Non-Abelian statistics versus the Witten anomaly

This paper is motivated by prospects for non-Abelian statistics of deconfined particle-like objects in 3+1 dimensions, realized as solitons with localized Majorana zeromodes. To this end, we study the fermionic collective coordinates of magnetic monopoles in 3+1 dimensional spontaneously-broken SU(2) gauge theories with various spectra of fermions. We argue that a single Majorana zeromode of the monopole is not compatible with cancellation of the Witten SU(2) anomaly. We also compare this approach with other attempts to realize deconfined non-Abelian objects in 3+1 dimensions.Comment: 11 pages, 3 figures; v2: added refs, minor corrections, published versio

Entanglement of purification: from spin chains to holography

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.Comment: 40 pages, multiple figures. v2: references added, typos correcte

Entangled Dilaton Dyons

Einstein-Maxwell theory coupled to a dilaton is known to give rise to extremal solutions with hyperscaling violation. We study the behaviour of these solutions in the presence of a small magnetic field. We find that in a region of parameter space the magnetic field is relevant in the infra-red and completely changes the behaviour of the solution which now flows to an $AdS_2\times R^2$ attractor. As a result there is an extensive ground state entropy and the entanglement entropy of a sufficiently big region on the boundary grows like the volume. In particular, this happens for values of parameters at which the purely electric theory has an entanglement entropy growing with the area, $A$, like $A \log(A)$ which is believed to be a characteristic feature of a Fermi surface. Some other thermodynamic properties are also analysed and a more detailed characterisation of the entanglement entropy is also carried out in the presence of a magnetic field. Other regions of parameter space not described by the $AdS_2\times R^2$ end point are also discussed.Comment: Some comments regarding comparison with weakly coupled Fermi liquid changed, typos corrected and caption of a figure modifie

Hidden Fermi surfaces in compressible states of gauge-gravity duality

General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, z, and a specific hyperscaling violation exponent, \theta. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. (arXiv:1111.1023). We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.Comment: 33 pages, 5 figures; (v2) added refs, corrected typos, and modified figure; (v3) added table summarizing result

Impact of a leptin single nucleotide polymorphism and zilpaterol hydrochloride on growth and carcass characteristics in finishing steers

A total of 4,178 steers (mean initial BW = 403.9 ± 16.04 kg) were used to test the interactive effects, if any, of leptin R25C genotypes (CC, CT, or TT) and zilpaterol hydrochloride (ZH) feeding duration on growth performance and carcass traits. Steers were blocked by arrival at the feed yard, genotyped for the leptin SNP, allotted to genotype-specific pens (90 steers/pen), and assigned randomly within genotype and block to 0 or 21 d of dietary ZH. All pens within a block were slaughtered on the same day (132.1 ± 10.9 d on feed). Final BW of steers fed ZH was 6.0 kg heavier (P = 0.008), and ZH-fed steers had greater (P = 0.003) ADG than steers not fed ZH. Feeding ZH decreased DMI in steers with increased frequency of the T allele (9.67, 9.53, and 9.28 kg/d for CC, CT, and TT, respectively), but DMI increased with the frequency of the T allele (9.68, 9.90, and 10.1 kg for CC, CT, and TT, respectively) when ZH was not fed (leptin genotype × ZH, P = 0.011). At the conclusion of the study, ultrasonic fat was greatest for TT steers (11.4 ± 0.28 mm) and least (P = 0.003) for CC steers (11.0 ± 0.25 mm). Regardless of ZH-feeding duration, TT steers produced a greater (P = 0.006) percentage of USDA yield grade (YG) 4 or higher carcasses (5.4 vs. 2.7%) and a lesser (P = 0.006) percentage of YG 1 carcasses (17.7 vs. 26.8%) than CC steers. In addition, ZH-fed steers produced a greater (P \u3c 0.001) percentage of USDA YG 1 carcasses (25.9 vs. 16.2%) and a lesser (P \u3c 0.001) percentage of YG 4 or higher carcasses (1.6 vs. 6.0%) than steers fed the control diet. Marbling scores and the percentage of carcasses grading USDA Choice and Prime were greater in TT than CC steers when fed diets devoid of ZH, but both marbling and quality grades did not differ among leptin genotypes when fed ZH for 21 d (leptin genotype × ZH, P ≤ 0.03). The amount of HCW gain tended to be less (P = 0.095) for steers of the TT genotype (12.7 kg) than either CC (16.3 kg) or CT (17.0 kg) genotypes. Results indicated that leptin R25C genotype impacted most traits associated with fatness whereas feeding ZH for 21 d affected HCW and ADG positively but impacted feed intake, marbling, and USDA quality grades negatively

String theory duals of Lifshitz-Chern-Simons gauge theories

We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern-Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic dictionary, we identify the bulk fields that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories realized here exhibit a mass gap.Comment: 25+14 pages, 3 figures; v2: significant corrections regarding IR geometry, resulting in new section 5; journal versio

Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.Comment: 42pages, 9figures, reference added, minor chang

Large-density field theory, viscosity, and "2kF2k_F" singularities from string duals

We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is completely stable, and we find that the existing string-theoretic solution of this model yields two interesting results. First, it indicates that the shear viscosity is not corrected by $\alpha'$ effects in this system. For flow perpendicular to the F1 strings the viscosity to entropy ratio take the usual value $1/4\pi$, but for flow parallel to the F1's it vanishes as $T^2$ at low temperature. Secondly, it encodes singularities in correlation functions coming from low-frequency modes at a finite value of the momentum along the $T^4$ directions. This may provide a strong coupling analogue of finite density condensed matter systems for which fermionic constituents of larger operators contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched strings on the gravity side play the role of these composite operators. We explore the analogue for our system of the Luttinger relation between charge density and the volume bounded by these singular surfaces. This model provides a clean example where the string-theoretic UV completion of the gravity dual to a finite density field theory plays a significant and calculable role.Comment: 28 pages. v2: added reference

Moduli Spaces of Cold Holographic Matter

We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental representation of SU(Nc), with n=3,2,1. In particular, we study zero-temperature states with a nonzero baryon number charge density, which we call holographic matter. We demonstrate that a moduli space of such states exists in these theories, specifically a Higgs branch parameterized by the expectation values of scalar operators bilinear in the hypermultiplet scalars. At a generic point on the Higgs branch, the R-symmetry and gauge group are spontaneously broken to subgroups. Our holographic calculation consists of introducing a single probe Dp-brane into AdS5 times S^5, with p=2n+1=7,5,3, introducing an electric flux of the Dp-brane worldvolume U(1) gauge field, and then obtaining explicit solutions for the worldvolume fields dual to the scalar operators that parameterize the Higgs branch. In all three cases, we can express these solutions as non-singular self-dual U(1) instantons in a four-dimensional space with a metric determined by the electric flux. We speculate on the possibility that the existence of Higgs branches may point the way to a counting of the microstates producing a nonzero entropy in holographic matter. Additionally, we speculate on the possible classification of zero-temperature, nonzero-density states described holographically by probe D-branes with worldvolume electric flux.Comment: 56 pages, 8 PDF images, 4 figure

Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions

We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidence that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the R\ue9nyi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the R\ue9nyi entropy of order 1/2