623 research outputs found
BPS Saturated Amplitudes and Non-perturbative String Theory
The study of the special F^4 and R^4 in the effective action for the
Spin(32)/Z_2 and type II strings sheds some light on D-brane calculus and on
instanton contribution counting. The D-instanton case is discussed separately.Comment: latex 4 pages, crckapb style used. Cargese 1997 Gong show.v2 English
corrected. v3 correction correcte
A Feynman integral via higher normal functions
We study the Feynman integral for the three-banana graph defined as the
scalar two-point self-energy at three-loop order. The Feynman integral is
evaluated for all identical internal masses in two space-time dimensions. Two
calculations are given for the Feynman integral; one based on an interpretation
of the integral as an inhomogeneous solution of a classical Picard-Fuchs
differential equation, and the other using arithmetic algebraic geometry,
motivic cohomology, and Eisenstein series. Both methods use the rather special
fact that the Feynman integral is a family of regulator periods associated to a
family of K3 surfaces. We show that the integral is given by a sum of elliptic
trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm
value is related to the regulator of a class in the motivic cohomology of the
K3 family. We prove a conjecture by David Broadhurst that at a special
kinematical point the Feynman integral is given by a critical value of the
Hasse-Weil L-function of the K3 surface. This result is shown to be a
particular case of Deligne's conjectures relating values of L-functions inside
the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications.
Version to appear in Compositio Mathematic
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and
string theory. Eisenstein series have appeared systematically in the
determination of spectrums and partition functions, in the description of
non-perturbative effects, in higher-order corrections of scalar-field spaces,
... The latter often appear as gravitational instantons i.e. as special
solutions of Einstein's equations. In the present lecture notes we present a
class of such solutions in four dimensions, obtained by requiring (conformal)
self-duality and Bianchi IX homogeneity. In this case, a vast range of
configurations exist, which exhibit interesting modular properties. Examples of
other Einstein spaces, without Bianchi IX symmetry, but with similar features
are also given. Finally we discuss the emergence and the role of Eisenstein
series in the framework of field and string theory perturbative expansions, and
motivate the need for unravelling novel modular structures.Comment: 45 pages. To appear in the proceedings of the Besse Summer School on
Quasimodular Forms - 201
Scattering Equations and String Theory Amplitudes
Scattering equations for tree-level amplitudes are viewed in the context of
string theory. As a result of the comparison we are led to define a new dual
model which coincides with string theory in both the small and large
limit, and whose solution is found algebraically on the surface of solutions to
the scattering equations. Because it has support only on the scattering
equations, it can be solved exactly, yielding a simple resummed model for
-corrections to all orders. We use the same idea to generalize
scattering equations to amplitudes with fermions and any mixture of scalars,
gluons and fermions. In all cases checked we find exact agreement with known
results.Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be
published in PR
A note on topological amplitudes in hybrid string theory
We study four-dimensional compactifications of type II superstrings on
Calabi-Yau spaces in the hybrid formalism. Chiral and twisted-chiral
interactions are rederived, which involve the coupling of the compactification
moduli to two powers of the Weyl-tensor and of the derivative of the universal
tensor field-strength. We review the formalism and provide details of some of
its technicalities.Comment: v1: 18 pages, harvmac. v2: v2: 32 pages, substantially expanded
version to appear in the ICMP 2006 proceedings. LaTeX forma
Intra- and intertaxon stable O and C isotope variability of fossil fish otoliths: an early Eocene test case
Knowledge of basic data variability is essential for the interpretation of any proxy-based paleotemperature record. To evaluate this for d18O stable isotope paleothermometry based on early Paleogene fish otoliths from marginal marine environments, an intra- and interspecific stable O and C isotope study was performed at a single locality in the southern North Sea Basin (Ampe Quarry, Egem, Belgium), where shallow marine sands and silts are exposed. The age of the deposits is early late Ypresian (ca. 50.9 Ma) and falls within the early Eocene climatic optimum (EECO) interval. In each of four fossiliferous levels sampled, the same three otolith species were analyzed (Platycephalus janeti, Paraconger papointi and “genus Neobythitinorum” subregularis). Intrataxon stable isotope spread amounts on average 2.50-3.00‰ for all taxa and is present in all levels. This implies that each sample level comprises substantial variability, which can be attributed to a combination of temporal and taphonomic effects. More importantly, intertaxon offsets of 4.60‰ in d13C and 2.20‰ in d18O between the mean values of the three otolith species are found, with “N.” subregularis representing more positive values relative to the other species. We hypothesize that freshwater influence of coastal waters is the most likely cause for these discrepancies. Similar analyses on two coastal bivalve species (Venericardia sulcata and Callista laevigata) corroborate this hypothesis. Accordingly, d18O values measured on “N.” subregularis otoliths probably represent a more open oceanic signal, and therefore seem well-suited for d18O stable isotope paleothermometry. This study highlights the importance of investigating data variability of a biogenic carbonate paleotemperature proxy at the species level, before applying paleotemperature equations and interpreting the outcome
Assessing paleotemperature and seasonality during the early Eocene climatic optimum (EECO) in the Belgian basin by means of fish otolith stable O and C isotopes
The Paleogene greenhouse world comprises variable paleoclimate conditions providing an indispensable deep-time perspective for the possible effects of human-induced climate change. In this paper, paleotemperature data of the Early Eocene Climatic Optimum (EECO) from the mid-latitude marginal marine Belgian Basin are discussed. They are derived from fish otolith d18O compositions of four non-migratory species belonging to the families Congridae and Ophidiidae. Otoliths from several levels and localities within the middle to late Ypresian were selected. After manual polishing, bulk and incremental microsamples were drilled and analyzed by a mass spectrometer. A cross-plot of bulk otolith d18O vs. d13C results shows a discrepancy between both families used. Ophidiid data probably represent true bottom water temperatures of the Belgian Basin. The mean annual temperature (MAT) of the EECO is calculated at 27.5 °C, which is in line with other proxy results. However, variations in MAT up to 6 °C occur, suggesting a pronounced expression of climate variability in mid-latitude marginal basins. Incremental analyses revealed a ~9.5 °C mean annual range of temperatures, similar to modern seasonality. These results show that marginal marine environments such as the Belgian Basin are well suited to infer high-resolution paleoclimate variability
A note on topological amplitudes in hybrid string theory
We study four-dimensional compactifications of type II superstrings on Calabi-Yau spaces using the formalism of hybrid string theory. Chiral and twisted-chiral interactions are rederived, which involve the coupling of the compactification moduli to two powers of the Weyl-tensor and of the derivative of the universal tensor field-strength
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