STRING COSMOLOGY

2000 ◽  
Vol 15 (12) ◽  
pp. 1707-1756 ◽  
Author(s):  
G. V. KRANIOTIS
Keyword(s):  
String Theory ◽  
Modular Forms ◽  
Big Bang ◽  
String Cosmology ◽  
Target Space ◽  
Modular Invariant ◽  
Heisenberg Uncertainty Principle ◽  
Duality Symmetry ◽  
Cosmological Inflation ◽  
String Models

In this work, we review recent work on string cosmology. The need for an inflationary era is well known. Problems of Standard Cosmology such as horizon, flatness, monopole and entropy find an elegant solution in the inflationary scenario. On the other hand no adequate inflationary model has been constructed so far. In this review we discuss the attempts that have been made in the field of string theory for obtaining an adequate Cosmological Inflationary Epoch. In particular, orbifold compactifications of string theory which are constrained by target-space duality symmetry offer as natural candidates for the role of inflatons the orbifold moduli. Orbifold moduli dynamics is very constrained by duality symmetry and offers a concrete framework for discussing Cosmological Inflation. We discuss the resulting cosmology assuming that nonperturbative dynamics generates a moduli potential which respects target-space modular invariance. Various modular forms for the nonperturbative superpotential and Kähler potential which include the absolute modular invariant j(T) besides the Dedekind eta function η(T) are discussed. We also review scale-factor duality and pre-Big-Bang scenarios in which inflation is driven by the kinetic terms of the dilaton modulus. In this context we discuss the problem of graceful exit and review recent attempts for solving the problem of exiting from inflation. The possibility of obtaining inflation through the D-terms in string models with anomalous UA(1) and other Abelian factors is reviewed. In this context we discuss how the slow-roll problem in supergravity models with F-term inflation can be solved by D-term inflation. We also briefly review the consequences of duality for a generalized Heisenberg uncertainty principle and the structure of space–time at short scales. The problem of the Cosmological Constant is also briefly discussed.

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 KÄHLER STABILIZED, MODULAR INVARIANT HETEROTIC STRING MODELS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1451-1588 ◽  
Author(s):  
MARY K. GAILLARD ◽  
BRENT D. NELSON
Keyword(s):  
Heterotic String ◽  
Target Space ◽  
Modular Invariant ◽  
Heterotic String Theory ◽  
Effective Lagrangian ◽  
Parity Conservation ◽  
Weakly Coupled ◽  
String Models ◽  
Early Universe Cosmology

We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kähler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Binétruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed.

scholarly journals STRONG–WEAK COUPLING DUALITY IN FOUR-DIMENSIONAL STRING THEORY

1994 ◽  
Vol 09 (21) ◽  
pp. 3707-3750 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
String Theory ◽  
Weak Coupling ◽  
Bound States ◽  
Target Space ◽  
Duality Transformation ◽  
Heterotic String Theory ◽  
Yukawa Couplings ◽  
Duality Symmetry ◽  
The Relationship ◽  
Electrically Charged

We present several pieces of evidence for strong–weak coupling duality symmetry in the heterotic string theory, compactified on a six-dimensional torus. They include symmetry of the (1) low energy effective action, (2) allowed spectrum of electric and magnetic charges in the theory, (3) allowed mass spectrum of particles saturating the Bogomol'nyi bound, and (4) Yukawa couplings between massless neutral particles and massive charged particles saturating the Bogomol'nyi bound. This duality transformation exchanges the electrically charged elementary string excitations with the magnetically charged soliton states in the theory. It is shown that the existence of a strong–weak coupling duality symmetry in four-dimensional string theory makes definite predictions about the existence of new stable monopole and dyon states in the theory with specific degeneracies, including certain supersymmetric bound states of monopoles and dyons. The relationship between strong–weak coupling duality transformation in string theory and target space duality transformation in the five-brane theory is also discussed.

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 Modular invariant models of leptons at level 7

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Gui-Jun Ding ◽  
Stephen F. King ◽  
Cai-Chang Li ◽  
Ye-Ling Zhou
Keyword(s):  
Modular Forms ◽  
Galois Field ◽  
Special Linear Group ◽  
Type I ◽  
Time Level ◽  
Projective Special Linear Group ◽  
Modular Invariant ◽  
Seesaw Mechanism ◽  
Linearly Independent ◽  
First Time

Abstract We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group Γ7, which is isomorphic to PSL(2, Z7), the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as PSL2(7) or Σ(168). At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of Γ7. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on Γ7 are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.

scholarly journals The pre-big bang scenario in string cosmology

2003 ◽  
Vol 373 (1-2) ◽  
pp. 1-212 ◽  
Author(s):  
M. Gasperini ◽  
G. Veneziano
Keyword(s):  
Big Bang ◽  
String Cosmology

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

scholarly journals Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fabian Fischbach ◽  
Albrecht Klemm ◽  
Christoph Nega
Keyword(s):  
String Duality ◽  
Modular Forms ◽  
Black Hole Entropy ◽  
Siegel Modular Forms ◽  
Partition Functions ◽  
Twisted Sector ◽  
Duality Symmetry ◽  
Iwahori Subgroup ◽  
M Theory ◽  
Bonnet Term

Abstract Motivated by recent advances in Donaldson-Thomas theory, four-dimensional $$ \mathcal{N} $$ N = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of “untwisted” quarter-BPS dyons in the heterotic ℤ2 CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) ⊂ Sp4(ℤ) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 × T2)/ℤ2, as suggested by string duality with type IIA theory on X.

scholarly journals Computational Tools for Cohomology of Toric Varieties

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Ralph Blumenhagen ◽  
Benjamin Jurke ◽  
Thorsten Rahn
Keyword(s):  
Software Package ◽  
Computational Algorithm ◽  
Toric Varieties ◽  
Dual Pair ◽  
Target Space ◽  
Toric Geometry ◽  
Computational Tools ◽  
String Compactifications ◽  
String Models

Novel nonstandard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle-valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software packagecohomCalg, its utility is highlighted on a new target space dual pair of(0,2)heterotic string models.

scholarly journals Target space duality in string theory

1994 ◽  
Vol 244 (2-3) ◽  
pp. 77-202 ◽  
Author(s):  
Amit Giveon ◽  
Massimo Porrati ◽  
Eliezer Rabinovici
Keyword(s):  
String Theory ◽  
Target Space
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