772 research outputs found
Strong Magnetic Limit of String Theory
We show that there exists a certain limit in type I and type II superstring
theory in the presence of a suitable configuration of magnetic U(1) fields
where all string excitations get an infinite mass, except for the neutral
massless sector and for the boson and fermion string states lying on the
leading Regge trajectory. For a supersymmetric configuration of magnetic fields
in internal directions, the resulting theory after the limit is a 3+1 Lorentz
invariant supersymmetric theory. Supersymmetry can be broken by introducing
extra components of the magnetic field or else by finite temperature. In both
cases we compute the one-loop partition function for the type I string model
after taking the limit, which turns out to be different from the Yang-Mills
result that arises by a direct limit. In the case of finite
temperature, no Hagedorn transition appears, in consistency with the reduction
of the string spectrum. In type II superstring theory, the analogous limit is
constructed by starting with a configuration of Melvin twists in two or more
complex planes. The resulting theory contains gravitation plus an infinite
number of states of the leading Regge trajectory.Comment: 10 pages. Minor correction
Naked and Thunderbolt Singularities in Black Hole Evaporation
If an evaporating black hole does not settle down to a non radiating remnant,
a description by a semi classical Lorentz metric must contain either a naked
singularity or what we call a thunderbolt, a singularity that spreads out to
infinity on a spacelike or null path. We investigate this question in the
context of various two dimensional models that have been proposed. We find that
if the semi classical equations have an extra symmetry that make them solvable
in closed form, they seem to predict naked singularities but numerical
calculations indicate that more general semi classical equations, such as the
original CGHS ones give rise to thunderbolts. We therefore expect that the semi
classical approximation in four dimensions will lead to thunderbolts. We
interpret the prediction of thunderbolts as indicating that the semi classical
approximation breaks down at the end point of black hole evaporation, and we
would expect that a full quantum treatment would replace the thunderbolt with a
burst of high energy particles. The energy in such a burst would be too small
to account for the observed gamma ray bursts.Comment: 21 pages (10 diagrams available on request
Lines on projective varieties and applications
The first part of this note contains a review of basic properties of the
variety of lines contained in an embedded projective variety and passing
through a general point. In particular we provide a detailed proof that for
varieties defined by quadratic equations the base locus of the projective
second fundamental form at a general point coincides, as a scheme, with the
variety of lines. The second part concerns the problem of extending embedded
projective manifolds, using the geometry of the variety of lines. Some
applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added;
typos correcte
A Proof of the Generalized Second Law for Two-Dimensional Black Holes
We investigate the generalized second law for two-dimensional black holes in
equilibrium (Hartle-Hawking) and nonequilibrium (Unruh) with the heat bath
surrounding the black holes. We obtain a simple expression for the change of
total entropy in terms of covariant thermodynamic variables, which is valid not
only for the Hartle-Hawking state but also for the Unruh state up to leading
order, without assuming a quasi-stationary evolution of the black holes. Using
this expression, it is shown that the rate of local entropy production is
non-negative in the two-dimensional black hole systems.Comment: 15 pages, boundary condition of static black hole is added to clarify
the situation, abstract and section 4 (concluding remarks) is rewritten, and
minor corrections, references adde
PP-Wave / CFT_2 Duality
We investigate the pp-wave limit of the AdS_3\times S^3\times K3
compactification of Type IIB string theory from the point of view of the dual
Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave
geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the
string bits of the latter being composed of twist operators. The massive
fundamental string oscillators correspond to certain twisted Virasoro
generators in the effective string. It is shown that both the ground states and
the genus expansion parameter (at least in the orbifold limit of the CFT)
coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2
which might have been expected. We demonstrate a leading-order agreement
between the pp-wave and CFT particle spectra. For a degenerate special case
(one NS 5-brane) an intriguing complete agreement is found.Comment: JHEP3 LaTeX, 20 pages; discussion of WZW levels clarified, reference
adde
Superstrings in type IIB R-R plane-wave in semi-light-cone gauge and conformal invariance
We reconsider the analysis done by Kazama and Yokoi in arXiv:0801.1561
(hep-th). We find that although the right vacuum of the theory is the one
associated to massless normal ordering (MNO), phase space normal ordering (PNO)
plays crucial role in the analysis in the following way. While defining the
quantum energy-momentum (EM) tensor one needs to take into account the field
redefinition relating the space-time field and the corresponding world-sheet
coupling. We argue that for a simple off-shell ansatz for the background this
field redefinition can be taken to be identity if the interaction term is
ordered according to PNO. This definition reproduces the correct physical
spectrum when the background is on-shell. We further show that the right way to
extract the effective equation of motion from the Virasoro anomaly is to first
order the anomaly terms according to PNO at a finite regularization parameter
\eps and then take the \eps \to 0 limit. This prescription fixes an
ambiguity in taking the limit for certain bosonic and fermionic contributions
to the Virasoro anomaly and is the natural one to consider given the above
definition of the EM tensor.Comment: 22 page
Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
The constraints imposed by maximal supersymmetry on multi-loop contributions
to the scattering of four open superstrings in the U(N) theory are examined by
use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2
(where k represents an external momentum and F the Yang--Mills field strength)
only receives contributions from L<=2 (where L is the loop number) while the
single-trace term k^2 t_8(tr F^4) receives contributions from all L. We
verified these statements up to L=5, but arguments based on supersymmetry
suggest they extend to all L. This explains why the single-trace contributions
to low energy maximally supersymmetric Yang--Mills field theory are more
divergent in the ultraviolet than the double-trace contributions. We also
comment further on the constraints on closed string amplitudes and their
implications for ultraviolet divergences in N=8 supergravity.Comment: 25 pages. 2 eps figures. Harvmac format. v2 qualifications regarding
comments on closed strings. References adde
N=2 Sigma Models for Ramond-Ramond Backgrounds
Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric
sigma models are constructed for the Type IIB superstring in Ramond-Ramond
backgrounds. The Kahler potential in these N=2 sigma models depends on four
chiral and antichiral bosonic superfields and two chiral and antichiral
fermionic superfields. When the Kahler potential is quadratic, the model is a
free conformal field theory which describes a flat ten-dimensional target space
with Ramond-Ramond flux and non-constant dilaton. For more general Kahler
potentials, the model describes curved target spaces with Ramond-Ramond flux
that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric
implies the on-shell conditions for the background up to the usual four-loop
conformal anomaly.Comment: 19 pages harvma
On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity
parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added
remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.
Rotating Strings in Confining AdS/CFT Backgrounds
We study semiclassical rotating strings in AdS/CFT backgrounds that exhibit
both confinement and finite-size effects. The energy versus spin dispersion
relation for short strings is the expected Regge trajectory behaviour, with the
same string tension as is measured by the Wilson loop. Long strings probe the
interplay between confinement and finite-size effects. In particular, the
dispersion relation for long strings shows a characteristic dependence on the
string tension and the finite-size scale.Comment: 18 pages, 3 figures. v2: minor changes, refs. adde
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