The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N$1/N$ expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D  -ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N$1/N$. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.     

More about chiral symmetry restoration at finite temperature in the planar limit

In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge configuration by gauge configuration, have distributions described by a Gaussian Hermitian matrix model. However, combinations of eigenvalues that are scale and shift invariant only on the average, do not match this matrix model.     

A generalization of the Virasoro algebra to arbitrary dimensions

Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimensions.     

Phase transition in dually weighted colored tensor models

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent.     

Critical behavior of colored tensor models in the large N limit

Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.     

A holomorphic and background independent partition function for matrix models and topological strings

We study various properties of a nonperturbative partition function which can be associated with any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N$1/N$ expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi–Yau 3-folds.     

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar–Parisi–Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ$XXZ$-type Hamiltonians.     

Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

Axial charges of octet baryons in two-flavor lattice QCD

We evaluate the strangeness-conserving NN, ΣΣ, ΞΞ, ΛΣ and the strangeness-changing ΛN, ΣN, ΛΞ, ΣΞ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson–octet-baryon coupling constants so as to include πΞΞ, KΛΞ and KΣΞ   coupling constants. We find that the axial charges have rather weak quark mass dependence and the breaking in SU(3)$\mathrm{SU}(3)$-flavor symmetry is small at each quark-mass point we consider.     

Is BTZ a separate superselection sector of CTMG?

We exhibit exact solutions of (positive) matter coupled to original “wrong G-sign” cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate “superselection” sector, one that unlike in GR, is not reachable by physical sources.     

The Dilute Potts Model on Random Surfaces

We present a new solution of the asymmetric two-matrix model in the large-N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.     

Peculiar magnetic aftereffect of highly diluted frozen magnetic fluids

A very stably dispersed magnetic fluid (mother MF) and its 1000-times diluted solution were independently zero-field-cooled from room temperature to 5 K followed by application of a magnetic field of 2.86 MA/m for 300 s. After the field was removed (t=0)$(t=0)$, its residual magnetization M was measured as a function of time t for 80 000 s. After measurement, the MF sample was heated to room temperature, and the experiment was repeated after cooling to 5 K and again applying and removing the 2.86 MA/m field. We performed the same experiment several times, and obtained a different M vs t curve each time. With each cycle, the average M increased and the M vs t curve converged to a universal curve. In the initial few cycles, the value of M is very small, fluctuates and surprisingly increases with t in some time region. These characteristics are common in both the mother MF and diluted MF. We consequently propose the following physical model. When the MF is cooled, the isolated surfactant molecules in the solvent trigger the generation of magnetic colloid micelles. In other words, there occurs a phase transition from the magnetic colloids’ monodispersed phase to a micelle phase. The magnetic dipoles of the micelle's colloids make a closed magnetic flux loop. That is the origin of the anomalously small value of the residual magnetization in the early cycles. After a certain time elapses the micelles spontaneously break due to their residual stress, and a finite magnetic moment of the individual micelle develops. Consequently, M increases with t during this period.     

Compact complex surfaces with geometric structures related to split quaternions

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperkähler, are analogs of the hypercomplex, hyperhermitian and hyperkähler structures in the definite case. We show that a compact 4-manifold carries a para-hyperkähler structure iff it has a metric of split signature together with two parallel, null, orthogonal, pointwise linearly independent vector fields. Every compact complex surface admitting a para-hyperhermitian structure has vanishing first Chern class and we show that, unlike the definite case, many of these surfaces carry infinite-dimensional families of such structures. We provide also compact examples of complex surfaces with para-hyperhermitian structures which are not locally conformally para-hyperkähler. Finally, we discuss the problem of non-existence of para-hyperhermitian structures on Inoue surfaces of type S⁰$S^0$ and provide a list of compact complex surfaces which could carry para-hypercomplex structures.     

Cross sections for (d–t) neutron interaction with germanium isotopes

The cross sections for (n,x)$(n,x)$ reactions with Ge isotopes were measured at (d–t) neutron energies around 14 MeV with the activation technique using metal discs of natural composition. Calculations of detector efficiency, incident neutron spectrum and correction factors were performed with the Monte Carlo technique (MCNP4C code). Cross sections data are presented for ⁷⁰Ge(n,2n$n,2n$)⁶⁹Ge, ⁷⁴Ge(n,α$n,\alpha$)^71mZn, ⁷⁶Ge(n,2n$n,2n$)^75(m + g)Ge, ⁷⁰Ge(n,p$n,p$)⁷⁰Ga and ⁷²Ge(n,2n$n,2n$)^71gGe reactions. The cross section results for ⁷²Ge(n,2n$n,2n$)^71gGe reaction were reported for the first time. Some other cross sections were obtained with higher precision, including the ⁷⁰Ge(n,p$n,p$)⁷⁰Ga reaction. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values. Data were included in the EXFOR database.     

A first-order system approach for diffusion equation. II: Unification of advection and diffusion

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the first-order system approach introduced for the diffusion equation [J. Comput. Phys., 227 (2007) 315–352] to the advection–diffusion equation. Specifically, we construct a unified hyperbolic advection–diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it. Naturally then, we develop upwind schemes for this entire   system; there is thus no need to develop two different schemes, i.e., advection and diffusion schemes. We show that numerical schemes constructed in this way can be automatically uniformly accurate, allow O(h)$O(h)$ time step, and compute the solution gradients (viscous stresses/heat fluxes for the Navier–Stokes equations) simultaneously to the same order of accuracy as the main variable, for all Reynolds numbers. We present numerical results for boundary-layer type problems on non-uniform grids in one dimension and irregular triangular grids in two dimensions to demonstrate various remarkable advantages of the proposed approach. In particular, we show that the schemes solving the first-order advection–diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them. We conclude the paper with discussions on further developments to come.     

Constraints on dark energy and modified gravity models by the Cosmological Redshift Drift test

We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R)$f(R)$ gravity model).