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55
A Standard Model from the E8 × E8 Heterotic Superstring
, 2005
"... In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In this paper, the requisite vector bundles are formulated; spec ..."
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Cited by 41 (17 self)
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In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In this paper, the requisite vector bundles are formulated; specifically, stable, holomorphic bundles with structure group SU(N) on smooth Calabi-Yau threefolds with Z3×Z3 fundamental group. A method for computing bundle cohomology is presented and used to evaluate the cohomology groups of the standard model bundles. It is shown how to determine the Z3 × Z3 action on these groups. Finally, using an explicit method of “doublet-triplet splitting”, the low-energy particle spectrum is computed.
The spectra of heterotic standard model vacua
- JHEP
"... A formalism for determining the massless spectrum of a class of realistic heterotic string vacua is presented. These vacua, which consist of SU(5) holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental group Z2, lead to low energy theories with standard model gauge group (SU(3)C ..."
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Cited by 41 (26 self)
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A formalism for determining the massless spectrum of a class of realistic heterotic string vacua is presented. These vacua, which consist of SU(5) holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental group Z2, lead to low energy theories with standard model gauge group (SU(3)C × SU(2)L × U(1)Y)/Z6 and three families of quarks and leptons. A methodology for determining the sheaf cohomology of these bundles and the representation of Z2 on each cohomology group is given. Combining these results with the action of a Z2 Wilson line, we compute, tabulate and discuss the massless spectrum.
Standard-Model Bundles on Non-Simply Connected . . .
, 2000
"... We give a proof of the existence of G = SU(5), stable holomorphic vector bundles on elliptically fibered Calabi–Yau threefolds with fundamental group Z2. The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis ..."
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Cited by 40 (21 self)
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We give a proof of the existence of G = SU(5), stable holomorphic vector bundles on elliptically fibered Calabi–Yau threefolds with fundamental group Z2. The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We
Elliptic Calabi-Yau Threefolds with Z3 x Z3 Wilson Lines
, 2004
"... A torus fibered Calabi-Yau threefold with first homotopy group�3 �3 is constructed as a free quotient of a fiber product of two dP9 surfaces. Calabi-Yau threefolds of this type admit�3 �3 Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three gen ..."
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Cited by 36 (21 self)
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A torus fibered Calabi-Yau threefold with first homotopy group�3 ×�3 is constructed as a free quotient of a fiber product of two dP9 surfaces. Calabi-Yau threefolds of this type admit�3 ×�3 Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three generation models of particle physics with a right handed neutrino and a U(1)B−L gauge factor, in addition to the SU(3)C × SU(2)L × U(1)Y standard model gauge group. This factor helps to naturally suppress nucleon decay. The moduli space and Dolbeault cohomology of the threefold is also discussed.
Vector bundle extensions, sheaf cohomology, and the heterotic standard model
, 2005
"... Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the ..."
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Cited by 33 (21 self)
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Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic
Torus-Fibered Calabi-Yau Threefolds with non-trivial fundamental group
- JHEP 0305 (2003) 040
, 2003
"... We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP9 base, with fundamental group π1 = Z2 × Z2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a Z2 × Z2 group of automorphisms. One then cons ..."
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Cited by 26 (20 self)
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We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP9 base, with fundamental group π1 = Z2 × Z2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a Z2 × Z2 group of automorphisms. One then constructs Calabi-Yau threefolds X as the fiber product of two such dP9 surfaces, demonstrating that the involutions on the surfaces lift to a freely acting Z2 × Z2 group of automorphisms on X. The threefolds Z are then obtained as the quotient Z = X/(Z2 × Z2). These Calabi-Yau spaces Z admit stable, holomorphic SU(4) vector bundles which, in conjunction with Z2 × Z2 Wilson lines, lead to standard-like models of particle physics with naturally suppressed
Fourier–Mukai transform and mirror symmetry for D–branes on elliptic Calabi-Yau
, 2000
"... Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-fold X is seen to have an expected adiabatic form for its induced cohomology operation only when an appropriately twisted operation resp. twisted charge is defined. Some differences with the case of K3 as well ..."
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Cited by 26 (7 self)
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Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-fold X is seen to have an expected adiabatic form for its induced cohomology operation only when an appropriately twisted operation resp. twisted charge is defined. Some differences with the case of K3 as well as connections with the spectral cover construction for bundles on X are pointed out. In the context of mirror symmetry Kontsevich’s association of line bundle twists (resp. a certain ’diagonal ’ operation) with monodromies (esp. the conifold monodromy) is made explicit and checked for two example models. Interpreting this association as a relation between FM transforms and monodromies, we express the fibrewise FM transform through known monodromies. The operation of fibrewise duality as well as the notion of a certain index relevant to the computation of the moduli space of the bundle is transported to the sLag side. Finally the moduli space for D4-branes and its behaviour under the FM transform is considered with an application to the spectral cover.
Standard-model bundles
, 2002
"... We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6. We also sho ..."
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Cited by 23 (8 self)
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We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6. We also show that for each bundle V in our family, c2(Z) − c2(V) is the class of an effective curve on Z. These conditions ensure that Z and V can be used for a phenomenologically relevant compactification of Heterotic M-theory.
Gauge - mediated supersymmetry breaking in string compactifications
- JHEP
"... We provide string theory examples where a toy model of a SUSY GUT or the MSSM is embedded in a compactification along with a gauge sector which dynamically breaks supersymmetry. We argue that by changing microscopic details of the model (such as precise choices of flux), one can arrange for the domi ..."
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Cited by 22 (1 self)
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We provide string theory examples where a toy model of a SUSY GUT or the MSSM is embedded in a compactification along with a gauge sector which dynamically breaks supersymmetry. We argue that by changing microscopic details of the model (such as precise choices of flux), one can arrange for the dominant mediation mechanism transmitting SUSY breaking to the Standard Model to be either gravity mediation or gauge mediation. Systematic improvement of such examples may lead to top-down models incorporating a solution to the SUSY flavor problem.
