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The $$ T\overline{T} $$ T T ¯ deformed 2D CFTs correspond to AdS3 gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed boundary condition at spatial infinity. In this work, we use the latter perspective and Chern-Simons formalism of AdS3 gravity to construct the surface charges and associated algebra in $$ T\overline{T} $$ T T ¯ deformed theories. Starting from the Bañados geometry, we obtain the Chern-Simons gauge fields for the $$ T\overline{T} $$ T T ¯ deformed geometry, which are parametrized by two independent charges. With help of the mixed boundary condition, the residual gauge symmetries of the deformed gauge fields and the associated surface charges were obtained respectively. The charge algebra turns out to be a non-linear deformed Virasoro algebra, which was obtained in different way by applying the cutoff perspective. Finally, we propose a way to construct the time-independent charges from these surface charges and they satisfy the field-dependent Virasoro algebra.

Dual field driven caloric effect has aroused great interest in recent years. Hydrostatic pressure can shift the temperature zone of magnetocaloric effect(MCE), but seldom enhance its magnitude. Here, a large enhancement of MCE driven by pressure under magnetic field available by permanent magnet has been achieved in HoCuSi compound without introducing hysteresis loss, which is favorable for developing hybrid field driven refrigeration applications at low temperature regions. A distinct mechanism is revealed. Pressure largely regulates non-collinear spin structure and magnetizing process through affecting crystal field interactions and spin-spin coupling, hence resulting in the significant impact on magnetic properties and MCE.

Zero thermal expansion (ZTE) materials, particularly metals, have important applications in precision manufacturing. Here, ultra-low thermal expansion over a significantly broadened temperature interval is realized by tuning Gd content in ferrimagnetic(FIM) Gdx(Dy0.5Ho0.5)1-xCo2 compounds. The achieved coefficients of thermal expansion αl ~+1.3 × 10−6K−1 (5-220K), -1.5 × 10−6K−1 (220-280K) for x=0.5 are even better than the well-known ZTE Invar alloy Fe0.65Ni0.35, while the operation temperature interval is much wider. The origin is closely related to the regulation of magnetostrictive process by rare earth ions along c-axis in the rhombohedral FIM structure. Our work highlights the advantageous ways to generate ultra-low thermal expansion in magnetocaloric materials.

The narrow temperature span, ΔTspan, of first-order magnetocaloric materials is a serious problem that limits the application as refrigerants. Here we report tunable phase transition and magnetocaloric effect controlled by ferroelectric (FE) domains in FeRh films grown on (001)- and (011)-cut PMN-PT substrates. Adjacent two-step phase transition, and hence significantly broadened ΔTspan, has been achieved in FeRh films by utilizing the multi-domain structure of PMN-PT substrates. The results of aberration corrected (ac)-STEM, EELS and EDX analysis revealed that a 3~4 nm buffer layer with AB2O4-type spinel structure is naturally formed at the interface, which largely reduces the lattice mismatch between FeRh and PMN-PT and plays a key role for the successful growth of epitaxial (oriented) FeRh film on either (001)- or (011)-oriented PMN-PT. The switched FE domains by electric field govern the phase transition of FeRh films. As a result, regulated entropy change and refrigeration capacity in a wide temperature span have been achieved. On this basis, a feasible magnetic refrigeration cycle facilitated by electric field is designed. The present study provides an experimental basis for expanding the refrigeration temperature span by ferroelectric domain engineering, which is significant for promoting refrigeration application of first-order magnetocaloric materials particularly in micro-devices.

In this work we consider ${\mathrm{AdS}}_{3}$ gravitational theory with certain mixed boundary conditions at infinity. Using the Chern-Simons formalism of ${\mathrm{AdS}}_{3}$ gravity, we find that these mixed boundary conditions lead to nontrivial boundary terms, which, in turn, produce exactly the spectrum of the $T\overline{T}/J\overline{T}$-deformed conformal field theories (CFTs). We then follow the procedure for constructing asymptotic boundary dynamics of ${\mathrm{AdS}}_{3}$ to derive the constrained $T\overline{T}$-deformed Wess-Zumino-Witten (WZW) model from Chern-Simons gravity. The resulting theory turns out to be the $T\overline{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a $U(1)$ gauge field associated to the current $J$, we obtain one type of the $J\overline{T}$-deformed WZW model, and show that its action can also be constructed from the gravity side. These results provide a check on the correspondence between the $T\overline{T}/J\overline{T}$-deformed CFTs and the deformations of boundary conditions of ${\mathrm{AdS}}_{3}$, the latter of which may be regarded as coordinate transformations.

