Effective Tachyonic Potential in Closed String Field Theory

We calculate the effective tachyonic potential in closed string field theory up to the quartic term in the tree approximation. This involves an elementary four-tachyon vertex and a sum over the infinite number of Feynman graphs with an intermediate massive state. We show that both the elementary term and the sum can be evaluated as integrals of some measure over different regions in the moduli space of four-punctured spheres. We show that both elementary and effective coupling give negative contributions to the quartic term in the tachyon potential. Numerical calculations show that the fourth order term is big enough to destroy a local minimum which exists in the third order approximation.Comment: 41 pages, LaTeX + psfig macro package, 15 uuencoded tar-compressed postscript figures include

Thermodynamics of phase transition in higher dimensional Reissner-Nordstr\"{o}m-de Sitter black hole

It is well known that there are black hole and the cosmological horizons for the Reissner-Nordstr\"{o}m-de Sitter spacetime. Although the thermodynamic quantities on the horizons are not irrelevant, they satisfy the laws of black hole thermodynamics respectively. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in $(n+2)$-dimensional Reissner-Nordstr\"{o}m-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed, moreover, the critical temperature, critical pressure and critical volume are obtained. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid--gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid--gas systems.Comment: 18 pages, 7 figures, 1 tabl

On the Background Independence of String Field Theory: III. Explicit Field Redefinitions

Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two string field theories. The analysis is carried out completely for quadratic and cubic terms in the action. Although a general proof of existence of field redefinitions which relate higher point vertices is not given, specific examples are discussed. Equivalence of string field theories formulated around two conformal field theories which are not close to each other, but are related to each other by a series of marginal deformations, is also discussed. The analysis can also be applied to study the equivalence of different formulation of string field theories around the same background.Comment: 46 page

Phase transition of the higher dimensional charged Gauss-Bonnet black hole in de Sitter spacetime

We study the phase transition of charged Gauss-Bonnet-de Sitter (GB-dS) black hole. For black holes in de Sitter spacetime, there is not only black hole horizon, but also the cosmological horizon. The thermodynamic quantities on the both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are additional connections between them. Using the effective temperature approach, we obtained the effective thermodynamic quantities of charged GB-dS black hole. According to Ehrenfest classification, we calculate some response functions and plot their figures, from which one can see that the spacetime undergoes a second-order phase transition at the critical point. It is shown that the critical values of effective temperature and pressure decrease with the increase of the value of GB parameter $\alpha$.Comment: 9 pages, 16 figure

catena-Poly[[[diaquacadmium(II)]bis[μ-2-(pyridinium-1-yl)butanedioato]-κ2 O 1:O 4;κ2 O 4:O 1] tetrahydrate], a polymeric chain structure

In the title complex, {[Cd(C9H8NO4)2(H2O)2]·4H2O}n, the CdII atom (site symmetry 2) is coordinated by six O atoms from four crystallographically related 1-(1,2-dicarboxyl­ate)pyridin-1-ium ligands (L) and from two water molecules in a distorted octahedral geometry. Paired L ligands connect CdII atoms into a chain motif parallel to [001], which is further inter­linked by O—H⋯O hydrogen bonds into a three-dimensional supra­molecular net

Gauge and General Coordinate Invariance in Non-Polynomial Closed String Field Theory

An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low energy effective field theory. A set of string field theoretic symmetries that act on the fields in low energy effective field theory as general coordinate transformation and antisymmetric tensor gauge transformation is identified. The analysis is carried out to first order in the fields; thus the symmetry transformations in string field theory reproduce the linear and the first non-linear terms in the gauge transformations in the low energy effective field theory.Comment: 29 page

Fractional phase transitions of RN-AdS black hole at Davies points

We perform a study of phase transitions of RN-AdS black hole at its Davies points according to a generalized Ehrenfest classification of phase transition established on the basis of fractional derivatives. Davies points label the positions where heat capacity diverges. According to the usual Ehrenfest classification, second-order phase transitions occur there. For RN-AdS black hole, the Davies points can be classified into two types. The first type corresponds to the extreme values of temperature and the second type corresponds to the infection point(namely the critical point) of temperature. Employing the generalized Ehrenfest classification, we find that the orders of phase transition at the two types of Davies points are different. It is $3/2$-order for the first type and $4/3$-order for the second type. Thus this finer-grained classification can discriminate phase transitions that are supposed to be in the same category, which may provide some new insights toward a better understanding of black hole thermodynamics.Comment: 13 pages, 4 figures, to be published in Chinese Physics

5,6-Dimethyl-1,2,4-triazin-3-amine

In the crystal structure of the title compound, C5H8N4, adjacent mol­ecules are connected through N—H⋯N hydrogen bonds, resulting in a zigzag chain along [100]. The amino groups and heterocyclic N atoms are involved in further N—H⋯N hydrogen bonds, forming R 2 2(8) motifs