arXiv subjects

Roberto Valandro

Publications and source records attributed to Roberto Valandro.

At least 37 records · Page 2Linked to original sources

arXiv2019

High electric charges in M-theory from quiver varieties

M-theory on a Calabi-Yau threefold admitting a small resolution gives rise to an Abelian vector multiplet and a charged hypermultiplet. We introduce into this picture a procedure to construct threefolds that naturally host matter with electric charges up to six. These are built as families of Du Val ADE surfaces (or ALE spaces), and the possible charges correspond to the Dynkin labels of the adjoint of the ADE algebra. In the case of charge two, we give a new derivation of the answer originally obtained by Curto and Morrison, and explicitly relate this construction to the Morrison-Park geometry. We also give a procedure for constructing higher-charge cases, which can often be applied to F-theory models.

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arXiv2018

Counting Associatives in Compact $G_2$ Orbifolds

We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M-theory compactifications. Under a chain of dualities, these can be mapped to F-theory on a Calabi-Yau fourfold, and we find that they are dual to an example studied by Donagi, Grassi and Witten. Finally, we give two different descriptions of our main example and the associative submanifolds as a twisted connected sum.

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arXiv2018

High U(1) charges in type IIB models and their F-theory lift

We construct models with U(1) gauge group and matter with charges up to 6, in the context of type IIB compactifications. We show explicitly that models with charges up to 4 can be derived from corresponding models in F-theory by applying the Sen weak coupling limit. We derive which type IIB models should be the limit of charge 5 and 6 F-theory models. Explicit six dimensional type IIB models with maximal charge 5 and 6 are constructed on an algebraic K3 surface that is the double cover of $\mathbb{CP}^2$. By using type IIB results we are also able to rediscover the F-theory charge 4 model in a straightforward way.

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arXiv2018

Geometric engineering on flops of length two

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example, which we affectionately think of as the $\it{conifold\ 2.0}$. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer's example.

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arXiv2017

Global Orientifolded Quivers with Inflation

We describe global embeddings of fractional D3 branes at orientifolded singularities in type IIB flux compactifications. We present an explicit Calabi-Yau example where the chiral visible sector lives on a local orientifolded quiver while non-perturbative effects, $α'$ corrections and a T-brane hidden sector lead to full closed string moduli stabilisation in a de Sitter vacuum. The same model can also successfully give rise to inflation driven by a del Pezzo divisor. Our model represents the first explicit Calabi-Yau example featuring both an inflationary and a chiral visible sector.

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arXiv2017

T-branes, monopoles and S-duality

M2 branes probing T-brane backgrounds in M-theory with ADE surface singularities perceive deformations on their worldvolume superpotentials by monopole operators. The dynamics and moduli spaces of the resulting theories can be studied using a dual description involving conventional superpotential terms and (the dimensional reduction of) class S trinion theories. By using the S-dual description of N=2 SU(N) SQCD with 2N flavors in four dimensions, we are able to study T-branes corresponding to all minimal nilpotent orbits for the whole ADE series. Our proposed dualities are supported by the match in squashed sphere partition functions.

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arXiv2017

Weak coupling limit of F-theory models with MSSM spectrum and massless U(1)'s

We consider the Sen limit of several global F-theory compactifications, some of which exhibit an MSSM-like spectrum. We show that these indeed have a consistent limit where they can be viewed as resulting from an intersecting D-brane configuration in type IIB. We discuss the match of the fluxes and the chiral spectrum in detail. We find that some D5-tadpole canceling gauge fluxes do not lift to harmonic vertical four-form fluxes in F-theory. We discuss the connection between splitting of curves at weak coupling and remnant discrete symmetries.

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arXiv2016

Moduli Stabilisation with Nilpotent Goldstino: Vacuum Structure and SUSY Breaking

We study the effective field theory of KKLT and LVS moduli stabilisation scenarios coupled to an anti-D3-brane at the tip of a warped throat. We describe the presence of the anti-brane in terms of a nilpotent goldstino superfield in a supersymmetric effective field theory. The introduction of this superfield produces a term that can lead to a de Sitter minimum. We fix the Kaehler moduli dependence of the nilpotent field couplings by matching this term with the anti-D3-brane uplifting contribution. The main result of this paper is the computation, within this EFT, of the soft supersymmetry breaking terms in both KKLT and LVS for matter living on D3-brane (leaving the D7-brane analysis to an appendix). A handful of distinct phenomenological scenarios emerge that could have low energy implications, most of them having a split spectrum of soft masses. Some cosmological and phenomenological properties of these models are discussed. We also check that the attraction between the D3-brane and the anti-D3-brane does not affect the leading contribution to the soft masses and does not destabilise the system.

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arXiv2016

T-branes through 3d mirror symmetry

T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this paper, we make this data manifest, by probing the geometry with an M2-brane. We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce supersymmetry from N=4 to N=2. Our main tool is 3d mirror symmetry. Through this language, a very concrete framework is developed for understanding T-branes in M-theory. This leads us to uncover a new class of N=2 quiver gauge theories, whose Higgs branches mimic those of membranes at ADE singularities, but whose Coulomb branches differ from their N=4 counterparts.

