On the origin of supergravity boundary terms in the AdS /CFT correspondence

The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian formulation of the supergravity action, which does not require any boundary terms. Then all the boundary terms of the standard formulation naturally appear by passing from the Hamiltonian version to the Lagrangian one. As examples the graviton part of the supergravity action on the product of AdS_d+1 with a compact Einstein manifold ϵ and fermions on AdS_d+1, are considered. We also discuss conformal transformations of gravity fields on the boundary of AdS and show that they are induced by the isometrics of AdS.     

Towards a quantum field theory of primitive string fields

We denote generating functions of massless even higher-spin fields ??primitive string fields?? (PSF??s). In an introduction we present the necessary definitions and derive propagators and currents of these PDF??s on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF??s. In subsequent sections we exploit the fact that higher-spin field theories in AdS _d+1 are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 ?? N ??? play for us the role of ??standard models??, for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = ??. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s ?? 4, they are distinguished by their anomalous dimensions (in CFT ₃) or by theirmass (in AdS ₄). We sum over these multiplets and the spins to obtain ??string type fields??, one for each such monomial.     

R~4 corrections to holographic Schwinger effect

We consider R4 corrections to the holographic Schwinger effect in an AdS black hole background and a confining D3-brane background. The potential between a test particle pair are performed for both backgrounds. We find there is no potential barrier in the critical electric field, which means that the system becomes catastrophically unstable. It is shown that for both backgrounds, increasing the inverse 't Hooft coupling parameter 1/λ enhances the Schwinger effect. We also discuss the possible relation between the Schwinger effect and the viscosity-entropy ratioη/s in strong coupling.     

Gauged Kaluza-Klein AdS pseudo-supergravity

We obtain the pseudo-supergravity extension of the D-dimensional Kaluza-Klein theory, which is the circle reduction of pure gravity in D+1 dimensions. The fermionic partners are pseudo-gravitino and pseudo-dilatino. The full Lagrangian is invariant under the pseudo-supersymmetric transformation, up to quadratic order in fermion fields. We find that the theory possesses a U(1) global symmetry that can be gauged so that all the fermions are charged under the Kaluza-Klein vector. The gauging process generates a scalar potential that has a maximum, leading to the AdS vacuum. Whist the highest dimension for gauged AdS supergravity is seven, our gauged AdS pseudo-supergravities can exist in arbitrary dimensions.     

Supersymmetric AdS_4 vacua in N=3 gauged supergravity

We study the maximally supersymmetric AdS backgrounds of matter-coupled N=3 gauged supergravity in four dimensions. We find that to admit supersymmetric AdS vacua, the gauge group can only be of the form G_0×H?SO(3,n) with G_0 =SO(3),SO(3,1) or SL(3,R) and H a compact group of dimension n+3-dim(G_0). We also show that these AdS vacua have no moduli, namely they correspond to critical points in field space.     

Negative magnetoresistance and nonlinear conduction in Ti0.99V0.01Se2

Both magnetic and electric field dependences of transport coefficients are investigated on the layered material Ti_1-xV_xSe₂ (x = 0.01). In contrast to semimetallic TiSe₂, the resistivity of the V-doped samples increases with decrease of temperature even in the low temperature region. At liquid helium temperatures it is found that the resistivity is strongly dependent on electric field strength. The behaviour of the nonlinear conduction is similar to that observed in 1T-TaS₂. In the low field (Ohmic) region anomalously large negative mangetoresistance is observed, Δ?/?₀ = -80% at 1.6 K and 60 KOe. Moreover the Hall coefficient is also found to depend on both magnetic and electric fields. All the experimental data suggests that mobile carriers are excited by the applied fields.     

Gauge boson exchange in AdSd+1

We study the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in anti-de Sitter space. In the AdS/CFT correspondence this amplitude describes the contribution of conserved flavor symmetry currents to 4-point functions of scalar operators in the boundary conformal theory. A concise, covariant, Y2K compatible derivation of the gauge boson propagator in AdS_{d + 1} is given. Techniques are developed to calculate the two bulk integrals over AdS space leading to explicit expressions or convenient, simple integral representations for the amplitude. The amplitude contains leading power and sub-leading logarithmic singularities in the gauge boson channel and leading logarithms in the crossed channel. The new methods of this paper are expected to have other applications in the study of the Maldacena conjecture.     