Spin structure of a magnetic system results from the competition of various exchange couplings. Pressure-driven spin structure evolution, through altering interatomic distance, and hence, electronic structure produces baromagnetic effect (BME), which has potential applications in sensor/actuator field. Here, we report a new spin structure(CyS-AFMb) with antiferromagnetic(AFM) nature in Fe-doped Mn0.87Fe0.13NiGe. Neutron powder diffraction (NPD) under in situ hydrostatic pressure and magnetic field was conducted to reveal the spin configuration and its instabilities. We discovered that a pressure higher than 4 kbar can induce abnormal change of Mn(Fe)-Mn(Fe) distances and transform the CyS-AFMb into a conical spiral ferromagnetic(FM) configuration(45°-CoS-FMa) with easily magnetized but shortened magnetic moment by as much as 22%. The observed BME far exceeds previous reports. Our first-principles calculations provide theoretical supports for the enhanced BME. The compressed lattice by pressure favors the 45°-CoS-FMa and significantly broadened 3d bandwidth of Mn(Fe) atoms, which leads to the shortened magnetic moment and evolution of spin structure.

Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and environment friendliness. A common feature of giant magnetocaloric materials is the simultaneous magnetic and lattice transitions, while some of them undergo negative expansion, i.e., lattice contraction, during the transition from the ferromagnetic (FM) to the paramagnetic (PM) phase. Generally, a larger lattice volume indicates softer phonons and therefore a larger phonon entropy. However, experimental and theoretical studies have shown that there are great differences in the mechanism of phonon modes for different materials. In particular, the strengthening or softening of the phonon vibration mode during magnetic phase transition determines the magnitude and sign of lattice entropy change. Therefore, for the giant MCE materials with negative thermal expansion, whether the sign of lattice and spin entropy change is the same or the opposite has always been controversial. Combined with previous studies of nuclear resonance inelastic X-ray scattering (NRIXS), and by means of heat flow measurements and Debye theory calculations, we have clarified the sign of lattice and spin entropy change of giant magnetocaloric La(Fe, Si)13-based compounds and MM X alloys with negative thermal expansion. Results show that the lattice and spin entropy changes retain the same sign for La(Fe, Si)13-based compounds and MM′X (M, M′ = transition element, X = main element) alloys, which conforms to the principle of entropy increase. This work is helpful in fully understanding the intrinsic mechanism of giant magnetocaloric effect and its multi-field regulation for magnetostructural/magnetoelastic materials with negative thermal expansion during phase transition.

Induced by the Hagedorn instability, weakly-coupled $U(N)$ gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-$N$ limit. Recently we discover that the thermal entropy of a free theory on $\mathbb{S}^3$ gets reduced by a universal constant term, $-N^2/4$, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the corresponding $4+1 D$ bulk theory and the dimensionally reduced theory. First, entanglement entropy in the bulk theory contains the so-called "particle" contribution on the entangling surface, which naturally gives rise to an area-law term. The topological term results from the Gauss's constraint of these surface states. Secondly, the high-temperature limit also defines a dimensionally reduced theory. We calculate the geometric entropy in the reduced theory explicitly, and find that it is given by the same constant term after subtracting the leading term of ${\mathcal O}(\beta^{-1})$. The two procedures are then applied to the confining phase, by extending the temperature to the complex plane. Generalizing the recently proposed $2D$ modular description to an arbitrary matter content, we show the leading local term is missing and no topological term could be definitely isolated. For the special case of ${\mathcal N}=4$ super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation., Comment: Relation between the thermal entropy and entanglement entropy clarified, employing the Bisognano-Wichmann theorem, journal version

Multilevel nonvolatile regulation (MNR) is demonstrated in a heterostructure composed of an amorphous hard magnetic SmCo thin film and a (011)-oriented ferroelectric 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-PT) substrate. Two alternative ways of obtaining MNR are employed: the quasi-unipolar method and the quasi-minor-loop method, both of which utilize the transition from the rhombohedral (R) to monoclinic (MB) and then to orthorhombic (O) phase in a PMN-PT substrate. The mechanism is distinct from the conventional unipolar method inducing MNR, which mainly makes use of switching the ferroelectric domain in the R phase. The introduction of these two methods provides different ideas for achieving MNR in ferromagnetic/PMN-PT heterostructures. The observed MNR in an amorphous SmCo/(011) PMN-PT heterostructure demonstrates the potential applicability of hard magnetic materials for multifunctional information storage and spintronic devices.

