Improved generating technique for D=5 supergravities and squashed Kaluza-Klein Black Holes

Recently we suggested a solution generating technique for five-dimensional supergravity with three Abelian vector fields based on the hidden SO(4,4) symmetry of the three-dimensionally reduced theory. This technique generalizes the $G_{2(2)}$ generating technique developed earlier for minimal 5D supergravity (A. Bouchareb, G. Cl\'ement, C-M. Chen, D. V. Gal'tsov, N. G. Scherbluk, and Th. Wolf, Phys. Rev. D {\bf 76}, 104032 (2007)) and provides a new matrix representation for cosets forming the corresponding sigma-models in both cases. Here we further improve these methods introducing a matrix-valued dualisation procedure which helps to avoid difficulties associated with solving the dualisation equations in the component form. This new approach is used to generate a five-parametric rotating charged Kaluza-Klein black hole with the squashed horizon adding one parameter more to the recent solution by Tomizawa, Yasui and Morisawa which was constructed using the previous version of the $G_{2(2)}$ generating technique.Comment: 20 pages, revtex

Three-charge 2J black ring

Using recently proposed new solution generating technique, we construct the charged version of Pomeranski-Senkov doubly rotating black ring in the $U(1)^3$ five-dimensional supergravity. For arbitrary values of charges the solution is unbalanced, but the Dirac-Misner string is removed when two of the charges are set to zero. In this particular case our solution can be uplifted to some solution of six-dimensional vacuum gravity.Comment: 9 pages revtex

Extremal black holes in D=4 Gauss-Bonnet gravity

We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordstr\"om type $AdS_2\times S^2$. Such black holes exist for the dilaton coupling constant within the interval $0\leq a^2<a^2_{\rm cr}$. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they can not be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined $a_{\rm cr}\simeq 0.488219703$. For each value of the dilaton coupling $a$ within this interval and for a fixed value of the Gauss--Bonnet coupling $\alpha$ we have a family of black holes parameterized by their electric charge. Relation between the mass, the electric charge and the dilaton charge at both ends of the allowed interval of $a$ is reminiscent of the BPS condition for dilaton black holes in the Einstein-Maxwell-Dilaton theory. The entropy of the DGB extremal black holes is twice the Bekenstein-Hawking entropy.Comment: New material and references added, errors corrected including higher decimals in a_cr, figures improve

Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit

We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the "counting parameter". We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients.Comment: 11 pages, minor corrections, published versio

Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains

We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the quantum XY chain, the method reproduces the previously known phase diagram.Comment: 6 pages, section on Lee-Yang zeros added, published versio

Dispersion representations and anomalous singularities of the triangle diagram

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in $p_1^2$ and $p_2^2$, the appearance of the anomalous cut in the region $q^2>0$ is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of $p_1^2$ and/or $p_2^2$ above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.Comment: 10 pages, revtex, added a reference, version to be published in Phys. Rev.

FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

We consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett models for the multiple tunneling contacts connected by the chiral single-mode FQHE edges. It is shown that the compactness of the Wen- Fr\"ohlich chiral boson fields describing the FQHE edge modes plays a crucial role in eliminating the spurious non-locality of the electron transport properties of the FQHE interferometers arising in the regime of strong tunneling.Comment: 5 page

Global solutions for higher-dimensional stretched small black holes

Small black holes in heterotic string theory have vanishing horizon area at the supergravity level, but the horizon is stretched to the finite radius $AdS_2 \times S^{D-2}$ geometry once higher curvature corrections are turned on. This has been demonstrated to give good agreement with microscopic entropy counting. Previous considerations, however, were based on the classical local solutions valid only in the vicinity of the event horizon. Here we address the question of global existence of extremal black holes in the $D$-dimensional Einstein-Maxwell-Dilaton theory with the Gauss-Bonnet term introducing a variable dilaton coupling $a$ as a parameter. We show that asymptotically flat black holes exist only in a bounded region of the dilaton couplings $0 < a < a_{\rm cr}$ where $a_{\rm cr}$ depends on $D$. For $D \geq 5$ (but not for $D = 4$) the allowed range of $a$ includes the heterotic string values. For $a > a_{\rm cr}$ numerical solutions meet weak naked singularities at finite radii $r = r_{\rm cusp}$ (spherical cusps), where the scalar curvature diverges as $|r - r_{\rm cusp}|^{-1/2}$. For $D \geq 7$ cusps are met in pairs, so that solutions can be formally extended to asymptotically flat infinity choosing a suitable integration variable. We show, however, that radial geodesics cannot be continued through the cusp singularities, so such a continuation is unphysical.Comment: 26 pages, 19 figures, minor correction