arXiv subjects

Thomas W. Grimm

Publications and source records attributed to Thomas W. Grimm.

At least 73 records · Page 4Linked to original sources

arXiv2014

On M-theory fourfold vacua with higher curvature terms

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kahler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions.

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arXiv2014

Axion Inflation in F-theory

We study the dynamics of axion-like fields in F-theory and suggest that they can serve as inflatons in models of natural inflation. The axions arise from harmonic three-forms on the F-theory compactification space and parameterize a complex torus that varies over the geometric moduli space. In particular, this implies that the axion decay constants depend on the complex structure moduli that can be fixed by background fluxes. This might allow tuning them to be super-Planckian in a controlled way and allow for interesting single field inflationary models. We argue that this requires a localization of the three-forms near regions of strong string coupling, analogously to the reasoning that GUT physics requires the use of F-theory. These models can admit a tensor to scalar ratio r>0.1.

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arXiv2014

Self-Dual Tensors and Partial Supersymmetry Breaking in Five Dimensions

We study spontaneous supersymmetry breaking of five-dimensional supergravity theories from sixteen to eight supercharges in Minkowski vacua. This N=4 to N=2 breaking is induced by Abelian gaugings that require the introduction of self-dual tensor fields accompanying the vectors in the gravity multiplet and vector multiplets. These tensor fields have first-order kinetic terms and can become massive by a Stueckelberg-like mechanism. We identify the general class of N=2 vacua and show how the N=4 spectrum splits into massless and massive N=2 multiplets. In particular, we find a massive gravitino multiplet, containing two complex massive tensors, and a number of massive tensor multiplets and hypermultiplets. We determine the resulting N=2 effective action for the massless multiplets obtained by integrating out massive fields. We show that the metric and Chern-Simons terms of the vectors are corrected at one-loop by massive tensors as well as spin-1/2 and spin-3/2 fermions. These contributions are independent of the supersymmetry-breaking scale and thus have to be included at arbitrarily low energies.

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arXiv2013

From M-theory higher curvature terms to α' corrections in F-theory

We perform a Kaluza-Klein reduction of eleven-dimensional supergravity on a Calabi-Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional N=2 effective action. We focus on the effective Einstein-Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kahler potential and complex coordinates. The classical expressions for the Kahler coordinates are non-trivially modified, while the functional form of the Kahler potential is shown to be uncorrected. For elliptically fibered Calabi-Yau fourfolds the corrections can be uplifted to a four-dimensional F-theory compactification. We argue that also the four-dimensional N=1 Kahler coordinates receive non-trivial corrections. We find a simple expression for the induced corrections for different Abelian and non-Abelian seven-brane configurations by scanning over many Calabi-Yau fourfolds with resolved singularities. The interpretation of this expression leads us to conjecture that the higher-curvature corrections correspond to α'^2 corrections that arise from open strings at the self-intersection of seven-branes.

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arXiv2013

On α' corrections in N=1 F-theory compactifications

We consider N=1 F-theory and Type IIB orientifold compactifications and derive new α' corrections to the four-dimensional effective action. They originate from higher derivative corrections to eleven-dimensional supergravity and survive the M-theory to F-theory limit. We find a correction to the Kahler moduli depending on a non-trivial intersection curve of seven-branes. We also analyze a four-dimensional higher curvature correction.

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arXiv2013

F-Theory on Spin(7) Manifolds: Weak-Coupling Limit

F-theory on appropriately fibered Spin(7) holonomy manifolds is defined to arise as the dual of M-theory on the same space in the limit of a shrinking fiber. A class of Spin(7) orbifolds can be constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic involution. The F-theory dual then exhibits one macroscopic dimension that has the topology of an interval. In this work we study the weak-coupling limit of a subclass of such constructions and identify the objects that arise in this limit. On the Type IIB side we find space-time filling O7-planes as well as O5-planes and orbifold five-planes with a (-1)^{F_L} factor localised on the interval boundaries. These orbifold planes are referred to as X5-planes and are S-dual to a D5-O5 system. For other involutions exotic O3-planes and X3-planes on top of a six-dimensional orbifold singularity can appear. We show that the objects present preserve a mutual supersymmetry of four supercharges in the bulk of the interval and two supercharges on the boundary. It follows that in the infinite-interval and weak-coupling limit full four-dimensional N=1 supersymmetry is restored, which on the Type IIA side corresponds to an enhancement of supersymmetry by winding modes in the vanishing interval limit.

