Algebraic description of G‐flux in F‐theory: new techniques for F‐theory phenomenology

Shaneson

2015

Commun. Math. Phys.

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even nonabelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in F-theory, to study non-abelian gauge symmetry. Since this branch of the moduli space also exists in the defining M-theory compactification, it provides the only known description of gauge theory states which exists in both pictures; they are string junctions in F-theory. We discuss how global deformations give rise to local deformations, and also give examples where local deformation can be utilized even in models where a global deformation does not exist. Utilizing deformations, we study a number of new examples, including non-perturbative descriptions of SU (3) and SU (2) gauge theories on seven-branes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these non-perturbative descriptions do not exist for higher rank SU (N ) theories.

Section: Introductionmentioning

confidence: 99%

Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-Theory

Grassi

Shaneson

2015

Commun. Math. Phys.

Section: Introductionmentioning

confidence: 99%

“…U (1) symmetries [50][51][52][53][54][55][56], instanton corrections [42,52,[57][58][59][60][61][62][63][64], and chirality inducing G 4 -flux [52,[64][65][66][67][68][69][70][71][72][73][74][75][76]; there has also been progress in understanding the landscape of six-dimensional F-theory compactifications [54,[77][78][79][80]. Singularity resolution was utilized heavily in many of these works.…”

mentioning

confidence: 99%

Matter from geometry without resolution

Grassi

Shaneson

2013

J. High Energ. Phys.

129

We utilize the deformation theory of algebraic singularities to study charged matter in compactifications of M-theory, F-theory, and type IIa string theory on elliptically fibered Calabi-Yau manifolds. In Ftheory, this description is more physical than that of resolution. We describe how two-cycles can be identified and systematically studied after deformation. For ADE singularities, we realize non-trivial ADE representations as sublattices of Z N , where N is the multiplicity of the codimension one singularity before deformation. We give a method for the determination of Picard-Lefschetz vanishing cycles in this context and utilize this method for one-parameter smooth deformations of ADE singularities. We give a general map from junctions to weights and demonstrate that Freudenthal's recursion formula applied to junctions correctly reproduces the structure of high-dimensional ADE representations, including the 126 of SO(10) and the 43,758 of E 6 . We identify the Weyl group action in some examples, and verify its order in others. We describe the codimension two localization of matter in F-theory in the case of heterotic duality or simple normal crossing and demonstrate the branching of adjoint representations. Finally, we demonstrate geometrically that deformations correctly reproduce the appearance of non-simply-laced algebras induced by monodromy around codimension two singularities, showing the reduction of D 4 to G 2 in an example. A companion mathematical paper will follow. IntroductionThe spectrum of particles which exist in Nature is detailed and rich. The quarks and leptons of the standard model of particle physics fill out non-trivial representations of the Lie algebra SU (3) × SU (2) × U (1), and these can be embedded into representations of higher rank groups, such as the 10 + 5 + 1 of SU (5) or the 16 of SO(10). Exotic particle representations are often introduced in phenomenologically motivated extensions of the standard model, sometimes of high dimension in grand unified theories.An important physical question is whether there exist theoretical constraints on the allowed particle representations. Though anomaly cancellation provides constraints on sets of fields in gauge theories, no individual representation is ruled out on theoretical grounds. By contrast, the possibilities 1 are more limited in four-dimensional compactifications of string theory, F-theory, and M-theory. For example, in the heterotic string matter representations typically arise from branching the adjoint of E 8 ; in weakly coupled type II string theory U (N ) gauge theories admit bifundamental, symmetric tensor, and antisymmetric tensor representations, together with their conjugates; in weakly coupled orientifold compactifications it is not possible to realize the phenomenologically relevant 16 of SO(10).Interestingly, more possibilities can be realized outside of the weakly coupled regime in M-theory [1] or F-theory [2]. In these theories massless matter representations are encoded in the structure of a singular compactificati...

“…This approach to GUT model building uniquely combines two advantages of the heterotic and type II superstrings, giving rise to interesting GUT physics through the presence of exceptional gauge structures while localizing the gauge degrees of freedom in the internal space. In addition to many works on local model-building, there have been many attempts to construct global models [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and properly understand chirality inducing G 4 -flux [29][30][31][32][33][34][35][36][37][38][39] and abelian symmetries [30,[40][41][42][43]. A proper understanding of chirality inducing flux and abelian symmetries is crucial for the understanding of instanton physics in the weakly coupled type IIb limit, and given the recent progress on these issues in F-theory one would hope to understand F-theoretic instantons in this light.…”

Section: Introductionmentioning

confidence: 99%

On seven-brane dependent instanton prefactors in F-theory

Cvetič

Donagi

et al. 2012

J. High Energ. Phys.

We study the moduli-dependent prefactor of M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications. In light of the M-theory and type IIb limits and also heterotic duality, we propose that the explicit moduli dependence of the prefactor can be computed by a study of zero modes localized at intersections between the instanton and seven-branes. We present an instanton prefactor in an E 6 F-theory GUT which does not admit a heterotic dual and show that it vanishes if and only if a point of E 8 enhancement is present in the instanton worldvolume. More generically, we discuss the relationship between points of E 8 and superpotential zeroes and give sufficient conditions for such a point to cause a zero, even for an SU (5) GUT. We scan a large class of compactifications for instanton physics and demonstrate that many instantons have the same prefactor structure. We discuss the associated implications and complications for moduli stabilization. We present an explicit resolution and construction of G-flux in a generic E 6 GUT and identify a global compactification of the local model spectral cover which happens to facilitate prefactor computations. Via a Leray spectral sequence, we demonstrate the relationship between right-movers of heterotic worldsheet instantons, 3-3 strings of euclidean D3 instantons, and the Fermi zero modes of M5-instantons.