We propose a symmetry of T T ¯ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter μ, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS3. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-York's quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get T T ¯ deformed conformal killing vectors and the associated conserved charges are also studied.

Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and its environmentally friendly impact. Many materials exhibiting magnetostructural/magnetoelastic transitions have been identified by their giant MCE as promising refrigerants. The common feature of these materials is their simultaneous magnetic and lattice transitions; some also undergo negative expansions, i.e., lattice contractions, along with a ferromagnetic (FM) to paramagnetic (PM) transition. For these materials, whether the signs of lattice and spin entropy change are the same or opposite has become a controversial issue, noting that a larger unit cell volume usually indicates softer phonons and therefore a bigger phonon entropy. On the basis of our experiments and published data, we demonstrate that the lattice and spin entropy changes retain the same sign at least for La(Fe,Si)13-based compounds and MM’X alloys with giant MCE, for which the lattice undergoes negative expansion along with a FM to PM transition on heating. The clarification of the sign of lattice entropy change in the total entropy change is of particular importance for a comprehensive understanding of new materials with giant magnetocaloric effect and their design.

Ni2In-type hexagonal compounds MM′X (M, M′ = transition metals, X = main element) involving magnetostructural transition (MST) have attracted much attention due to their giant magnetocaloric effect (MCE). Physical pressure, as an effective method, has been used to adjust the MST and the resultant MCE. Enhanced and diminished MCEs by hydrostatic pressure were both reported previously, but the underlying mechanism is unclear. Here, we report our neutron diffraction study on MST and MCE regulated by hydrostatic pressure in MnNi1 – xFexSi1 – yGey alloys. Careful refinements indicate that the martensitic phase shows a linear ferromagnetic structure with spin moment confined on Mn sites, which remains almost unchanged at pressures lower than 5 kbar even though slight compressions of Mn–Mn bond lengths can be identified. The MST keeps sharp under pressures lower than 5 kbar, while the derived volume change (ΔV/V) across MST reduces 7%, i.e., from 2.84% (0 kbar) to 2.63% (2.1 kbar), due to the effect of pressure on two-phase coexistence. Accordingly, the estimated lattice entropy change (ΔSLatt) based on the Debye approximation reduces by 10% from 37.1 J/kg K (0 kbar) to 33.5 J/kg K (2.1 kbar). These ΔSLatt values, driven by temperature, are all somewhat larger than the magnetic entropy change driven by a 5 T magnetic field. This result may imply that a magnetic field of 5 T is not sufficient for the MST to complete. As the pressure reaches 5 kbar, the MST notably slows down. This may originate from the extended temperature region of two-phase coexistence but not the decoupling of MST.

The multicaloric effect refers to the thermal response of a solid material driven by simultaneous or sequential application of more than one type of external field. For practical applications, the multicaloric effect is a potentially interesting strategy to improve the efficiency of refrigeration devices. Here, the state of the art in multi-field driven multicaloric effect is reviewed. The phenomenology and fundamental thermodynamics of the multicaloric effect are well established. A number of theoretical and experimental research approaches are covered. At present, the theoretical understanding of the multicaloric effect is thorough. However, due to the limitation of the current experimental technology, the experimental approach is still in progress. All these researches indicated that the thermal response and effective reversibility of multiferroic materials can be improved through multicaloric cycles to overcome the inherent limitations of the physical mechanisms behind single-field-induced caloric effects. Finally, the viewpoint of further developments is presented.

We extend the work of 1401.3746 about gravitational waves by a massive orbiting star in an extremal Kerr black hole to an extremal Kerr-Newman black hole for the scalar radiation, and we still find that it has a CFT interpretation from Kerr-Newman/CFT, because our scalar is neutral although the black hole is a charged one. When the charge of black hole is zero, we can get the result of 1401.3746, so we give a new evidence on Kerr-Newman/CFT. In addition, we investigate on electromagnetic radiation with Kerr/CFT in detail which isn't given by 1401.3746.

