arXiv subjects

Timo Weigand

Publications and source records attributed to Timo Weigand.

At least 55 records · Page 3Linked to original sources

arXiv2018

6d SCFTs and U(1) Flavour Symmetries

We study the behaviour of abelian gauge symmetries in six-dimensional N=(1,0) theories upon decoupling gravity and investigate abelian flavour symmetries in the context of 6d N=(1,0) SCFTs. From a supergravity perspective, the anomaly cancellation mechanism implies that abelian gauge symmetries can only survive as global symmetries as gravity is decoupled. The flavour symmetries obtained in this way are shown to be free of ABJ anomalies, and their 't Hooft anomaly polynomial in the decoupling limit is obtained explicitly. In an F-theory realisation the decoupling of abelian gauge symmetries implies that a mathematical object known as the height pairing of a rational section is not contractible as a curve on the base of an elliptic Calabi-Yau threefold. We prove this prediction from supergravity by making use of the properties of the Mordell-Weil group of rational sections. In the second part of this paper we study the appearance of abelian flavour symmetries in 6d N=(1,0) SCFTs. We elucidate both the geometric origin of such flavour symmetries in F-theory and their field theoretic interpretation in terms of suitable linear combinations of geometrically massive U(1)s. Our general results are illustrated in various explicit examples.

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arXiv2017

The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua

We study the structure of gauge and gravitational anomalies in 2d N=(0,2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N=(1,0) and 4d N=1 theories obtained from F-theory.

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arXiv2017

Chiral 2d Theories from N=4 SYM with Varying Coupling

We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.

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arXiv2017

Algebraic Cycles and Local Anomalies in F-Theory

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in six- and four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.

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arXiv2017

Gauge Backgrounds and Zero-Mode Counting in F-Theory

Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.

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arXiv2017

The Gravitational Sector of 2d (0,2) F-theory Vacua

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S^1 reduction of the dual F-theory.

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arXiv2017

F-theory and 2d (0,2) Theories

F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.

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arXiv2016

Terminal Singularities, Milnor Numbers, and Matter in F-theory

We initiate a systematic investigation of F-theory on elliptic fibrations with singularities which cannot be resolved without breaking the Calabi-Yau condition, corresponding to $\mathbb Q$-factorial terminal singularities. It is the purpose of this paper to elucidate the physical origin of such non-crepant singularities in codimension two and to systematically analyse F-theory compactifications containing such singularities. The singularities reflect the presence of localised matter states from wrapped M2-branes which are not charged under any massless gauge potential. We identify a class of $\mathbb Q$-factorial terminal singularities on elliptically fibered Calabi-Yau threefolds for which we can compute the number of uncharged localised hypermultiplets in terms of their associated Milnor numbers. These count the local complex deformations of the singularities. The resulting six-dimensional spectra are shown to be anomaly-free. We exemplify this in a variety of cases, including models with non-perturbative gauge groups with both charged and uncharged localised matter. The underlying mathematics will be discussed further in a forthcoming publication.

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arXiv2016

G4-Flux and Standard Model Vacua in F-theory

We study the geometry of gauge fluxes in four-dimensional F-theory vacua with gauge group SU(3)xSU(2)xU(1)xU(1) and its implications for phenomenology. The models are defined by a previously introduced class of elliptic fibrations whose fibre is given as a cubic hypersurface in ${\rm Bl}_2{\mathbb P}^2$, with the non-abelian gauge group factors SU(3)xSU(2) engineered torically via the top construction. To describe gauge fluxes on these fibrations we provide a classification of the primary vertical middle cohomology group in a fashion valid for any choice of base space. Using the ideal theoretic technique of primary decomposition we compute the cohomology classes of the matter surfaces associated with states charged under the non-abelian gauge group. These expressions allow us to interpret the cancellation of the pure and mixed non-abelian anomalies geometrically as a result of the general form of the matter surfaces, without reference to a specific type of gauge flux. Explicit results for the chiral indices of all matter states are obtained in terms of intersection numbers of the base and can be directly applied to any choice of base consistent with the fibration. As a demonstration we scan for globally consistent F-theory vacua on $\mathbb P^3$, ${\rm Bl}_1\mathbb P^3$ and ${\rm Bl}_2 \mathbb{P}^3$, and find a globally consistent flux configuration with the chiral Standard Model spectrum plus an extra triplet pair, which may be lifted by a recombination process.

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arXiv2015

Fluxes in F-theory Compactifications on Genus-One Fibrations

We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5) x Z2. The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5) x U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z2 gauge anomalies as required by general consistency considerations.

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arXiv2015

Non-perturbative selection rules in F-theory

We discuss the structure of charged matter couplings in 4-dimensional F-theory compactifications. Charged matter is known to arise from M2-branes wrapping fibral curves on an elliptic or genus-one fibration Y. If a set of fibral curves satisfies a homological relation in the fibre homology, a coupling involving the states can arise without exponential volume suppression due to a splitting and joining of the M2-branes. If the fibral curves only sum to zero in the integral homology of the full fibration, no such coupling is possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral matter curves can induce a D-term which is volume suppressed. We elucidate the consequences of this pattern for the appearance of massive U(1) symmetries in F-theory and analyse the structure of discrete selection rules in the coupling sector. The weakly coupled analogue of said M2-instantons is worked out to be given by D1-F1 instantons. The generation of an exponentially suppressed F-term requires the formation of half-BPS bound states of M2 and M5-instantons. This effect and its description in terms of fluxed M5-instantons is discussed in a companion paper.

