1,720,977 research outputs found
Vector-like pairs and Brill–Noether theory
No full textAbstractHow likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric and geometric phase compactification of F-theory and Heterotic dual. Quantisation of the number of generations (or net chiralities in more general term) is also discussed along the way. Self-dual nature of the fourth cohomology of Calabi–Yau fourfolds is essential for the latter issue, while we employ Brill–Noether theory to set upper bounds on the number ℓ of vector-like pairs of chiral multiplets in the SU(5)GUT (5+5¯) representations. For typical topological choices of geometry for F-theory compactification for SU(5) unification, the range of 0≤ℓ≲4 for perturbative unification is not in immediate conflict with what is already understood about F-theory compactification at this moment
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Modular parametrization as Polyakov path integral: cases with CM elliptic curves as target spaces
No full textFor an elliptic curve E over an abelian extension k/K with CM by K of Shimura type, the L-functions of its [k : K] Galois representations are Mellin transforms of Hecke theta functions; a modular parametrization (surjective map) from a modular curve to E pulls back the 1-forms on E to give the Hecke theta functions. This article refines the study of our earlier work and shows that certain class of chiral correlation functions in Type II string theory with [E](C) (E as real analytic manifold) as a target space yield the same Hecke theta functions as objects on the modular curve. The Kahler parameter of the target space [E](C) in string theory plays the role of the index (partially ordered) set in defining the projective/direct limit of modular curves
Towards Hodge Theoretic Characterizations of 2d Rational SCFTs: II
Get PDFA characterization of rational superconformal field theories (SCFTs) on 1+1
dimensions with Ricci-flat Kahler targets was proposed by S. Gukov and C. Vafa
in terms of the Hodge structure of the target space. The article
[arXiv:2205.10299] refined this idea and extracted a set of necessary
conditions for a -target N=(1,1) SCFT to be rational; only a partial
effort was made, however, to study whether it also constitutes a sufficient
condition. It turns out that the set of conditions in [arXiv:2205.10299] is not
sufficient, and that it becomes a set of necessary and sufficient conditions by
adding one more condition in the case of . The Strominger--Yau--Zaslow
fibration in the mirror correspondence plays an essential role there. At the
end, we also propose a refined version of Gukov--Vafa's idea for general
Ricci-flat Kahler target spaces.Comment: 32 pages; minor corrections in v
A note on varieties of weak CM-type
Get PDFCM-type projective varieties X of complex dimension n are characterized by
their CM-type rational Hodge structures on the cohomology groups. One may
impose such a condition in a weakest form when the canonical bundle of X is
trivial; the rational Hodge structure on the level-n subspace of is
required to be of CM-type. This brief note addresses the question whether this
weak condition implies that the Hodge structure on the entire is
of CM-type. We study in particular abelian varieties when the dimension of the
level-n subspace is two or four, and K3 . It turns out that the
answer is affirmative. Moreover, such an abelian variety is always isogenous to
a product of CM-type elliptic curves or abelian surfaces. This extends a result
of Shioda and Mitani in 1974.Comment: v2: 20+13 pages. appendix on multiple definitions of CM-type adde
A stable proton without R-parity: Implications for the LSP
No full textAbstractThe proton decays too rapidly in supersymmetric theories if a dimension-4 operator 5¯⋅10⋅5¯ exists in the superpotential. The conventional idea is to impose the R-parity to kill this operator with a stable lightest supersymmetry particle (LSP) as a direct consequence. However, the SUSY-zero mechanism is also able to kill the operator without an unbroken R-parity. In this article, we provide a firm theoretical justification for the absence of the dimension-4 proton decay operator under the SUSY-zero mechanism, by using some input from string theory. The LSP may be unstable without the R-parity and, indeed, some dimension-5 R-parity violating operators may be generated in effective theories. This suggests that the dark matter is an axion in this string theory inspired model. An insight on the SUSY-zero mechanism is also obtained
String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
Get PDFIt is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Boltzmann-weighted (qL0-c/24-weighted) sum of U(1) charges with FeiF insertion computed in the Ramond sector
Absence of Rapid Proton Decay and Origin of Low-Energy Particlesand Yukawa Couplings
Get PDFIn string theory, massless particles often originate from a symmetry breaking of a large gauge symmetry G to its subgroup H. The absence of dimension-4 proton decay in supersymmetric theories suggests that ({bar D},L) are different from {bar H}({bar 5}) in their origins. In this article, we consider a possibility that they come from different irreducible components in g/h. Requiring that all the Yukawa coupling constants of quarks and leptons be generated from the super Yang-Mills interactions of G, we found in the context of Georgi-Glashow H = SU(5) unification that the minimal choice of G is E{sub 7} and E{sub 8} is the only alternative. This idea is systematically implemented in Heterotic String, M theory and F theory, confirming the absence of dimension 4 proton decay operators. Not only H = SU(5) but also G constrain operators of effective field theories, providing non-trivial information
GUT relations from string theory compactifications
No full textAbstractWilson line on a non-simply connected manifold is a nice way to break SU(5) unified symmetry, and to solve the doublet–triplet splitting problem. This mechanism also requires, however, that the two Higgs doublets are strictly vector-like under all underlying gauge symmetries, and consequently there is a limit in a class of modes and their phenomenology for which the Wilson line can be used. An alternative is to turn on a non-flat line bundle in the U(1)Y direction on an internal manifold, which does not have to be non-simply connected. The U(1)Y gauge field has to remain in the massless spectrum, and its coupling has to satisfy the GUT relation. In string theory compactifications, however, it is not that easy to satisfy these conditions in a natural way; we call it U(1)Y problem. In this article, we explain how the problem is solved in some parts of moduli space of string theory compactifications. Two major ingredients are an extra strongly coupled U(1) gauge field and parametrically large volume for compactification, which is also essential in accounting for the hierarchy between the Planck scale and the GUT scale. Heterotic M-theory vacua and F-theory vacua are discussed. This article also shows that the toroidal orbifold GUT approach using discrete Wilson lines corresponds to the non-flat line-bundle breaking above when orbifold singularities are blown up. Thus, the orbifold GUT approach also suffers from the U(1)Y problem, and this article shows how to fix it
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