Holographic screening length in a hot plasma of two sphere

We study the screening length \(L_{\mathrm{max}}\) of a moving quark–antiquark pair in a hot plasma, which lives in a two sphere, \(S^2\), using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild–AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark–antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity \(\omega \). The screening length and total energy H of the quark–antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer \(P_c\) of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark–antiquark pair, in which the background metrics are “Boost-AdS” and Kerr–AdS black holes. Comparing both black holes, we argue that the mass parameters \(M_{\mathrm{Sch}}\) of the Schwarzschild–AdS black hole and \(M_{\mathrm{Kerr}}\) of the Kerr–AdS black hole are related at high temperature by \(M_{\mathrm{Kerr}}=M_{\mathrm{Sch}}(1-a^2l^2)^{3/2}\), where a is the angular momentum parameter and l is the AdS curvature.     

Hot gluon matter in a constantA 0 background

We compute the effective action of finiteT SU(3) gauge theory in a constant diagonal background fieldA ₀(t,x)=B ₀ ³ T₃+B ₀ ⁸ T₈ in the general covariant background gauge up to terms of orderg ³.B ₀ ^3,8 shield the infrared singularities and the aim is to study whether the minimum of the effective action would determine their values dynamically. We find that the orderg ² term depends explicitly on the gauge fixing parameter ξ. Since the background field screens already at the tree diagram level the interactions of the six non-diagonal gluon fields they do not contribute to the plasmon-likeg ³ term. The two diagonal fieldsA ₀ ³ ,A ₀ ⁸ do, but the electric mass squared they develop will become negative if the background fields are larger than aboutT/g. Hence large background fields make the system unstable.     

On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s   fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2$s=2$) partition function. We compute the corresponding spin s   Weyl anomaly coefficients _as${\mathrm{a}}_s$ and _cs${\mathrm{c}}_s$. Our result for _as${\mathrm{a}}_s$ reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S⁴$S^4$ to a ratio of known partition functions of massless higher-spin field in AdS₅ with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic _as${\mathrm{a}}_s$ coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.     

Hysteresis phenomena in the course of polarization evolution in a sinusoidal electric field in lead magnesium niobate crystals

The processes of polarization evolution in single crystals of the PbMg_1/3Nb_2/3O₃ model ferroelectric relaxor in a sinusoidal electric field are investigated at temperatures near and above the temperature T _d 0 of destruction of the induced ferroelectric state upon heating in zero electric field. The polarization switching current loops are measured in the ac electric field applied along the 〈111〉 and 〈110〉 pseudocubic directions. The electroluminescence intensity loops are obtained under the combined action of ac and dc electric fields applied along the 〈100〉 direction. In a certain temperature range above T _d 0 and the freezing temperature T _f in lead magnesium niobate, there are electric current anomalies, that correspond to the dynamic formation and subsequent destruction of the ferroelectric macroregions throughout each half-cycle of the ac electric field. The measurements of electroluminescence hysteresis loops demonstrate that the observed depolarization delay (related to the ac electric field amplitude) increases with an increase in the dc electric field and decreases as the ac field amplitude increases. The nature of the observed phenomena is discussed.     

Aspects of holography in the AdS/CFT correspondence

We study quantities which are important for the realization of the holographic principle in the AdS/CFT correspondence: boundaries, geodesics and the propagators of scalar fields. They should play a role in the holographic setup in the BMN limit as well. We review the backgrounds and their relations that are relevant in the AdS/CFT correspondence and in its BMN limit. We describe the realization of the holographic principle in the AdS/CFT correspondence and summarize proposals of how to translate it in the BMN limit. We analyze the boundaries, geodesics and propagators of scalar fields in detail and observe how they behave in the limiting process from AdS₅×S⁵ to the 10‐dimensional plane wave, which is the spacetime in the BMN limit.     