We study the scalar and fermionic retarded Green's function on the background with hyperscaling violation by means of the prescriptions proposed in [J. High Eergy Phys. 09 (2002) 042; Fortsch. Phys. 57 (2009) 367]. For scalar field, we consider both massless and massive cases, and for spinor field, we further calculate the finite temperature correlator with the black hole background.

We study holographic insulator/superconductor phase transition in the framework of Born-Infeld electrodynamics both numerically and analytically. First we numerically study the effects of the Born-Infeld electrodynamics on the phase transition, find that when the Born-Infeld parameter increases, the critical chemical potential keeps invariant but the gap frequency becomes larger. Then we employ the variational method for the Sturm-Liouville eigenvalue problem to study the phase transition analytically. The analytical results obtained are found to be consistent with the numerical results.

Using amino nitrogen content ( AN for short ) as standards, the conditions of low molecular weight polypeptides with three kinds of enzymes hydrolysis as well as the sequence and way of adding enzymes with microwave heating was found in this paper, which was examined by fluorescence analysis method, seperated by Sephadex G-50. The result shows that three kinds of enzymes hydrolysis were prefer to one enzyme obviously, amino nitrogen was higher for 2813.4 mg/L, the relative molecular mass of soybean polypeptides was mostly below 1000 D. Soybean polypeptide was well tested and seperated by Sephadex G-50 and fluorescence analysis method.

The important zinc borate of 2ZnO · 3B 2 O 3 · 3H 2 O has been synthesized and characterized by means of chemical analysis, XRD, FT-IR, and DTA–TG techniques. The molar enthalpies of solution of H 3 BO 3 (s) in HCl · 54.561H 2 O, of ZnO(s) in the mixture of HCl · 54.561H 2 O and calculated amount of H 3 BO 3 , and of 2ZnO · 3B 2 O 3 · 3H 2 O(s) in HCl · 54.604H 2 O were measured, respectively. With the use of the standard molar enthalpies of formation for ZnO(s), H 3 BO 3 (s), and H 2 O(l), the standard molar enthalpy of formation of −(5561.7 ± 4.9) kJ · mol −1 for 2ZnO · 3B 2 O 3 · 3H 2 O(s) was obtained. Thermodynamic properties of this compound were also calculated by a group contribution method.

Two pure zinc borates, Zn2B6O11·7H2O and Zn3B10O18·14H2O have been synthesized and characterized by XRD, FT-IR, DTA–TG techniques and chemical analysis. The molar enthalpies of solution of Zn2B6O11·7H2O(s) and Zn3B10O18·14H2O(s) in 1 mol dm−3 HCl(aq) were measured to be 15.42 ± 0.03 kJ mol−1 and 57.78 ± 0.11 kJ mol−1, respectively. The molar enthalpy of solution of ZnO(s) in (HCl + H3BO3)(aq) was determined to be −80.01 ± 0.15 kJ mol−1. With incorporation of the previously determined enthalpy of solution of H3BO3(s) in 1 mol dm−3 HCl(aq), and the standard molar enthalpies of formation for ZnO(s), H3BO3(s), and H2O(l), the standard molar enthalpies of formation of −6738.1 ± 4.8 kJ mol−1 for Zn2B6O11·7H2O and −11,786.4 ± 8.0 kJ mol−1 for Zn3B10O18·14H2O were obtained.

Recently lattice simulation in pure Yang-Mills theory exposes significant quadratic corrections for both the thermodynamic quantities and the renormalized Polyakov loop in the deconfined phase. These terms are previously found to appear naturally for ${\mathcal N}=4$ Super Yang-Mills~(SYM) on a sphere at strong coupling, through the gauge/gravity duality. Here we extend the investigation to the weak coupling regime, and for general large-$N$ gauge theories. Employing the matrix model description, we find some novel behavior in the deconfined phase, which is not noticed in the literature. Due to the non-uniform eigenvalue distribution of the holonomy around the time circle, the deviation of the Polyakov loop from one starts from $1/T^3$ instead of $1/T^2$. Such a power is fixed by the space dimension and do not change with different theories. This statement is also true when perturbative corrections to the single-particle partition functions are included. The corrections to the Polyakov loop and higher moments of the distribution function combine to give a universal term, $T/4$, in the free energy. These differences between the weak and strong coupling regime could be easily explained if a strong/weak coupling phase transition occurs in the deconfined phase of large-$N$ gauge theories on a compact manifold., Discussion on the small-$\lambda$ corrections improved

