Conformal description of horizon's states

The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal transformations of two-dimensional space ($r-t$ sector of the total space-time). The corresponding algebra recovered at the horizon is one copy of the Virasoro algebra. For general relativity in $d$ dimensions we find an effective two-dimensional theory governing the conformal dynamics at the horizon universally for any $d\geq 3$. The corresponding Virasoro algebra has central charge $c$ proportional to the Bekenstein-Hawking entropy. Identifying the zero-mode configuration we calculate $L_0$. The counting of states of this horizon's conformal field theory by means of Cardy's formula is in complete agreement with the Bekenstein-Hawking expression for the entropy of black hole in $d$ dimensions.Comment: 13 pages, latex, no figures; the final version to appear in Phys. Lett.

UV divergence-free QFT on noncommutative plane

We formulate Noncommutative Qauntum Field Theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No *-product is needed in this formulation and noncommutativity is carried by a modified Fourier transform of fields. As a result the theory is UV finite and the cutoff is provided by the noncommutative parameter theta.Comment: 6 pages, Latex, no figures. Accepted for publication in J.Phys.A. New references adde

Single State Supermultiplet in 1+1 Dimensions

We consider multiplet shortening for BPS solitons in N=1 two-dimensional models. Examples of the single-state multiplets were established previously in N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the fermion parity $(-1)^F$ due to boundary effects. This implies the disappearance of the boson-fermion classification resulting in abnormal statistics. We discuss an appropriate index that counts such short multiplets. A broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space is considered. Our index turns out to be related to the index of the Dirac operator on the soliton reduced moduli space (the moduli space is reduced by factoring out the translational modulus). The index vanishes in most cases implying the absence of shortening. In particular, it vanishes when there are only two critical points on the compact target space and the reduced moduli space has nonvanishing dimension. We also generalize the anomaly in the central charge to take into account the target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds. M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The paper is drastically revised compared to the first version. We add sections treating the following issues: (i) a new index counting one-state supermultiplets; (ii) analysis of hybrid models of general type; (iii) generalization of the anomaly in the central charge accounting for the target space metri

Defying jet-gas alignment in two radio galaxies at z~2 with extended light profiles: Similarities to brightest cluster galaxies

We report the detection of extended warm ionized gas in two powerful high-redshift radio galaxies, NVSS J210626-314003 at z=2.10 and TXS 2353-003 at z=1.49, that does not appear to be associated with the radio jets. This is contrary to what would be expected from the alignment effect, a characteristic feature of distant, powerful radio galaxies at z> 0.6. The gas also has smaller velocity gradients and line widths than most other high-z radio galaxies with similar data. Both galaxies are part of a systematic study of 50 high-redshift radio galaxies with SINFONI, and are the only two that are characterized by the presence of high surface-brightness gas not associated with the jet axis and by the absence of such gas aligned with the jet. Both galaxies are spatially resolved with ISAAC broadband imaging covering the rest-frame R band, and have extended wings that cannot be attributed to line contamination. We argue that the gas and stellar properties of these galaxies are more akin to gas-rich brightest cluster galaxies in cool-core clusters than the general population of high-redshift radio galaxies at z>2. In support of this interpretation, one of our sources, TXS 2353-003, for which we have H\alpha\ narrowband imaging, is associated with an overdensity of candidate H\alpha\ emitters by a factor of 8 relative to the field at z=1.5. We discuss possible scenarios of the evolutionary state of these galaxies and the nature of their emission line gas within the context of cyclical AGN feedback.Comment: A&A in pres

Solutions of the Klein-Gordon equation on manifolds with variable geometry including dimensional reduction

We develop the recent proposal to use dimensional reduction from the four-dimensional space-time D=(1+3) to the variant with a smaller number of space dimensions D=(1+d), d < 3, at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation on a few toy examples ("educational toys") of a space-time with variable special geometry, including a transition to a dimensional reduction. The examples considered contain a combination of two regions with a simple geometry (two-dimensional cylindrical surfaces with different radii) connected by a transition region. The new technique of transforming the study of solutions of the Klein-Gordon problem on a space with variable geometry into solution of a one-dimensional stationary Schr\"odinger-type equation with potential generated by this variation is useful. We draw the following conclusions: (1) The signal related to the degree of freedom specific to the higher-dimensional part does not penetrate into the smaller-dimensional part because of an inertial force inevitably arising in the transition region (this is the centrifugal force in our models). (2) The specific spectrum of scalar excitations resembles the spectrum of the real particles; it reflects the geometry of the transition region and represents its "fingerprints". (3) The parity violation due to the asymmetric character of the construction of our models could be related to violation of the CP symmetry.Comment: laTeX file, 9 pages, 8 figures. Significant corrections in the title, abstract, text. Corrected formulas and figures. Added new references, amendments in English. Acceptred for publication in Theoretical and Mathematical Physics. To appear in vol. 167, may 201

Planckian AdS2×S2AdS_2 \times S_2 space is an exact solution of the semiclassical Einstein equations

The product space configuration $AdS_2\times S_2$ (with $l$ and $r$ being radiuses of the components) carrying the electric charge $Q$ is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the classical Bertotti-Robinson space ($r=l=Q$) with no quantum corrections added. In general, the analysis involves the quadratic curvature coupling $\lambda$ appearing in the effective action. The solutions we find are of the following types: i) (for arbitrary $\lambda$) charged configuration which is quantum deformation of the Bertotti-Robinson space; ii) ($\lambda >\lambda_{cr}$) Q=0 configuration with $l$ and $r$ being of the Planck order; iii) ($\lambda<\lambda_{cr}$) $Q\neq 0$ configuration ($l$ and $r$ are of the Planck order) not connected analytically to the Bertotti-Robinson space. The interpretation of the solutions obtained and an indication on the internal structure of the Schwarzschild black hole are discussed.Comment: 14 pages, latex, 1 figure; v2: a note on S2*S2 type solutions adde