The goldstone fields of interacting higher spin field theory in AdS(4)

A higher spin field theory on AdS(4) possesses a conformal theory on the boundary R(3) which can be identified with the critical O(N) sigma model of O(N) invariant fields only. The notions of quasiprimary and secondary fields can be carried over to the AdS theory. If de Donder’s gauge is applied, the traceless part of the higher spin field on AdS(4) is quasiprimary and the Goldstone fields are quasiprimary fields to leading order too. Those fields corresponding to the Goldstone fields in the critical O(N) sigma model are odd-rank symmetric tensor currents which vanish in the free-field limit. The text was submitted by the author in English.     

f(R) Black Holes as Heat Engines

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ? ΔP, the efficiency of isobar-isochore cycles running between high temperature T_H and low temperature T_C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.     

Field history dependence of nonlinear dielectric properties of Ba0.6Sr0.4TiO3 ceramics under bias electric field: Polarization behavior of polar nano-regions

Nonlinear dielectric properties of Ba_0.6Sr_0.4TiO₃ ceramics prepared by citrate method were investigated under bias electric field with respect to field history. X-ray diffraction analysis and temperature dependence of the dielectric constant (ε_r) confirmed a macroscopically paraelectric state for the specimen at room temperature. A slim polarization versus electric field (P-E) hysteresis loop of the specimen at room temperature indicated the existence of polar nano-regions (PNRs) superimposed on the paraelectric background. The nonlinear dielectric properties in continuous cycles of bias field sweep displayed a strong sensitivity to the field history. This phenomenon was qualitatively explained in terms of an irreversible polarization evolution of the PNRs under the bias fields. A considerable decline of the tunability with the cycle number suggests an appreciable contribution of the PNRs to the dielectric nonlinearity. The polarization and size of the PNRs were determined by fitting the dielectric constants to a multipolarization mechanism model.     

Level-crossing-Experiment zur Untersuchung des Einflusses eines elektrischen Feldes auf die Hyperfeinstruktur des 4p 2 P 3/2-Terms im Cu I-Spektrum

Level-crossing technique applying parallel electric and magnetic fields has been used to investigate the influence of an electric fieldE _z on the hyperfine structure of the 4p ² P _3/2-state. The Stark shift of the level-crossing nearH _z =155 Oe and the modification of the magnetic zero-field level-crossing signal due to the electric fieldE _z was observed. Both experimental results can be explained with a Stark-constantβ=7.2(1.1)kc(kV/cm)^?2.     

Black hole vacua and rotation

Recent developments suggest that the near-region of rotating black holes behaves like a CFT. To understand this better, I propose to study quantum fields in this region. An instructive approach for this might be to put a large black hole in AdS and to think of the entire geometry as a toy model for the “near-region”. Quantum field theory on rotating black holes in AdS can be well-defined (unlike in flat space), if fields are quantized in the co-rotating-with-the-horizon frame. First, some generalities of constructing Hartle–Hawking Green functions in this approach are discussed. Then as a specific example where the details are easy to handle, I turn to 2+1$2+1$ dimensions (BTZ), write down the Green functions explicitly starting with the co-rotating frame, and observe some structural similarities they have with the Kerr-CFT scattering amplitudes. Finally, in BTZ, there is also an alternate construction for the Green functions: we can start from the covering AdS₃${\mathit{AdS}}_3$ space and use the method of images. Using a 19th century integral formula, I show the equality between the boundary correlators arising via the two constructions.     

The magnetic properties of GaAs parabolic quantum dot in the presence of donor impurity,magnetic and electric fields

The magnetization and the magnetic susceptibility quantities of a single electron moving in a two-dimensional (2D) parabolic quantum dot are studied under the influence of external uniform electric and magnetic fields, in the presence of a donor impurity. The Hamiltonian was solved using shifted 1/N expansion method within the effective mass approximation. The results have been displayed as a function of physical parameters: confinement strength ω₀, magnetic field strength ω_c, temperature T and electric field strength F.