scholarly journals Non-linear σ-models in noncommutative geometry: fields with values in finite spaces

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2371-2379 ◽  
Author(s):  
Ludwik Dabrowski ◽  
Thomas Krajewski ◽  
Giovanni Landi
Keyword(s):  
Projective Space ◽  
Noncommutative Geometry ◽  
Moduli Space ◽  
Topological Charge ◽  
Complex Structure ◽  
Noncommutative Tori ◽  
Noncommutative Spaces ◽  
Non Linear ◽  
Finite Spaces

We study σ-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space [Formula: see text].

scholarly journals On a gauge action on sigma model solitons

2018 ◽  
Vol 21 (02) ◽  
pp. 1850008
Author(s):  
Hyun Ho Lee
Keyword(s):  
Noncommutative Geometry ◽  
Sigma Model ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Target Space ◽  
Gauge Action ◽  
Noncommutative Tori ◽  
Linear Formula ◽  
Non Linear

In this paper, we consider a gauge action on sigma model solitons over noncommutative tori as source spaces, with a target space made of two points introduced in [L. Dabrowski, T. Krajewski and G. Landi, Some properties of non-linear [Formula: see text]-models in noncommutative geometry, Int. J. Mod. Phys. B 14 (2000) 2367–2382]. Using new classes of solitons from Gabor frames, we quantify the condition about how to gauge a Gaussian to a prescribed Gabor frame.

scholarly journals Weak gravity bounds in asymptotic string compactifications

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Brice Bastian ◽  
Thomas W. Grimm ◽  
Damian van de Heisteeg
Keyword(s):  
Black Holes ◽  
Moduli Space ◽  
Mass Formula ◽  
Complex Structure ◽  
Mass Ratio ◽  
De Sitter ◽  
String Compactifications ◽  
Type Iib String Theory ◽  
Bps States ◽  
Weak Gravity

Abstract We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

scholarly journals Codimension One Holomorphic Distributions on the Projective Three-space

2018 ◽  
Vol 2020 (23) ◽  
pp. 9011-9074 ◽  
Author(s):  
Omegar Calvo-Andrade ◽  
Maurício Corrêa ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Tangent Bundle ◽  
Projective Variety ◽  
Arbitrary Degree ◽  
Codimension One ◽  
Quot Scheme ◽  
Space Of Distributions ◽  
Three Space

Abstract We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck’s Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety. Finally, we prove that every rational foliation and certain logarithmic foliations have stable tangent sheaves.

scholarly journals COMPLEX GRAVITY AND NONCOMMUTATIVE GEOMETRY

2001 ◽  
Vol 16 (05) ◽  
pp. 759-766 ◽  
Author(s):  
ALI H. CHAMSEDDINE
Keyword(s):  
Noncommutative Geometry ◽  
Space Time ◽  
Specific Form ◽  
Antisymmetric Tensor ◽  
Gauge Invariant ◽  
Diffeomorphism Invariance ◽  
Open Strings ◽  
Noncommutative Spaces

The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to gravity one discovers that the metric becomes complex. Complex gravity is constructed by gauging the symmetry U(1, D-1). The resulting action gives one specific form of nonsymmetric gravity. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. It is argued that for this theory to be consistent one must prove the existence of generalized diffeomorphism invariance. The results are easily generalized to noncommutative spaces.

On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons

2002 ◽  
Vol 45 (3) ◽  
pp. 417-421
Author(s):  
Yasuhiko Kamiyama ◽  
Shuichi Tsukuda
Keyword(s):  
Moduli Space ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Fano Manifold ◽  
Complex Dimension ◽  
Holomorphic Sections

AbstractFor an integer n ≥ 3, let Mn be the moduli space of spatial polygons with n edges. We consider the case of odd n. Then Mn is a Fano manifold of complex dimension n − 3. Let ΘMn be the sheaf of germs of holomorphic sections of the tangent bundle TMn. In this paper, we prove Hq(Mn, ΘMn) = 0 for all q ≥ 0 and all odd n. In particular, we see that the moduli space of deformations of the complex structure on Mn consists of a point. Thus the complex structure on Mn is locally rigid.

scholarly journals Infinite non-linear programming

1963 ◽  
Vol 3 (3) ◽  
pp. 294-300 ◽  
Author(s):  
M. A. Hanson
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Calculus Of Variations ◽  
Continuous Variable ◽  
Infinitely Divisible ◽  
Non Linear Programming ◽  
Non Linear ◽  
Mathematical Reason ◽  
Finite Spaces ◽  
Infinitely Divisible Processes

In recent years there has been extensive development in the theory and techniques of mathematical programming in finite spaces. It would be very useful in practice to extend this development to infinite spaces, in order to treat more realistically the problems that arise for example in economic situations involving infinitely divisible processes, and in particular problems involving time as a continuous variable. A more mathematical reason for seeking such generalisation is possibly that of obtaining a unification mathematical programming with other branches of mathematics concerned with extrema, such as the calculus of variations.

scholarly journals PROJECTIVE GROUP ALGEBRAS

1999 ◽  
Vol 14 (01) ◽  
pp. 129-146 ◽  
Author(s):  
R. CASALBUONI
Keyword(s):  
Algebraic Theory ◽  
Equivalence Classes ◽  
Irreducible Representations ◽  
Group Algebras ◽  
Projective Group ◽  
Noncommutative Tori ◽  
Noncommutative Spaces ◽  
Simple Generalization ◽  
Vector Representations ◽  
M Theory

In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the M theory on noncommutative tori. This turns out to be an interesting field of applications, since the space [Formula: see text] of the equivalence classes of the vector unitary irreducible representations of the group under examination becomes, in the projective case, a prototype of noncommuting spaces. For vector representations the algebraic integration is equivalent to integrate over [Formula: see text]. However, its very definition is related only at the structural properties of the group algebra, therefore it is well defined also in the projective case, where the space [Formula: see text] has no classical meaning. This allows a generalization of the usual group harmonic analysis. Particular attention is given to Abelian groups, which are the relevant ones in the compactification problem, since it is possible, from the previous results, to establish a simple generalization of the ordinary calculus to the associated noncommutative spaces.

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