Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Bulk and surface localized modes on a magnetic nonlinear impurity

We study localized modes on a single magnetic impurity positioned in the bulk or at the surface of a one-dimensional chain, in the presence of a magnetic field B acting at the impurity site. The strong on-site nonlinear interaction U between two electrons of opposite spin at the impurity site, modelled here as a nonlinear local term, and the presence of the external field induce a strong correlation between parallel and antiparallel spin bound states. We find that, for an impurity in the bulk, a localized vector mode (with up and down spin components) is always possible for any given value of U and B, while for a surface impurity, a minimum value of both, U and B is needed to create a vector mode. In this case, up to two localized modes are possible, but only one of them is stable. The presence of the surface seems to destabilize the bulk mode in the parameter region U∼B, creating a “forbidden strip” region in parameter space, bounded by U=B+V and U=B−V, approximately.     

Nonlinear massive spin-2 field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein’s gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called “(Helmholtz-)Jordan frame” and “Einstein frame.” In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory II

In arXiv:1202.4298 gauge invariant interacting equations were written down for the spin 2 and spin 3 massive modes using the exact renormalization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant “field strengths” and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invariant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher-dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space–time and this is also outlined.     

A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T.D. Frank

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory.     

Un-graviton corrections to the Schwarzschild black hole

We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation   of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension dU$d_U$.     

Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi₂Sr₂CaCu₂O_8 + δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.     

Topologically massive AdS gravity

We analyze (2+1)$(2+1)$-dimensional gravity with a Chern–Simons term and a negative cosmological constant, primarily at the weak field level. The full theory is expressible as the sum of two higher derivative SL(2,R)$\mathrm{SL}(2,\mathbb{R})$ “vector” Chern–Simons terms, while the physical bulk degrees of freedom correspond to a single massive scalar field, just as for Λ=0$\Lambda =0$. The interplay of Λ and the mass parameter μ can be studied, and any physical mass—including the conformal value with null propagation—is accessible by tuning μ. The single bulk mode yields a complete set of normalizable positive energy wave packets, as long as one chooses the usual, “wrong” sign of G   necessary to connect smoothly with the known Λ=0$\Lambda =0$ limit. The chiral Chern–Simons coupling leads to gauge invariant linearized curvatures propagating with chirality-dependent masses. Linearized metric fluctuations have a finite asymptotic Fefferman–Graham expansion about the Poincaré metric for any mass value greater or equal to a “critical” one, where various amusing effects appear, such as vanishing of one of the two “vector” Chern–Simons terms and an equivalence between tensor and vector excitations. We also find a set of chiral, pp-wave metrics that exactly solve the full nonlinear equations.     

Spin-3 topologically massive gravity

In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS₃ vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W₃ algebra and central charge cR=3l/G.     

Two-dimensional Brownian vortices

We introduce a stochastic model of 2D Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (“plasma” case) and at negative temperatures, like-sign vortices attract each other (“gravity” case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N→+∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.     

OPE for null Wilson loops and open spin chains

Maximal helicity-violating scattering amplitudes in N=4$N=4$ supersymmetric Yang–Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle “heavy”–light operators, where the “heavy” fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one-loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.     

Probing type I′i string theory using D0 and D4-branes

We analyse the velocity-dependent potentials seen by D0 and D4-brane probes moving in Type I′ background for head-on scattering off the fixed planes. We find that at short distances (compared to string length) the D0-brane probe has a nontrivial moduli space metric, in agreement with the prediction of Type I′ matrix model; however, at large distances it is modified by massive open strings to a flat metric, which is consistent with the spacetime equations of motion of Type I′ theory. We discuss the implication of this result for the matrix model proposal for M-theory. We also find that the nontrivial metric at short distances in the moduli space action of the D0-brane probe is reflected in the coefficient of the higher dimensional ν⁴ term in the D4-brane probe action.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find interference effects between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing mass without mass and charge without charge. We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh _v =g _v –n _v . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the gravitational constant). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.     

Nature of the quantum spin correlations through the superconducting-normal phase transition in electron-doped superconducting Pr0.88LaCe0.12CuO4

We use neutron scattering and specific heat measurements to relate the response of the spin fluctuations and static antiferromagnetic (AF) order to the superconductivity in the electron-doped high-transition-temperature superconductor, Pr_.88LaCe_.12CuO_4−δ (PLCCO) (T_c=24 K), as the system is tuned via a magnetic field applied beyond the upper critical field (H_c2) and driven into the normal state. The strength of the collective magnetic excitation commonly termed “resonance” decreases smoothly with increasing field and vanishes in the normal state, paralleling the behavior of the superconducting condensation energy. The suppression of superconductivity is accompanied by a smooth reduction in the very low energy spin fluctuations, and the concomitant emergence of static AF order. Our results suggest an intimate connection between the resonance and the superconducting condensation energy.