Recent lattice simulation has uncovered many interesting properties of SU(N) gauge theory at finite temperature. Especially, above the deconfinement phase transition all the thermodynamics quantities acquire significant quadratic contributions in inverse temperature. Such a term is also found to dominate the logarithmic of the renormalized Polyakov loop. Using the Hawking-Page transition in Anti-de Sitter space as an example, we show how such contributions can be naturally generated in the holographic approach., 18 pages, 3 figures

We present an elementary and detailed analysis of the Penner model with operators inserted. From a general point of view, correlation functions and loop amplitudes of this model may be related to each other by means of the dual transformation of Feynman diagrams. Such a relationship is shown to manifest the duality symmetry under t →- t−1 and N → Nt, after suppressing a quadratic term in the matrix model potential defined on the dual lattice. It is argued that this term is immaterial at the critical point tc = -1, thus permitting to give an explicit description of the macroscopic loops via the determination of correlators. We carry out the nonperturbative construction of all such correlators in concrete terms, compute their large-N expansions and define the continuum limit. Some applications are also discussed, among which is a comparison between the n-point function of the Penner model and that of c = 1 strings.

We construct a positive matrix model by modifying the Penner potential. Solving such a model exactly both at the lattice level and in the continuum limit, we find that it shares with the Penner model the same free energy in the double scaling limit and thus resembles the theory of strings at c = 1. A further comparison shows that the continuum one-point function of our model is different from that of the Penner model as well as c = 1 strings, at least on the torus. This opens up the interesting possibility of approaching some non-(p, q) strings via integration over positive random matrices. The result may also raise complications associated with the physical identification of the Penner model.

The title co-crystal, C(6)H(12)N(2)·C(6)H(6)O(2), is composed of neutral resorcinol and triethyl-enediamine mol-ecules in which the resorcinol mol-ecules came from the in situ deca-rboxylation of 2,4-dihy-droxy-benzoic acid. In the crystal, the components are connected by O-H⋯N hydrogen bonds, forming a chain in the b-axis direction.

We consider a noncritical holographic model constructed from an intersecting brane configuration D4/$\bar{\rm{D4}}$-D4 with an external magnetic field. We investigate the influences of this magnetic field on strongly coupled dynamics by the gauge/gravity correspondence., Comment: 18 pages, references added and typos revised

We consider a holographic model constructed from the intersecting brane configuration D4-$\bar{\rm{D4}}$/D4 in noncritical string theory. We study the chiral phase diagram of this holographic QCD-like model with a finite baryon chemical potential through the supergravity dual approximation., Comment: 14 pages, reference added

In this paper, we will consider the chiral symmetry breaking in the holographic model constructed from the intersecting brane configuration, and investigate the Nambu-Goldstone bosons associated with this symmetry breaking., Comment: 16 pp, minor changes, to appear PRD

We construct a D2-D8-$\bar{D8}$ configuration in string theory, it can be described at low energy by two dimensional field theory. In the weak coupling region, the low energy theory is a nonlocal generalization of Gross-Neveu(GN) model which dynamically breaks the chiral flavor symmetry $U(N_f)_L \times U(N_f)_R$ at large $N_c$ and finite $N_f$. However, in the strong coupling region, we can use the SUGRA/Born-Infeld approximation to describe the low energy dynamics of the system. Also, we analyze the low energy dynamics about the configuration of wrapping the one direction of D2 brane on a circle with anti-periodic boundary condition of fermions. The fermions and scalars on D2 branes get mass and decouple from the low energy theory. The IR dynamics is described by the $QCD_2$ at weak coupling. In the opposite region, the dynamics has a holographic dual description. And we have discussed the phase transition of chiral symmetry breaking at finite temperature. Finally, after performing T-duality, this configuration is related to some other brane configurations., 30 pages, 3 figures, minor changes

