We use entangled multimode coherent states to produce entangled giant graviton states, in the context of gauge/gravity duality. We make a smeared distribution of the entangled multimode coherent states on the circle, or on the five-sphere, in the hig
her dimensional view. In gauge/gravity duality, we analyze the superposition of giant graviton states, and the entangled pairs of giant graviton states. We map a class of angular distribution functions to unitary operations on the pairs. We also use Young tableau states to construct cat states and qudit states. Various bipartite quantum states involving Young tableau states are analyzed, including micro-macro entangled states. Mixed states of Young tableau states are generated, by using ensemble mixing using angular distribution functions, and also by going through noisy quantum channels. We then produce mixed entangled pair of giant graviton states, by including interaction with the environment and using noisy quantum channels.
Motivated by the recent discovery of superconductivity in infinite-layer nickelate thin films, we report on a synthesis and magnetization study on bulk samples of the parent compounds ${R}$NiO$_{2}$ (${R}$=La, Pr, Nd). The frequency-dependent peaks o
f the AC magnetic susceptibility, along with remarkable memory effects, characterize spin-glass states. Furthermore, various phenomenological parameters via different spin glass models show strong similarity within these three compounds as well as with other rare-earth metal nickelates. The universal spin-glass behaviour distinguishes the nickelates from the parent compound CaCuO$_{2}$ of cuprate superconductors, which has the same crystal structure and $d^9$ electronic configuration but undergoes a long-range antiferromagnetic order. Our investigations may indicate a distinctly different nature of magnetism and superconductivity in the bulk nickelates than in the cuprates.
We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the
superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.
In type II superstring theory, the vacuum amplitude at a given loop order $g$ can receive contributions from the boundary of the compactified, genus $g$ supermoduli space of curves $overline{mathfrak M}_g$. These contributions capture the long distan
ce or infrared behaviour of the amplitude. The boundary parametrises degenerations of genus $g$ super Riemann surfaces. A holomorphic projection of the supermoduli space onto its reduced space would then provide a way to integrate the holomorphic, superstring measure and thereby give the superstring vacuum amplitude at $g$-loop order. However, such a projection does not generally exist over the bulk of the supermoduli spaces in higher genera. Nevertheless, certain boundary divisors in $partialoverline{mathfrak M}_g$ may holomorphically map onto a bosonic space upon composition with universal morphisms, thereby enabling an integration of the holomorphic, superstring measure here. Making use of ansatz factorisations of the superstring measure near the boundary, our analysis shows that the boundary contributions to the three loop vacuum amplitude will vanish in closed oriented type II superstring theory with unbroken spacetime supersymmetry.
We construct a class of backgrounds with a warp factor and anti-de Sitter asymptotics, which are dual to boundary systems that have a ground state with a short-range two-point correlation function. The solutions of probe scalar fields on these backgr
ounds are obtained by means of confluent hypergeometric functions. The explicit analytical expressions of a class of short-range correlation functions on the boundary and the correlation lengths $xi$ are derived from gravity computation. The two-point function calculated from gravity side is explicitly shown to exponentially decay with respect to separation in the infrared. Such feature inevitably appears in confining gauge theories and certain strongly correlated condensed matter systems.
We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the cohomology groups
of sheaves for subvarieties of the ambient product space of projective spaces. We then prove an equivalence between configuration matrices of complete intersection Calabi-Yau manifolds. We also present a formula of the genus of curves in generalized complete intersection manifolds. Some of these curves arise as the fixed point locus of certain symmetry group action on the generalized complete intersection Calabi-Yau manifolds. We also make a blowing-up along the curves, by which one can generate new Calabi-Yau manifolds. Moreover, an approach on spectral sequences is used to compute Hodge numbers of generalized complete intersection Calabi-Yau manifolds and the genus of curves therein.
By using solid-state reactions, we successfully synthesize new oxyselenides CsV$_2$Se$_{2-x}$O (x = 0, 0.5). These compounds containing V$_2$O planar layers with a square lattice crystallize in the CeCr$_2$Si$_2$C structure with the space group of $P
4/mmm$. Another new compound V$_2$Se$_2$O which crystallizes in space group $I4/mmm$ is fabricated by topochemical deintercalation of cesium from CsV$_2$Se$_2$O powder with iodine in tetrahydrofuran(THF). Resistivity measurements show a semiconducting behavior for CsV$_2$Se$_2$O, while a metallic behavior for CsV$_2$Se$_{1.5}$O, and an insulating feature for V$_2$Se$_2$O. A charge- or spin-density wave-like anomaly has been observed at 168 K for CsV$_2$Se$_2$O and 150 K for CsV$_2$Se$_{1.5}$O, respectively. And these anomalies are also confirmed by the magnetic susceptibility measurements. The resistivity in V$_2$Se$_2$O exhibits an anomalous log(1/$T$) temperature dependence, which is similar to the case in parent phase or very underdoped cuprates indicating the involvement of strong correlation. Magnetic susceptibility measurements show that the magnetic moment per V-site in V$_2$Se$_2$O is much larger than that of CsV$_2$Se$_{2-x}$O, which again suggests the correlation induced localization effect in the former.
In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of g
ravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.
BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent states. Here
we provide a construction of quarter BPS coherent states. They are coherent states built with two matrix fields, generalizing the half BPS case. These states are both the eigenstates of annihilation operators and in the kernel of dilatation operator. Another useful labeling of quarter BPS states is by representations of Brauer algebras and their projection onto a subalgebra $mathbb{C}[S_ntimes S_m]$. Here, the Schur-Weyl duality for the Walled Brauer algebra plays an important role in organizing the operators. One interesting subclass of these Brauer states are labeled by representations involving two Young tableaux. We obtain the overlap between quarter BPS Brauer states and quarter BPS coherent states, where the Schur polynomials are used. We also derive superposition formulas transforming a truncated version of quarter BPS coherent states to quarter BPS Brauer states. The entanglement entropy of Brauer states as well as the overlap between Brauer states and squeezed states are also computed.
By using high pressure synthesis method, we have fabricated the potassium doped para-terphenyl. The temperature dependence of magnetization measured in both zero-field-cooled and field-cooled processes shows step like transitions at about 125 K. This
confirms earlier report about the possible superconductivity like transition in the same system. However, the magnetization hysteresis loop exhibits a weak ferromagnetic background. After removing this ferromagnetic background, a Meissner effect like magnetic shielding can be found. A simple estimate on the diamagnetization of this step tells that the diamagnetic volume is only about 0.0427% at low temperatures, if we assume the penetration depth is much smaller than the size of possible superconducting grains. This magnetization transition does not shift with magnetic field but is suppressed and becomes almost invisible above 1.0 T. The resistivity measurements are failed because of an extremely large resistance. By using the same method, we also fabricated the potassium doped para-quaterphenyl. A similar step like transition at about 125 K was also observed by magnetization measurement. Since there is an unknown positive background and the diamagnetic volume is too small, it is insufficient to conclude that this step is derived from superconductivity although it looks like.