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arXiv2013

Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors

An algorithm to systematically construct all Calabi-Yau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors. The basic data consists of a top over each toric divisor in the base together with compactification data giving the embedding into a reflexive polytope. The allowed choices of compactification data are integral points in an auxiliary polytope. In order to ensure the existence of a low-energy gauge theory, the elliptic fibration must be flat, which is reformulated into conditions on the top and its embedding. In particular, flatness of SU(5) fourfolds imposes additional linear constraints on the auxiliary polytope of compactifications, and is therefore non-generic. Abelian gauge symmetries arising in toric F-theory compactifications are studied systematically. Associated to each top, the toric Mordell-Weil group determining the minimal number of U(1) factors is computed. Furthermore, all SU(5)-tops and their splitting types are determined and used to infer the pattern of U(1) matter charges.

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arXiv2013

Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds

We propose a novel approach to obtain non-supersymmetric four-dimensional effective actions by considering F-theory on manifolds with special holonomy Spin(7). To perform such studies we suggest that a duality relating M-theory on a certain class of Spin(7) manifolds with F-theory on the same manifolds times an interval exists. The Spin(7) geometries under consideration are constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic and isometric involution. The three-dimensional minimally supersymmetric effective action of M-theory on a general Spin(7) manifold with fluxes is determined and specialized to the aforementioned geometries. This effective theory is compared with an interval Kaluza-Klein reduction of a non-supersymmetric four-dimensional theory with definite boundary conditions for all fields. Using this strategy a minimal set of couplings of the four-dimensional low-energy effective actions is obtained in terms of the Spin(7) geometric data. We also discuss briefly the string interpretation in the Type IIB weak coupling limit.

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arXiv2013

New Global F-theory GUTs with U(1) symmetries

We construct global F-theory GUTs with SU(5) x U(1) gauge group defined by specifying a fully resolved Calabi-Yau fourfold and consistent four-form G-flux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1) does not follow from an underlying higgsed E8 gauge group (2) leaves the class of theories that can be analyzed with current split-spectral cover techniques. This avoids recently proposed no-go theorems for models with hypercharge flux, as required to break the GUT group. The appearance of additional fields is related geometrically to considering a more general class of sections and 4-1 splits. We show explicitly that the four-dimensional chiral matter index can still be computed using three-dimensional one-loop Chern-Simons terms.

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arXiv2013

Effective action of 6D F-Theory with U(1) factors: Rational sections make Chern-Simons terms jump

We derive the six-dimensional (1,0) effective action arising from F-theory on an elliptically fibered Calabi-Yau threefold with multiple sections. The considered theories admit both non-Abelian and Abelian gauge symmetries. Our derivation employs the M-theory to F-theory duality in five-dimensions after circle reduction. Five-dimensional gauge and gravitational Chern-Simons terms are shown to arise at one-loop by integrating out massive Coulomb branch and Kaluza-Klein modes. In the presence of a non-holomorphic zero section, we find an improved systematic for performing the F-theory limit by using the concept of the extended relative Mori cone. In this situation Kaluza-Klein modes can become lighter than Coulomb branch modes and a jump in the Chern-Simons levels occurs. By determining Chern-Simons terms for various threefold examples we are able to compute the complete six-dimensional charged matter spectrum and show consistency with six-dimensional anomalies.

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arXiv2013

Exploring 6D origins of 5D supergravities with Chern-Simons terms

We consider five-dimensional supergravity theories with eight or sixteen supercharges with Abelian vector fields and ungauged scalars. We address the question under which conditions these theories can be interpreted as effective low energy descriptions of circle reductions of anomaly free six-dimensional theories with (1,0) or (2,0) supersymmetry. We argue that classical and one-loop gauge- and gravitational Chern-Simons terms are instrumental for this question.

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arXiv2013

Gauged supergravities and their symmetry-breaking vacua in F-theory

We first derive a class of six-dimensional (1,0) gauged supergravities arising from threefold compactifications of F-theory with background fluxes. The derivation proceeds via the M-theory dual reduction on an SU(3)-structure manifold with four-form G_4-flux. We then show that vacuum solutions of these six-dimensional theories describes four-dimensional flat space times a compact two-dimensional internal space with additional localized sources. This induces a spontaneous compactification to four space-time dimensions and breaks the supersymmetry from N=2 to N=1, which allows the reduced theory to have a four-dimensional chiral spectrum. We perform the reduction explicitly and derive the N=1 characteristic data of the four-dimensional effective theory. The match with fourfold reductions of F-theory is discussed and many of the characteristic features are compared. We comment, in particular, on warping effects and one-loop Chern-Simons terms generically present in four-dimensional F-theory reductions.