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arXiv2015

Hidden Selection Rules, M5-instantons and Fluxes in F-theory

We introduce a new approach to investigate the selection rules governing the contributions of fluxed M5-instantons to the F-theory four-dimensional effective action, with emphasis on the generation of charged matter F-terms. The structure of such couplings is unraveled by exploiting the perturbative and non-perturbative homological relations, introduced in our companion paper arXiv:1506.06764, which encode the interplay between the self-dual 3-form flux on the M5-brane, the background 4-form flux and certain fibral curves. The latter are wrapped by time-like M2-branes representing matter insertions in the instanton path integral. In particular, we clarify how fluxed M5-instantons detect the presence of geometrically massive $U(1)$s which are responsible for `hidden' selection rules. We discuss how for non-generic embeddings the M5-instanton can probe `locally massless' $U(1)$ symmetries if the rank of its Mordell-Weil group is enhanced compared to that of the bulk. As a phenomenological off-spring we propose a new type of non-perturbative corrections to Yukawa couplings which may change the rank of the Yukawa matrix. Along the way, we also gain new insights into the structure of massive $U(1)$ gauge fluxes in the stable degeneration limit.

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arXiv2015

On Discrete Symmetries and Torsion Homology in F-Theory

We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a $\mathbb Z_2$ symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a $\mathbb Z_2$ gauge symmetry. We show that the resulting five-dimensional theories do not have a $\mathbb Z_2$ symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit discrete torsion. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a $\mathbb Z_2$ symmetry in five dimensions and, accordingly, we find explicitly an associated discrete torsion. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.

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arXiv2015

Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications

We study F-Theory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genus-one fibration with a bi-section. From a four-dimensional field-theory perspective they are remnant symmetries from a Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an additional SU(5) symmetry and associated matter fields, giving a geometric prescription for calculating the induced discrete charge for the matter curves and showing the absence of Yukawa couplings that are forbidden by this charge. We present a detailed map between the field theory and the geometry, including an identification of the Higgs field and the massless states before and after the Higgsing. Finally we show that the Higgsing of the U(1) induces a G-flux which precisely accounts for the change in the Calabi-Yau Euler number so as to leave the D3 tadpole invariant.

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arXiv2014

Towards the Standard Model in F-theory

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F-theory. To this end we construct elliptic fibrations with gauge group SU(3)xSU(2)xU(1)xU(1) as suitable restrictions of a ${\rm Bl}_2{\mathbb P}^2$-fibration with rank-two Mordell-Weil group. We analyse the five inequivalent toric enhancements to gauge group SU(3)xSU(2) along two independent divisors W_3 and W_2 in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental (3,2), three types of (1,2) representations and five types of (3,1) representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero-modes in these representations depends on the 3-form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U(1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right-handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension-four and -five proton decay operators.

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arXiv2014

D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation

We analyze the quantum-corrected moduli space of D7-brane position moduli with special emphasis on inflationary model building. D7-brane deformation moduli are key players in two recently proposed inflationary scenarios: The first, D7-brane chaotic inflation, is a variant of axion monodromy inflation which allows for an effective 4d supergravity description. The second, fluxbrane inflation, is a stringy version of D-term hybrid inflation. Both proposals rely on the fact that D7-brane coordinates enjoy a shift-symmetric Kahler potential at large complex structure of the Calabi-Yau threefold, making them naturally lighter than other fields. This shift symmetry is inherited from the mirror-dual Type IIA Wilson line on a D6-brane at large volume. The inflaton mass can be provided by a tree-level term in the flux superpotential. It induces a monodromy and, if tuned to a sufficiently small value, can give rise to a large-field model of inflation. Alternatively, by a sensible flux choice one can completely avoid a tree-level mass term, in which case the inflaton potential is induced via loop corrections. The positive vacuum energy can then be provided by a D-term, leading to a small-field model of hybrid natural inflation. In the present paper, we continue to develop a detailed understanding of the D7-brane moduli space focusing among others on shift-symmetry-preserving flux choices, flux-induced superpotential in Type IIB/F-theory language, and loop corrections. While the inflationary applications represent our main physics motivation, we expect that some of our findings will be useful for other phenomenological issues involving 7-branes in Type IIB/F-theory constructions.

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arXiv2014

Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory

We study the global structure of the gauge group $G$ of F-theory compactified on an elliptic fibration $Y$. The global properties of $G$ are encoded in the torsion subgroup of the Mordell-Weil group of rational sections of $Y$. Generalising the Shioda map to torsional sections we construct a specific integer divisor class on $Y$ as a fractional linear combination of the resolution divisors associated with the Cartan subalgebra of $G$. This divisor class can be interpreted as an element of the refined coweight lattice of the gauge group. As a result, the spectrum of admissible matter representations is strongly constrained and the gauge group is non-simply connected. We exemplify our results by a detailed analysis of the general elliptic fibration with Mordell-Weil group $\mathbb Z_2$ and $\mathbb Z_3$ as well as a further specialization to $\mathbb Z \oplus \mathbb Z_2$. Our analysis exploits the representation of these fibrations as hypersurfaces in toric geometry.

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arXiv2014

Towards large r from [p,q]-inflation

The recent discovery of B-mode polarizations in the CMB by the BICEP2 collaboration motivates the study of large-field inflation models which can naturally lead to significant tensor-to-scalar ratios. A class of such models in string theory are axion monodromy models, where the shift symmetry of an axion is broken by some branes. In type IIB string theory such models so far utilized NS5 branes which lead to a linear potential with an induced tensor-to-scalar ratio of $r \sim 0.07$. In this short note we study a modification of the scenario to include [p,q] 7-branes and show that this leads to an enhanced tensor-to-scalar ratio $r \sim 0.14$. Unlike 5-branes, 7-branes are in-principle compatible with supersymmetry, however we find that an implementation of the inflationary scenario requires an explicit breaking of supersymmetry by the 7-branes during inflation. This leads to similar challenges as in 5-brane models. We discuss the relation to high-scale supersymmetry breaking after inflation.

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