53 research outputs found
N=2 Supersymmetry and String-Loop Corrected Magnetic Black Holes
We study string-loop corrections to magnetic black hole. Four-dimensional
theory is obtained by compactification of the heterotic string theory on the
manifold or on a suitable orbifold yielding N=1 supersymmetry in
6D. The resulting 4D theory has N=2 local supersymmetry. Prepotential of this
theory receives only one-string-loop correction. The tree-level gauge couplings
are proportional to the inverse effective string coupling and decrease at small
distances from the center of magnetic black hole, so that loop corrections to
the gauge couplings are important in this region. We solve the system of spinor
Killing equations (conditions for the supersymmetry variations of the fermions
to vanish) and Maxwell equations. At the string-tree level, we reproduce the
magnetic black hole solution which can be also obtained by solving the system
of the Einstein-Maxwell equations and the equations of motion for the moduli.
String-loop corrections to the tree-level solution are calculated in the first
order in string coupling. The resulting corrections to the metric and dilaton
are large at small distances from the center of the black hole. Possible
smearing of the singularity at the origin by quantum corrections is discussed.Comment: Reference added; minor modification
Non-Localizability and Asymptotic Commutativity
The mathematical formalism commonly used in treating nonlocal highly singular
interactions is revised. The notion of support cone is introduced which
replaces that of support for nonlocalizable distributions. Such support cones
are proven to exist for distributions defined on the Gelfand-Shilov spaces
, where . This result leads to a refinement of previous
generalizations of the local commutativity condition to nonlocal quantum
fields. For string propagators, a new derivation of a representation similar to
that of K\"{a}llen-Lehmann is proposed. It is applicable to any initial and
final string configurations and manifests exponential growth of spectral
densities intrinsic in nonlocalizable theories.Comment: This version is identical to the initial one whose ps and pdf files
were unavailable, with few corrections of misprint
On The Universality Class Of Little String Theories
We propose that Little String Theories in six dimensions are quasilocal
quantum field theories. Such field theories obey a modification of Wightman
axioms which allows Wightman functions (i.e. vacuum expectation values of
products of fundamental fields) to grow exponentially in momentum space.
Wightman functions of quasilocal fields in x-space violate microlocality at
short distances. With additional assumptions about the ultraviolet behavior of
quasilocal fields, one can define approximately local observables associated to
big enough compact regions. The minimum size of such a region can be
interpreted as the minimum distance which observables can probe. We argue that
for Little String Theories this distance is of order {\sqrt N}/M_s.Comment: 25 pages, late
What We Don't Know about BTZ Black Hole Entropy
With the recent discovery that many aspects of black hole thermodynamics can
be effectively reduced to problems in three spacetime dimensions, it has become
increasingly important to understand the ``statistical mechanics'' of the
(2+1)-dimensional black hole of Banados, Teitelboim, and Zanelli (BTZ). Several
conformal field theoretic derivations of the BTZ entropy exist, but none is
completely satisfactory, and many questions remain open: there is no consensus
as to what fields provide the relevant degrees of freedom or where these
excitations live. In this paper, I review some of the unresolved problems and
suggest avenues for their solution.Comment: 24 pages, LaTeX, no figures; references added, brief discussion of
relation to string theory added; to appear in Class. Quant. Gra
Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra
Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole
using asymptotic Virasoro algebra. We apply Strominger's method to a black hole
solution found by Martinez and Zanelli (MZ). This is a solution of
three-dimensional gravity with a conformal scalar field. The solution is not
, but it is asymptotically ; therefore, it has the asymptotic
Virasoro algebra. We compute the central charge for the theory and compares
Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the
functional form does agree, but the overall numerical coefficient does not.
This is because this approach gives the "maximum possible entropy" for the
numerical coefficient.Comment: 26 pages, LaTeX; v2: minor correction
BTZ black holes and the near-horizon geometry of higher-dimensional black holes
We investigate the connection between the BTZ black holes and the
near-horizon geometry of higher-dimensional black holes. Under mild conditions,
we show that (i) if a black hole has a global structure of the type of the
non-extremal Reissner-Nordstrom black holes, its near-horizon geometry is
times a sphere, and further (ii) if such a black hole is obtained from
a boosted black string by dimensional reduction, the near-horizon geometry of
the latter contains a BTZ black hole. Because of these facts, the calculation
of the Bekenstein-Hawking entropy and the absorption cross-sections of scalar
fields is essentially reduced to the corresponding calculation in the BTZ
geometry under appropriate conditions. This holds even if the geometry is not
supersymmetric in the extremal limit. Several examples are discussed. We also
discuss some generalizations to geometries which do not have near the
horizon.Comment: 19 pages, LaTex, (v2) a comment on black holes with 2 and 3 charges
added, (v3) some phrases made more precise, references added, minor changes;
version to appear in Phys. Rev.
Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice
Inspired by the ideas from topological field theory it is possible to rewrite
the supersymmetric charges of certain classes of extended supersymmetric
Yang--Mills (SYM) theories in such a way that they are compatible with the
discretization on a Euclidean spacetime lattice. Such theories are known as
maximally twisted SYM theories. In this review we discuss the construction and
some applications of such classes of theories. The one-loop perturbative
renormalization of the four-dimensional lattice SYM is discussed
in particular. The lattice theories constructed using twisted approach play an
important role in investigating the thermal phases of strongly coupled SYM
theories and also the thermodynamic properties of their dual gravitational
theories.Comment: 74 pages, 15 figures, minor revision, references added, published
versio
Infrared Properties of QCD from Dyson-Schwinger equations
I review recent results on the infrared properties of QCD from
Dyson-Schwinger equations. The topics include infrared exponents of
one-particle irreducible Green's functions, the fixed point behaviour of the
running coupling at zero momentum, the pattern of dynamical quark mass
generation and properties of light mesons.Comment: 47 pages, 19 figures, Topical Review to be published in J.Phys.G, v2:
typos corrected and some references adde
Quantum Liouville theory and BTZ black hole entropy
In this paper I give an explicit conformal field theory description of
(2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field
theory I investigate the reducible Verma modules in the elliptic sector, which
correspond to certain irreducible representations of the quantum algebra
U_q(sl_2) \odot U_{\hat{q}}(sl_2). I show that there are states that decouple
from these reducible Verma modules in a similar fashion to the decoupling of
null states in minimal models. Because ofthe nonstandard form of the Ward
identity for the two-point correlation functions in quantum Liouville field
theory, these decoupling states have positive-definite norms. The explicit
counting from these states gives the desired Bekenstein-Hawking entropy in the
semi-classical limit when q is a root of unity of odd order.Comment: LaTeX, 33 pages, 4 eps figure
Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory
We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2
and
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