143 research outputs found
Eisenstein Series in String Theory
We discuss the relevance of Eisenstein series for representing certain
G(Z)-invariant string theory amplitudes which receive corrections from BPS
states only. The Eisenstein series are constructed using G(Z)-invariant mass
formulae and are manifestly invariant modular functions on the symmetric space
K\G(R) of non-compact type, with K the maximal compact subgroup of G(R). In
particular, we show how Eisenstein series of the T-duality group SO(d,d,Z) can
be used to represent one- and g-loop amplitudes in compactified string theory.
We also obtain their non-perturbative extensions in terms of the Eisenstein
series of the U-duality group E_{d+1(d+1)}(Z).Comment: 11 pages, Latex, submitted to Proceedings of Strings '99, published
versio
New Phase Diagram for Black Holes and Strings on Cylinders
We introduce a novel type of phase diagram for black holes and black strings
on cylinders. The phase diagram involves a new asymptotic quantity called the
relative binding energy. We plot the uniform string and the non-uniform string
solutions in this new phase diagram using data of Wiseman. Intersection rules
for branches of solutions in the phase diagram are deduced from a new Smarr
formula that we derive.Comment: 19 pages, 6 figures, v2: typos corrected, v3: refs. added, comment on
bounds on the relative binding energy n added in end of section
M-theory and the string genus expansion
The partition function of the membrane is investigated. In particular, the
case relevant to perturbative string theory of a membrane with topology is examined. The coupling between the string world sheet Euler
character and the dilaton is shown to arise from a careful treatment of the
membrane partition function measure. This demonstrates that the M-theory origin
of the dilaton coupling to the string world sheet is quantum in nature.Comment: 12 pages, late
Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order
The "dialogue of multipoles" matched asymptotic expansion for small black
holes in the presence of compact dimensions is extended to the Post-Newtonian
order for arbitrary dimensions. Divergences are identified and are regularized
through the matching constants, a method valid to all orders and known as
Hadamard's partie finie. It is closely related to "subtraction of
self-interaction" and shows similarities with the regularization of quantum
field theories. The black hole's mass and tension (and the "black hole
Archimedes effect") are obtained explicitly at this order, and a Newtonian
derivation for the leading term in the tension is demonstrated. Implications
for the phase diagram are analyzed, finding agreement with numerical results
and extrapolation shows hints for Sorkin's critical dimension - a dimension
where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio
On non-uniform smeared black branes
We investigate charged dilatonic black -branes smeared on a transverse
circle. The system can be reduced to neutral vacuum black branes, and we
perform static perturbations for the reduced system to construct non-uniform
solutions. At each order a single master equation is derived, and the
Gregory-Laflamme critical wavelength is determined. Based on the non-uniform
solutions, we discuss thermodynamic properties of this system and argue that in
a microcanonical ensemble the non-uniform smeared branes are entropically
disfavored even near the extremality, if the spacetime dimension is , which is the critical dimension for the vacuum case. However, the critical
dimension is not universal. In a canonical ensemble the vacuum non-uniform
black branes are thermodynamically favorable at , whereas the
non-uniform smeared branes are favorable at near the extremality.Comment: 24 pages, 2 figures; v2: typos corrected, submitted to
Class.Quant.Gra
SO(5,5) duality in M-theory and generalized geometry
We attempt to reformulate eleven dimensional supergravity in terms of an
object that unifies the three-form and the metric and makes the M-theory
duality group manifest. This short note deals with the case of where the
U-duality group SO(5,5) acts in five spatial dimensions.Comment: 7 pages, LaTex, v2: typos corrected and reference adde
Very Extended and at low levels, Gravity and Supergravity
We define a level for a large class of Lorentzian Kac-Moody algebras. Using
this we find the representation content of very extended and
(i.e. ) at low levels in terms of and
representations respectively. The results are consistent with the conjectured
very extended and symmetries of gravity and maximal supergravity
theories given respectively in hep-th/0104081 and hep-th/0107209. We explain
how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference
expanded
Deformed black strings in 5-dimensional Einstein-Yang-Mills theory
We construct the first examples of deformed non-abelian black strings in a
5-dimensional Einstein-Yang-Mills model. Assuming all fields to be independent
of the extra coordinate, we construct deformed black strings, which in the
4-dimensional picture correspond to axially symmetric non-abelian black holes
in gravity-dilaton theory. These solutions thus have deformed S^2 x R horizon
topology. We study fundamental properties of the black strings and find that
for all choices of the gravitational coupling two branches of solutions exist.
The limiting behaviour of the second branch of solutions however depends
strongly on the choice of the gravitational coupling.Comment: 8 Revtex pages; 4 eps figures; references adde
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