Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d   massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a c=1$c=1$ “barrier”, analogous to the c=1$c=1$ barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For d?1$d?1$ we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For d>1$d>1$ the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension _dH=3$d_H=3$. In the d>1$d>1$ sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Ho?ava–Lifshitz models.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

Superconducting cosmic strings and one dimensional extended supersymmetric algebras

In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional N=2$N=2$ supersymmetry and we find multiple N=2$N=2$, d=1$d=1$ supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with N_f$N_f$ flavors and these are N$N$-extended supersymmetric structures with non-trivial topological charges, with “N$N$” depending on the fermion flavors.     

A study on the relations between the topological parameter and entanglement

In this Letter, some relations between the topological parameter d   and concurrences of the projective entangled states have been presented. It is shown that for the case with d=n$d=n$, all the projective entangled states of two n  -dimensional quantum systems are the maximally entangled states (i.e. C=1$C=1$). And for another case with d≠n$d\ne n$, C   both approach 0 when d→+∞$d\to +\infty$ for n=2$n=2$ and 3. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang–Baxter Hamiltonian. It is found that the parameter d   influences not only the critical temperature _Tc$T_c$ but also the maximum entanglement value that the system can arrive at. And we also find that the parameter d has a great influence on the ESD.     

Einstein–Gauss–Bonnet black holes in de Sitter spacetime and the quasilocal formalism

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein–Gauss–Bonnet theory by using the counterterm method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d?7$d?7$. We apply this technique for several different solutions in Einstein–Gauss–Bonnet theory with a positive cosmological constant. Apart from known solutions, we consider also d=5$d=5$ vacuum rotating black holes with equal magnitude angular momenta. These solutions are constructed numerically within a nonperturbative approach, by directly solving the Einstein–Gauss–Bonnet equations with suitable boundary conditions.     

The fate of conformal symmetry in the non-linear Schrödinger theory

The free Schrödinger theory in d   space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the |Φ|⁴${|\Phi |}^4$-theory in d=2$d=2$. We compute the full quantum corrections to the 1PI 4-point function in d=2−?$d=2-\mathrm{?}$ dimensions and find a non-trivial β  -function completely given by the 1-loop result. We exhibit an explicit Ward-identity showing that scale-invariance is broken in the limit d=2$d=2$ by an anomalous contribution proportional to the β-function.     

A note on the UV behaviour of maximally supersymmetric Yang–Mills theories

The question of whether BPS invariants are protected in maximally supersymmetric Yang–Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F⁴$F^4$) are indeed protected while the double-trace one-quarter BPS invariant (d²F⁴$d^2{F}^4$) is not protected at two loops in D=7$D=7$, but is protected at three loops in D=6$D=6$ in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.     

MAP,MAC, and vortex-rings configurations in the Weinberg–Salam model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. When the ?$?$-winding number n=1$n=1$, and 2, the configurations are monopole–antimonopole pair (MAP) and monopole–antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the z$z$-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n=3$n=3$. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4πn/e$4\pi n/e$.     

Properties of CFTs dual to charged BTZ black hole

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1$1+1$ dimensions by studying the dual gravity theory—which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0$T=0$ and T≠0$T\ne 0$. In the T=0$T=0$ case we are also able to compare with analytical results based on AdS₂${\mathit{AdS}}_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current–current correlator) also vanishes as ω→0$\omega \to 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a “Fermi–Luttinger” liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger liquid like behavior (k  -independent non-analyticity at ω=0$\omega =0$) in the Green's function is discussed.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N$N$ vortices on line bundles over a closed Riemann surface Σ$\Sigma$ of genus g>1$g>1$, in the little explored situation where 1≤N<g$1\le N<g$. In the regime where the area of the surface is just large enough to accommodate N$N$ vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ$\Sigma$. For N=1$N=1$, we show that the metric on the moduli space converges to a natural Bergman metric on Σ$\Sigma$. When N>1$N>1$, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ$\Sigma$ at degree N$N$. We describe consequences of this phenomenon from the point of view of multivortex dynamics.     

If Gauss–Bonnet interaction plays the role of dark energy

A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞$q\to \infty$ and infinite equation of state parameter, w→∞$w\to \infty$. During evolution it subsequently passes through the stiff fluid era, q=2$q=2$, w=1$w=1$, the radiation dominated era, q=1$q=1$, w=1/3$w=1/3$ and the matter dominated era, q=1/2$q=1/2$, w=0$w=0$. Finally, deceleration halts, q=0$q=0$, w=−1/3$w=-1/3$, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1$q\to -1$, w→−1$w\to -1$. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)$(w<-1)$ the model.     

Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.     

Higher dimensional Yang–Mills black holes in third order Lovelock gravity

By employing the higher (N>5$N>5$)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α₂${\alpha }_2$) and third (α₃${\alpha }_3$) order parameters. These parameters, where α₂${\alpha }_2$ is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞$r\to \infty$), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like.     

Supertwistors and massive particles

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N$N$-extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1$N=1$ and BPS-saturated N=2$N=2$ superparticle actions. We also find the supertwistor form of the action for “spinning particles” with N$N$-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2$N=2$ case.     

Transition between monopole and antimonopole for electrically charged monopole–antimonopole chain system of solutions

The dependence of physical properties of the electrically charged monopole–antimonopole pair (MAP) solutions in the Higgs self-coupling constant is previously investigated. In this paper we study the three-poles monopole–antimonopole chain (MAC) solutions. The study includes ?$?$-winding number n=2,3$n=2,3$, and 4. For the case of n=2$n=2$, no bifurcation and geometrical transition is detected for the interval of the study. For the case of n=3$n=3$, two geometrical transitions happen along the fundamental solution. Also two bifurcations and one joining point is detected for the interval of study. The case of n=4$n=4$ includes one bifurcation. There is also a geometrical transition along the fundamental solution and two transitions along the Higher energy bifurcating branch. This study implies that during some specific kind of geometrical transition, a magnetic and electric charge transition occurs for the pole which is located at the origin.