We generalize the work of Deser and Levin on the unified description of Hawking radiation and Unruh effect to general stationary motions in spherically symmetric black holes. We have also matched the chemical potential term of the thermal spectrum of the two sides for uncharged black holes., Comment: Latex file, 12 pages, no figure; v2: typos fixed; v3: minor corrections, final version published in JHEP

Quantum corrections to the energy of D0-branes in a constant RR 4-form background are studied. Using the Born-Oppenheimer approximation, we compute the long-range interaction between two spherical D2-D0 bound states. We extend this calculation to the case where some mass terms are added. For the special value of masses at which the classical energy vanishes, we find complete cancellations of two boson-fermion pairs in the quantum mechanical expression of the zero-point energy, suggesting possible restoration of (partial) supersymmetries. We also briefly discuss the interaction between a dielectric 2-brane and a single D0-brane., Comment: 27 pages, no figures

We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of monopole-like equations governing the 8-dimensional U(1) connections and spinors, which are supposed to be the dual theory of the nonabelian instantons. We also give a naive test of the generalized $S$-duality in the abelian sector of 8-dimensional Yang-Mills theory. Some problems in this approach are pointed out., Comment: 22+1 pages, no figures, using JHEP.cls; v2: typos corrected and refs updated, to appear in JHEP

The zinc borate 4ZnO·B2O3·H2O has been synthesized and characterized by means of chemical analysis, X-ray diffraction (XRD), FT-IR, and DTA-TG. The measured molar enthalpy of solution of 4ZnO·B2O3·H2O(s) in HCl·54.572H2O is −(265.64 ± 0.11) kJ·mol−1. With previously determined enthalpies of solution of H3BO3(s) in 1 mol·dm−3 HCl(aq) and of ZnO(s) in (HCl + H3BO3) aqueous solution, together with the use of the standard molar enthalpies of formation for ZnO(s), H3BO3(s), and H2O(l), the standard molar enthalpy of formation for 4ZnO·B2O3·H2O(s) was calculated as −(3030.46 ± 1.72) kJ·mol−1.

Hydrated strontium borate, SrB 4 O 7 ·3H 2 O, has been synthesized and characterized by XRD, FT-IR, DTA-TG and chemical analysis. The molar enthalpy of solution of SrB 4 O 7 ·3H 2 O in 1 mol dm −3 HCl(aq) was measured to be (21.15 ± 0.29) kJ mol −1 . With incorporation of the previously determined enthalpies of solution of Sr(OH) 2 ·8H 2 O(s) in [HCl(aq) + H 3 BO 3 (aq)] and H 3 BO 3 in HCl(aq), and the enthalpies of formation of H 2 O(l), Sr(OH) 2 ·8H 2 O(s) and H 3 BO 3 (s), the enthalpy of formation of SrB 4 O 7 ·3H 2 O was found to be −(4286.7 ± 3.3) kJ mol −1 .

D0-brane gas picture of Schwarzschild black hole (SBH) is considered in the large N regime of Matrix theory. An entropy formula, which reproduces the thermodynamics of SBH in the large N limit for all dimensions ($D\geq 6$), is proposed. The equations of states for low temperature are obtained. We also give a proof of the Newton gravitation law between two SBHs, whose masses are not equal. Our result in some extent supports that the physics of Matrix theory is Lorentz invariant., Comment: 9 pages, no figure;minor changes, reference added

We investigated quasinormal frequencies (QNFs) in black brane with hyperscaling violating by using the continued fractions method. We calculate QNF of massless scalar field and electromagnetic field both with zero spatial momentum, find that QNFs have negative imaginary frequency suggesting black brane with hyperscaling violation is stable under those perturbations.

We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a fairly generic discrete group $\Gamma$ acting isometrically on $AdS_{d+1}$. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary ${\bf S}^{d}/\Gamma$ can affect the underlying physical spectrum. In particular, the conformal dimension of the most relevant operators in the boundary CFT can increase as $\Gamma$ becomes ``large''. This phenomenon also has a natural explanation in terms of the bulk supergravity theory. The scalar two-point function is computed using this quotient version of the AdS/CFT correspondence, which agrees with the expected result derived from conformal invariance of the boundary theory., Comment: 28 pages, Latex, no figures. Minor changes, version to appear in JHEP