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arXiv2013

One-loop Chern-Simons terms in five dimensions

We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons terms induced by integrating out charged massive fields. The considered massive fields are spin-1/2 and spin-3/2 fermions, as well as complex two-forms with first order kinetic terms. Consistency with six-dimensional gravitational anomalies of (1,0) and (2,0) theories is shown by interpreting the massive fields as excited Kaluza-Klein modes in a circle compactification. The results are in accordance with the geometric predictions of the M-theory to F-theory duality as well as the comparison with an explicit one-loop computation in heterotic string theory compactified on K3 x S^1.

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arXiv2012

Anomaly Cancellation And Abelian Gauge Symmetries In F-theory

We study 4D F-theory compactifications on singular Calabi-Yau fourfolds with fluxes. The resulting N=1 effective theories can admit non-Abelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized Green-Schwarz mechanism. This requires the study of 3D N=2 theories obtained by a circle compactification and their M-theory duals. Reducing M-theory on resolved Calabi-Yau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D one-loop corrections of these massive states induce Chern-Simons terms. All 4D anomalies are captured by the one-loop terms. The ones corresponding to the mixed gauge-gravitational anomalies depend on the Kaluza-Klein vector and are induced by integrating out Kaluza-Klein modes of the U(1) charged matter. In M-theory all Chern-Simons terms classically arise from G_4-flux. We find that F-theory fluxes implement automatically the 4D Green-Schwarz mechanism if non-trivial geometric relations for the resolved Calabi-Yau fourfold are satisfied. We confirm these relations in various explicit examples and elucidate the general construction of U(1) symmetries in F-theory. We also compare anomaly cancellation in F-theory with its analog in Type IIB orientifold setups.

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arXiv2012

Non-Abelian Tensor Towers and (2,0) Superconformal Theories

With the aim to study six-dimensional (2,0) superconformal theories with non-Abelian tensor multiplets we propose a five-dimensional superconformal action with eight supersymmetries for an infinite tower of non-Abelian vector, tensor and hypermultiplets. It describes the dynamics of the complete spectrum of the (2,0) theories compactified on a circle coupled to an additional vector multiplet containing the circle radius and the Kaluza-Klein vector arising from the six-dimensional metric. All couplings are only given in terms of group theoretical constants and the Kaluza-Klein levels. After superconformal symmetry is reduced to Poincare supersymmetry we find a Kaluza-Klein inspired action coupling super-Yang-Mills theory to an infinite tower of massive non-Abelian tensors. We explore the possibility to restore sixteen supersymmetries by using techniques known from harmonic superspace. Namely, additional bosonic coordinates on a four-sphere are introduced to enhance the R-symmetry group. Maximally supersymmetric Yang-Mills theories and the Abelian (2,0) tensor theories are recovered as special cases of our construction. Finally, we comment on the generation of an anomaly balancing Wess-Zumino term for the R-symmetry vector at one loop.

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arXiv2012

Structure in 6D and 4D N=1 supergravity theories from F-theory

We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the Green-Schwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.

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arXiv2012

A Kaluza-Klein inspired action for chiral p-forms and their anomalies

The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza-Klein reduction on a circle. The massless modes are (p-1)-forms with standard kinetic terms and Chern-Simons couplings to the Kaluza-Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza-Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stueckelberg-like mechanism using (p-1)-forms. A Chern-Simons term for the Kaluza-Klein vector is generated at one loop by massive p-form modes. These findings are shown to be consistent with anomalies and supersymmetry for six-dimensional supergravity theories with chiral tensor multiplets.

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arXiv2012

Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds

The six-dimensional effective action of F-theory compactified on a singular elliptically fibred Calabi-Yau threefold is determined by using an M-theory lift. The low-energy data are derived by comparing a circle reduction of a general six-dimensional (1,0) gauged supergravity theory with the effective action of M-theory on the resolved Calabi-Yau threefold. The derivation includes six-dimensional tensor multiplets for which the (anti-) self-duality constraints are imposed on the level of the five-dimensional action. The vector sector of the reduced theory is encoded by a non-standard potential due to the Green-Schwarz term in six dimensions. This Green-Schwarz term also contains higher curvature couplings which are considered to establish the full map between anomaly coefficients and geometry. F-/M-theory duality is exploited by moving to the five-dimensional Coulomb branch after circle reduction and integrating out massive vector multiplets and matter hypermultiplets. The associated fermions then generate additional Chern-Simons couplings at one-loop. Further couplings involving the graviphoton are induced by quantum corrections due to excited Kaluza-Klein modes. On the M-theory side integrating out massive fields corresponds to resolving the singularities of the Calabi-Yau threefold, and yields intriguing relations between six-dimensional anomalies and classical topology.

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