Quantum corrections to the noncommutative kink

We calculate quantum corrections to the mass of noncommutative phi^4 kink in (1+1) dimensions for intermediate and large values of the noncommutativity parameter theta. All one-loop divergences are removed by a mass renormalization (which is different from the one required in the topologically trivial sector). For large theta quantum corrections to the mass grow linearly with theta signaling about possible break down of the perturbative expansion.Comment: 18 pages, v2: minor change

Quantum aspects of a noncommutative supersymmetric kink

We consider quantum corrections to a kink of noncommutative supersymmetric phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of time derivatives in the action, we are able to define supercharges and a Hamiltonian by using an unconventional canonical formalism. We calculate the quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of fluctuations) which coincides with its' value in corresponding commutative theory independently of the noncommutativity parameter. The renormalization also proceeds precisely as in the commutative case. The vacuum expectation value of the new Hamiltonian is also calculated and appears to be consistent with the value of the quantum energy E of the kink.Comment: 20 pages, v2: a reference adde

Thorny Spheres and Black Holes with Strings

We consider thorny spheres, that is 2-dimensional compact surfaces which are everywhere locally isometric to a round sphere $S^2$ except for a finite number of isolated points where they have conical singularities. We use thorny spheres to generate, from a spherically symmetric solution of the Einstein equations, new solutions which describe spacetimes pierced by an arbitrary number of infinitely thin cosmic strings radially directed. Each string produces an angle deficit proportional to its tension, while the metric outside the strings is a locally spherically symmetric solution. We prove that there can be arbitrary configurations of strings provided that the directions of the strings obey a certain equilibrium condition. In general this equilibrium condition can be written as a force-balance equation for string forces defined in a flat 3-space in which the thorny sphere is isometrically embedded, or as a constraint on the product of holonomies around strings in an alternative 3-space that is flat except for the strings. In the case of small string tensions, the constraint equation has the form of a linear relation between unit vectors directed along the string axes.Comment: 37 pages, 11 figure

New inequality for Wilson loops from AdS/CFT

The strong subadditivity is the most important inequality which entanglement entropy satisfies. Based on the AdS/CFT conjecture, entanglement entropy in CFT is equal to the area of the minimal surface in AdS space. It is known that a Wilson loop can also be holographically computed from the minimal surface in AdS space. In this paper, we argue that Wilson loops also satisfy a similar inequality, and find several evidences of it.Comment: 16 pages (removed unnecessary figures

Two-dimensional Quantum-Corrected Eternal Black Hole

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.Comment: Latex, 28 pges; minor corrections in text and abstract made and new references adde

Kaluza-Klein Method in Theory of Rotating Quantum Fields

Quantum fields on a stationary space-time in a rotating Killing reference frame are considered. Finding solutions of wave equations in this frame is reduced to a fiducial problem on a static background. The rotation results in a gauge connection in a way similar to appearance of gauge fields in Kaluza-Klein models. Such a Kaluza-Klein method in theory of rotating quantum fields enables one to simplify computations and get a number of new results similar to those established for static backgrounds. In particular, we find with its help functional form of free energy at high temperatures. Applications of these results to quantum fields near rotating black holes are briefly discussed.Comment: 23 pages, late

A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as conjugate to a conical deficit angle, and (iv) the pair creation approach of Garfinkle, Giddings, and Strominger. All of these approaches have a more restrictive domain of applicability than the Noether charge approach. Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions. However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach. In the course of our analysis, we generalize the definition of Brown and York's quasilocal energy to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity. In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Entanglement entropy of two dimensional systems and holography

In this note a new method for computing the entanglement entropy of a CFT holographically is explored. It consists of finding a bulk background with a boundary metric that has the conical singularities needed to compute the entanglement entropy in the usual QFT definition. An explicit calculation is presented for d=2.Comment: 20 pages, 1 figure: v2 typos fixed, references and comments adde

AdS/CFT and Strong Subadditivity of Entanglement Entropy

Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence. One of the most important properties of the entanglement entropy is known as the strong subadditivity. This requires that the entanglement entropy should be a concave function with respect to geometric parameters. It is a non-trivial check on the proposal to see if this property is indeed satisfied by the entropy computed holographically. In this paper we examine several examples which are defined by annuli or cusps, and confirm the strong subadditivity via direct calculations. Furthermore, we conjecture that Wilson loop correlators in strongly coupled gauge theories satisfy the same relation. We also discuss the relation between the holographic entanglement entropy and the Bousso bound.Comment: 29 pages, harvmac, 7 figures, references adde