern-Simons-matter theory obtained from non-chiral orbifold of ABJM theory. We work in both Minkowski spacetime and Euclidean space, and we construct 1/4 and 1/2 BPS Wilson loops. We also provide a complete proof that the difference between 1/4 and 1/2 Wilson loops is $Q$-exact with $Q$ being some supercharge that is preserved by both the 1/4 and 1/2 Wilson loops. This plays an important role in applying the localization techniques to compute the vacuum expectation values of Wilson loops. We also study the M-theory dual of the 1/2 BPS circular Wilson loop.

hep-th↗

arXiv2014

Holographic Rényi entropy for CFT with $W$ symmetry

In this paper we investigate the holographic Rényi entropy of two disjoint intervals on complex plane with small cross ratio $x$ for conformal field theory with $W$ symmetry in the ground state, which could be dual to a higher spin AdS$_3$ gravity. We focus on the cases of $W_3$ and $W_4$ symmetries. In order to see the nontrivial contributions from the $W$ fields, we calculate the Rényi entropy in the expansion of $x$ to order $x^8$ in both the gravity and the CFT sides. In the gravity side the classical contributions to the entanglement entropy is still given by the Ryu-Takayanagi area formula under the reasonable assumption, while the 1-loop quantum corrections have to take into account of the contributions not only from massless gravitons, but also from massless higher spin fields. In the CFT side we still use the operator product expansion of twist operators in the small interval limit, but now we need to consider the quasiprimary fields constructed from $W$ fields, besides the ones from Virasoro Verma module. In the large central charge limit, we obtain the classical, 1-loop, 2-loop, and 3-loop parts of the Rényi entropy. The classical and 1-loop results in the gravity and the CFT sides are in exact match. This confirms the higher spin gravity/CFT correspondence, and also supports the holographic computation of Rényi entanglement entropy, including the quantum correction, in both the AdS$_3$ gravity and the higher spin AdS$_3$ gravity.

hep-th↗