scholarly journals D-INSTANTON SUMS FOR MATTER HYPERMULTIPLETS

2004 ◽  
Vol 19 (35) ◽  
pp. 2645-2653 ◽  
Author(s):  
SERGEI V. KETOV ◽  
OSVALDO P. SANTILLAN ◽  
ANDREI G. ZORIN
Keyword(s):  
Infinite Number ◽  
Moduli Space ◽  
Quantum Corrections ◽  
The Real ◽  
Nontrivial Deformation

We calculate some nonperturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi–Yau threefold, near conifold singularities. We find a nontrivial deformation of the (real) 4n-dimensional hypermultiplet moduli space metric due to the infinite number of D-instantons, under the assumption of n tri-holomorphic commuting isometries of the metric, in the hyper-Kähler limit (i.e. in the absence of gravitational corrections).

scholarly journals On TCS G2 manifolds and 4D emergent strings

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Fengjun Xu
Keyword(s):  
Moduli Space ◽  
Quantum Corrections ◽  
Type Ii ◽  
Quantum Level ◽  
Weakly Coupled ◽  
G2 Manifolds ◽  
Fundamental Type ◽  
M Theory ◽  
Distance Limit ◽  
Refined Version

Abstract In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

MATRIX MODELS WITH NONEVEN POTENTIALS

1991 ◽  
Vol 06 (14) ◽  
pp. 2559-2568 ◽  
Author(s):  
CAREN MARZBAN ◽  
R. RAJU VISWANATHAN
Keyword(s):  
Matrix Models ◽  
Moduli Space ◽  
Statistical Models ◽  
Riemann Surfaces ◽  
Critical Values ◽  
Coupling Constants ◽  
The Real ◽  
Universality Classes ◽  
Definition Of ◽  
Polynomial Potentials

We study examples of Hermitian one-matrix models with even and odd terms present in the potential. A definition of criticality is presented which in these cases leads to multicritical models falling into the same universality classes as those of the purely even potentials. We also show that (in our examples) for polynomial potentials ending in odd powers (unbounded), the coupling constants, in addition to their expected real critical values, also admit critical values which alternate between imaginary/real values in the odd/even terms. We find that, remarkably, the ensuing statistical models are insensitive to the real/imaginary nature of these critical values. This feature may be of relevance in the recently studied connection between matrix models and the moduli space of Riemann surfaces.

scholarly journals THE FOUR-POINT FUNCTION ON A SURFACE OF INFINITE GENUS

1994 ◽  
Vol 09 (14) ◽  
pp. 1299-1307 ◽  
Author(s):  
SIMON DAVIS
Keyword(s):  
String Theory ◽  
Bosonic Strings ◽  
Infinite Number ◽  
Moduli Space ◽  
Ground State ◽  
Point Function ◽  
Intermediate States ◽  
Space Approach

The four-point function arising in the scattering of closed bosonic strings in their tachyonic ground state is evaluated on a surface of infinite genus. The amplitude has poles corresponding to physical intermediate states and divergences at the boundary of moduli space, but no new types of divergences result from the infinite number of handles. The implications for the universal moduli space approach to string theory are briefly discussed.

scholarly journals The Packing of Spheres in the Space lp

1958 ◽  
Vol 4 (1) ◽  
pp. 22-25 ◽  
Author(s):  
Jane A. C. Burlak ◽  
R. A. Rankin ◽  
A. P. Robertson
Keyword(s):  
Infinite Number ◽  
Unit Sphere ◽  
Complex Space ◽  
Infinite Sequence ◽  
Complex Numbers ◽  
The Real ◽  
The Space Lp ◽  
Fixed Radius ◽  
Image Position

A point x in the real or complex space lpis an infinite sequence,(x1, x2, x3,…) of real or complex numbers such that is convergent. Here p ≥ 1 and we writeThe unit sphere S consists of all points x ε lp for which ¶ x ¶ ≤ 1. The sphere of radius a≥ ≤ 0 and centre y is denoted by Sa(y) and consists of all points x ε lp such that ¶ x - y ¶ ≤ a. The sphere Sa(y) is contained in S if and only if ¶ y ¶≤1 - a, and the two spheres Sa(y) and Sa(z) do not overlap if and only if¶ y- z ¶≥ 2aThe statement that a finite or infinite number of spheres Sa (y) of fixed radius a can be packed in S means that each sphere Sa (y) is contained in S and that no two such spheres overlap.

scholarly journals On the Connectedness of the Real Part of Moduli Spaces of Vector Bundles on Real Algebraic Surfaces

2000 ◽  
Vol 68 (1) ◽  
pp. 41-54
Author(s):  
Edoardo Ballico
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Algebraic Surfaces ◽  
Stable Rank ◽  
Projective Surface ◽  
Chern Classes ◽  
The Real ◽  
Smooth Projective Surface ◽  
Real Algebraic Surfaces

AbstractLet X be a smooth projective surface with q(X) = 0 defined over R and M(X;r;c1;c2;H) the moduli space of H-stable rank r vector bundles on X with Chern classes c1 and c2. Assume either r = 3 and X(R) connected or r = 3 and X(R) =ø or r=2 and X(R) = ø. We prove that quite often M is connected.

scholarly journals On the real nerve of the moduli space of complex algebraic curves of even genus

2011 ◽  
Vol 55 (2) ◽  
pp. 479-494 ◽  
Author(s):  
Grzegorz Gromadzki ◽  
Ewa Kozłowska-Walania
Keyword(s):  
Moduli Space ◽  
Algebraic Curves ◽  
The Real

scholarly journals Center curves in the moduli space of the real cubic maps

1993 ◽  
Vol 69 (6) ◽  
pp. 179-184 ◽  
Author(s):  
Kiyoko Nishizawa ◽  
Asako Nojiri
Keyword(s):  
Moduli Space ◽  
The Real

scholarly journals Quantum Corrections in the Hypermultiplet Moduli Space

2000 ◽  
Vol 48 (1-3) ◽  
pp. 119-123 ◽  
Author(s):  
Holger Günther ◽  
Carl Herrmann ◽  
Jan Louis
Keyword(s):  
Moduli Space ◽  
Quantum Corrections
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