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arXiv2016

Global String Embeddings for the Nilpotent Goldstino

We discuss techniques for embedding a nilpotent Goldstino sector both in weakly coupled type IIB compactifications and F-theory models at arbitrary coupling, providing examples of both scenarios in semi-realistic compactifications. We start by showing how to construct a local embedding for the nilpotent Goldstino in terms of an anti D3-brane in a local conifold throat, and then discuss how to engineer the required local structure in globally consistent compact models. We present two explicit examples, the last one supporting also chiral matter and Kähler moduli stabilisation.

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arXiv2015

De Sitter from T-branes

Hidden sector D7-branes with non-zero gauge flux are a generic feature of type IIB compactifications. A non-vanishing Fayet-Iliopoulos term induced by non-zero gauge flux leads to a T-brane configuration. Expanding the D7-brane action around this T-brane background in the presence of three-form supersymmetry breaking fluxes, we obtain a positive definite contribution to the moduli scalar potential which can be used as an uplifting source for de Sitter vacua. In this way we provide a higher-dimensional understanding of known 4D mechanisms of de Sitter uplifting based on hidden sector F-terms which are non-zero because of D-term stabilisation.

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arXiv2015

De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications

In arXiv:1407.7580 a mechanism to fix the closed string moduli in a de Sitter minimum was proposed: a D-term potential generates a linear relation between the volumes of two rigid divisors which in turn produces at lower energies a race-track potential with de Sitter minima at exponentially large volume. In this paper, we systematically search for implementations of this mechanism among all toric Calabi-Yau hypersurfaces with $h^{1,1}\leq 4$ from the Kreuzer-Skarke list. For these, topological data can be computed explicitly allowing us to find the subset of three-folds which have two rigid toric divisors that do not intersect each other and that are orthogonal to $h^{1,1}-2$ independent four-cycles. These manifolds allow to find D7-brane configurations compatible with the de Sitter uplift mechanism and we find an abundance of consistent choices of D7-brane fluxes inducing D-terms leading to a de Sitter minimum. Finally, we work out a couple of models in detail, checking the global consistency conditions and computing the value of the potential at the minimum.

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arXiv2015

On KKLT/CFT and LVS/CFT Dualities

We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifications. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large `central charge', find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry ($\mathcal{N}=1$ for KKLT and $\mathcal{N}=0$ for LVS) we find that the LVS CFT dual has only one scalar operator with $\mathcal{O}(1)$ conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of $h^{1,1}$ Kähler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explicitly compute the coefficient of the logarithmic contribution to the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case.

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arXiv2014

N=2 Heterotic-Type II duality and bundle moduli

Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ depend on a choice of hyperkähler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the $(0,2)$ superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-Kähler metric on hypermultiplet moduli space when $\mathfrak{S}$ is elliptically fibered, in the limit of a large fiber and even larger base. The result is in general agreement with expectations from Kaluza-Klein reduction, in particular the metric has a two-stage fibration structure, where the $B$-field moduli are fibered over bundle and metric moduli, while bundle moduli are themselves fibered over metric moduli. A more precise match must await a detailed analysis of $R^2$-corrected ten-dimensional supergravity.

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arXiv2014

The fate of U(1)'s at strong coupling in F-theory

U(1) gauge symmetries in F-theory are expected to manifest themselves as codimension three singularities of Calabi-Yau fourfolds. However, some of these are known to become massive at strong coupling via the Stückelberg mechanism. In this note, we propose a geometric picture for detecting all U(1)'s, and determining which ones are massive and which ones are massless. We find that massive gauge symmetries show up as codimension three singularities that only admit small, non-Kähler, resolutions. Our proposal passes several highly non-trivial tests, including a case with a non-diagonal mass matrix.

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arXiv2014

Hypercharge flux in F-theory and the stable Sen limit

IIB compactifications enjoy the possibility to break GUT groups via fluxes without giving mass to the hypercharge gauge field. Although this important advantage has greatly motivated F-theory constructions, no such fluxes have been constructed directly in terms of the M-theory $G_4$-form. In this note, we give a general prescription for constructing hypercharge G-fluxes. By using a stable version of Sen's weak coupling limit, we verify their connection with IIB fluxes. We illustrate the lift of fluxes in a number of examples, including a compact ${\rm SU}(5) \times {\rm U}(1)$ model with explicit realization of doublet-triplet splitting. Finally, we prove an equivalence conjectured in an earlier work as a by-product.

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arXiv2013

Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter

We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kaehler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kaehler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative alpha'-corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP_6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP_3 singularity.

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arXiv2013

D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation

In the framework of type IIB string compactifications on Calabi-Yau orientifolds we describe how to construct consistent global embeddings of models with fractional D3-branes and connected `flavour' D7-branes at del Pezzo singularities with moduli stabilisation. Our results are applied to build an explicit compact example with a left-right symmetric model at a dP_0 singularity which features three families of chiral matter and gauge coupling unification at the intermediate scale. We show how to stabilise the moduli obtaining a controlled de Sitter minimum and spontaneous supersymmetry breaking. We find an interesting non-trivial dynamical relation between the requirement of TeV-scale soft terms and the correct phenomenological values of the unified gauge coupling and unification scale.

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