scholarly journals D-instantons in Type IIA string theory on Calabi-Yau threefolds

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sergei Alexandrov ◽  
Ashoke Sen ◽  
Bogdan Stefański
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Mirror Symmetry ◽  
Homology Class ◽  
World Sheet ◽  
Perfect Agreement ◽  
Duality Symmetry ◽  
To Receive ◽  
Perturbative Corrections

Abstract Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.

scholarly journals Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sergei Alexandrov ◽  
Ashoke Sen ◽  
Bogdan Stefański
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Large Volume ◽  
Mirror Symmetry ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Perfect Agreement ◽  
Type Iib String Theory

Abstract We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

scholarly journals ON THE EVALUATION OF COMPTON SCATTERING AMPLITUDES IN STRING THEORY

1998 ◽  
Vol 13 (27) ◽  
pp. 4717-4757 ◽  
Author(s):  
ANDREA PASQUINUCCI ◽  
MICHELA PETRINI
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Moduli Space ◽  
Modular Forms ◽  
String Model ◽  
World Sheet ◽  
Electron Positron ◽  
The World ◽  
Spin Fields ◽  
Compton Amplitude

We consider the Compton amplitude for the scattering of a photon and an (massless) "electron/positron" at one loop (i.e. genus 1) in a four-dimensional fermionic heterotic string model. Starting from the bosonization of the world sheet fermions needed to explicitly construct the spin fields representing the space–time fermions, we present all the steps of the computation which leads to the explicit form of the amplitude as an integral of modular forms over the moduli space.

scholarly journals The eclectic flavor symmetry of the ℤ2 orbifold

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Alexander Baur ◽  
Moritz Kade ◽  
Hans Peter Nilles ◽  
Saúl Ramos-Sánchez ◽  
Patrick K. S. Vaudrevange
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Particle Physics ◽  
Mirror Symmetry ◽  
Modular Group ◽  
Complex Structure ◽  
Flavor Symmetry ◽  
Two Dimensional ◽  
Flavor Symmetries

Abstract Modular symmetries naturally combine with traditional flavor symmetries and $$ \mathcal{CP} $$ CP , giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ℤ2 orbifold, which is equipped with two modular symmetries SL(2, ℤ)T and SL(2, ℤ)U associated with two moduli: the Kähler modulus T and the complex structure modulus U. The resulting finite modular group is ((S3× S3) ⋊ ℤ4) × ℤ2 including mirror symmetry (that exchanges T and U) and a generalized $$ \mathcal{CP} $$ CP -transformation. Together with the traditional flavor symmetry (D8× D8)/ℤ2, this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and $$ \left\langle T\right\rangle =\left\langle U\right\rangle =\exp \left(\frac{\pi \mathrm{i}}{3}\right) $$ T = U = exp π i 3 . This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

DUALITY IN STRING THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360003
Author(s):  
YOLANDA LOZANO
Keyword(s):  
String Theory ◽  
Recent Work ◽  
Moduli Space ◽  
Target Space ◽  
Duality Symmetry ◽  
Abelian Case ◽  
Superstring Theories ◽  
M Theory

Duality symmetries have played a key role in the discovery that the five consistent superstring theories in 10 dimensions emerge as different corners of the moduli space of a single unifying theory, known as M-theory. Focusing on the target space, or T, duality symmetry, we show how it can be formulated in spacetimes with abelian and non-abelian isometries. Finally, we discuss some recent work that realizes non-abelian T-duality as a consistent truncation to seven-dimensional supergravity, thus generalizing to the non-abelian case the realization of abelian T-duality at the supergravity level.

scholarly journals DUALITY AND SELF-DUAL TRIPLET SOLUTIONS IN EUCLIDEAN GRAVITY

1996 ◽  
Vol 11 (34) ◽  
pp. 2669-2679
Author(s):  
SWAPNA MAHAPATRA
Keyword(s):  
String Theory ◽  
The Self ◽  
Target Space ◽  
De Sitter ◽  
Gravitational Instanton ◽  
Duality Symmetry ◽  
Sitter Solution

Starting from the self-dual “triplet” of gravitational instanton solutions in Euclidean gravity, we obtain the corresponding instanton solutions in string theory by making use of the target space duality symmetry. We show that these dual triplet solutions can be obtained from the general dual Taub-NUT de Sitter solution through some limiting procedure as in the Euclidean gravity case. The dual gravitational instanton solutions obtained here are self-dual for some cases, with respect to certain isometries, but not always.

scholarly journals Moduli spaces of non-geometric type II/heterotic dual pairs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Yoan Gautier ◽  
Dan Israël
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Type Ii ◽  
Duality Group ◽  
Dual Pairs ◽  
Perturbative Correction ◽  
Singularity Structure ◽  
Four Dimensions ◽  
Geometric Type ◽  
Perturbative Corrections

Abstract We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

K3 surfaces from configurations of six lines in $\mathbb{P}^{2}$ and mirror symmetry II—$\lambda _{K3}$-functions

2019 ◽  
Author(s):  
Shinobu Hosono ◽  
Bong H Lian ◽  
Shing-Tung Yau
Keyword(s):  
Moduli Space ◽  
Mirror Symmetry ◽  
Theta Functions ◽  
K3 Surfaces ◽  
Double Cover ◽  
Special Boundary ◽  
Higher Dimensional ◽  
Genus 2 ◽  
Local Solutions

Abstract We continue our study on the hypergeometric system $E(3,6)$ that describes period integrals of the double cover family of K3 surfaces. Near certain special boundary points in the moduli space of the K3 surfaces, we construct the local solutions and determine the so-called mirror maps expressing them in terms of genus 2 theta functions. These mirror maps are the K3 analogues of the elliptic $\lambda $-function. We find that there are two nonisomorphic definitions of the lambda functions corresponding to a flip in the moduli space. We also discuss mirror symmetry for the double cover K3 surfaces and their higher dimensional generalizations. A follow-up paper will describe more details of the latter.

scholarly journals Moduli Space in Homological Mirror Symmetry

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Matsuo Sato
Keyword(s):  
Elliptic Curve ◽  
Configuration Space ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Feynman Diagrams ◽  
Holomorphic Curves ◽  
Homological Mirror Symmetry

We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the A∞ structure of the both models.

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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