93 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
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
No full textA 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
No full textCM-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
No full textIt 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
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