74,404 research outputs found
Emergent spacetime from modular motives
The program of constructing spacetime geometry from string theoretic modular
forms is extended to Calabi-Yau varieties of dimensions two, three, and four,
as well as higher rank motives. Modular forms on the worldsheet can be
constructed from the geometry of spacetime by computing the L-functions
associated to omega motives of Calabi-Yau varieties, generated by their
holomorphic forms via Galois representations. The modular forms that emerge
from the omega motive and other motives of the intermediate cohomology are
related to characters of the underlying rational conformal field theory. The
converse problem of constructing space from string theory proceeds in the class
of diagonal theories by determining the motives associated to modular forms in
the category of motives with complex multiplication. The emerging picture
indicates that the L-function can be interpreted as a map from the geometric
category of motives to the category of conformal field theories on the
worldsheet.Comment: 40 page
Multifield Reheating after Modular -Inflation
In the inflationary framework of cosmology the initial phase of rapid
expansion has to be followed by a reheating stage, which is envisioned to end
in a radiation dominated big bang. Key parameters that characterize this big
bang state are the temperature at the end of the reheating stage and the baryon
asymmetry. For general interacting theories these parameters are difficult to
obtain analytically because of the involved structure of the potential. In this
paper multifield reheating is considered for interacting theories in which the
inflaton trajectory is weakly curved. This scenario is realized in the model of
-inflation, a particular example of modular inflation, allowing an estimate
of the reheat temperature.Comment: 15 pages, improved approximation, added reference
Black Hole Probes of Automorphic Space
Over the past few years the arithmetic Langlands program has proven useful in
addressing physical problems. In this paper it is shown how Langlands'
reciprocity conjecture for automorphic forms, in combination with a
representation theoretic notion of motives, suggests a framework in which the
entropy of automorphic black holes can be viewed as a probe of spacetime that
is sensitive to the geometry of the extra dimensions predicted by string
theory. If it were possible to produce black holes with automorphic entropy in
the laboratory their evaporation would provide us with information about the
precise shape of the compact geometry.Comment: Gravity Research Foundation essa
Spin-Flavour Symmetry and Contractions Towards Classical Space-Time Symmetry
A classification scheme of hadrons is proposed on the basis of the division
algebra H of quaternions and an appropriate geometry. This scheme suggests
strongly to understand flavour symmetry in another manner than from standard
symmetry schemes. In our approach, we do not start from `exact' symmetry groups
like SU(2) \times SU(2) chiral symmetry and impose various symmetry breaking
mechanisms which collide with theorems wellknown from quantum field theory. On
the contrary, the approximate symmetry properties of the hadron spectrum at low
energies, usually classified by `appropriately' broken compact flavour groups,
emerge very naturally as a low energy reduction of the noncompact (dynamical)
symmetry group Sl(2,H). This quaternionic approach not only avoids most of the
wellknown conceptual problems of Chiral Dynamics but it also allows for a
general treatment of relativistic flavour symmetries as well as it yields a
direct connection towards classical relativistic symmetry.Comment: 6 pages, LaTeX (style file included). Talk given at the IWCQIS 1996,
Dubna, Russia. To appear in the proceeding
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