scholarly journals Jet differentials on toroidal compactifications of ball quotients

2021 ◽  
Vol 70 (6) ◽  
pp. 2331-2359
Author(s):  
Benoît Cadorel
Keyword(s):  
Toroidal Compactifications ◽  
Ball Quotients

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

scholarly journals K-RATIONAL D-BRANE CRYSTALS

2012 ◽  
Vol 27 (22) ◽  
pp. 1250112
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
String Theory ◽  
Algebraic Number ◽  
Special Class ◽  
Building Blocks ◽  
Number Fields ◽  
Central Point ◽  
Algebraic Number Fields ◽  
Special Values ◽  
Toroidal Compactifications ◽  
Base Points

In this paper the problem of constructing space–time from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of certain Calabi–Yau varieties. The collections of D-branes involved have algebraic base points, leading to the notion of K-arithmetic D-crystals for algebraic number fields K. This idea can be tested for D0-branes in the framework of toroidal compactifications via the conjectures of Birch and Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these conjectures can be interpreted as formulae that relate the canonical Néron–Tate height of the base points of the D-crystals to special values of the motivic L-function at the central point. In simple cases the knowledge of the D-crystals of Heegner type suffices to uniquely determine the geometry.

Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yongqiang Liu ◽  
Laurenţiu Maxim ◽  
Botong Wang
Keyword(s):  
Integral Homology ◽  
Algebraic Varieties ◽  
Finiteness Property ◽  
Rational Homology ◽  
Mellin Transformation ◽  
Hopf Conjecture ◽  
Ball Quotients ◽  
Proper Map ◽  
Complex Projective ◽  
Aspherical Manifolds

Abstract In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

scholarly journals Stringy dyonic solutions and clifford structures

2019 ◽  
Vol 16 (09) ◽  
pp. 1950138
Author(s):  
A. Belfakir ◽  
A. belhaj ◽  
Y. El Maadi ◽  
S. E. Ennadifi ◽  
Y. Hassouni ◽  
...  
Keyword(s):  
Black Hole ◽  
Gauge Symmetry ◽  
Standard Model ◽  
Clifford Algebras ◽  
Magnetic Monopole ◽  
Toroidal Compactifications ◽  
The Standard Model ◽  
Arbitrary Dimensions ◽  
Electrically Charged ◽  
Clifford Structures

Using the toroidal compactification of string theory on [Formula: see text]-dimensional tori, [Formula: see text], we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to [Formula: see text] dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model (SM) extensions. Then, we consider in some detail such black hole classes obtained from even-dimensional toroidal compactifications, and we find that they are linked to [Formula: see text] Clifford algebras using the vee product. It is believed that this analysis could be extended to dyonic objects which can be obtained from local Calabi–Yau manifold compactifications.

scholarly journals M-THEORY DUALITY AND BPS-EXTENDED SUPERGRAVITY

2001 ◽  
Vol 16 (05) ◽  
pp. 1002-1011 ◽  
Author(s):  
BERNARD DE WIT
Keyword(s):  
Lorentz Invariance ◽  
Space Time ◽  
Duality Group ◽  
Toroidal Compactifications ◽  
Maximal Supergravity ◽  
Bps States ◽  
M Theory

We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven space-time dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.

A NOTE ON DISCRETE SYMMETRIES IN TOROIDAL COMPACTIFICATIONS OF STRINGS

1990 ◽  
Vol 05 (22) ◽  
pp. 1779-1785 ◽  
Author(s):  
M. A. R. OSORIO
Keyword(s):  
Partition Function ◽  
Discrete Symmetries ◽  
Modular Invariance ◽  
World Sheet ◽  
Toroidal Compactifications ◽  
Instanton Contribution

In this paper we look for discrete invariances of the partition function in toroidal compactifications of strings. We show that besides world-sheet modular invariance, the partition function is invariant under GL (2d, ℤ) transformations ( GL (2d + 16, ℤ) when Wilson lines are present) acting upon the instanton contribution.

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