arXiv subjects

Mariana Graña

Publications and source records attributed to Mariana Graña.

At least 37 records · Page 2Linked to original sources

arXiv2021

The Tadpole Problem

We examine the mechanism of moduli stabilization by fluxes in the limit of a large number of moduli. We conjecture that one cannot stabilize all complex-structure moduli in F-theory at a generic point in moduli space (away from singularities) by fluxes that satisfy the bound imposed by the tadpole cancelation condition. More precisely, while the tadpole bound in the limit of a large number of complex-structure moduli goes like 1/4 of the number of moduli, we conjecture that the amount of charge induced by fluxes stabilizing all moduli grows faster than this, and is therefore larger than the allowed amount. Our conjecture is supported by two examples: K3 x K3 compactifications, where by using evolutionary algorithms we find that moduli stabilization needs fluxes whose induced charge is 44% of the number of moduli, and Type IIB compactifications on CP^3, where the induced charge of the fluxes needed to stabilize the D7-brane moduli is also 44% of the number of these moduli. Proving our conjecture would rule out de Sitter vacua obtained via antibrane uplift in long warped throats with a hierarchically small supersymmetry breaking scale, which require a large tadpole.

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arXiv2020

Oh, wait, O8 de Sitter may be unstable!

We analyze the stability of four-dimensional de Sitter vacua constructed by compactifying massive Type IIA supergravity in the presence of two O8 sources [1]. When embedded in String Theory the first source has a clear interpretation as an O8$_-$ plane, but the second one could correspond to either an O8$_+$ plane or to an O8$_-$ plane with 16 D8-branes on top. We find that this latter solution has a tachyonic instability, corresponding to the D8-branes moving away from the O8$_-$ plane. We comment on the possible ways of distinguishing between these sources.

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arXiv2020

Exploring the landscape of heterotic strings on T^d

Compactifications of the heterotic string on T^d are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)^{d+16} left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups. We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not. For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II_{1,17}. More general algorithms to explore the moduli space are also developed. For d=1 and 2 we list all the maximally enhanced gauge groups, moduli, and other relevant information about the embedding in II_{d,d+16}. In agreement with the duality between heterotic on T^2 and F-theory on K3, all possible gauge groups on T^2 match all possible ADE types of singular fibers of elliptic K3 surfaces. We also present a simple method to transform the moduli under the duality group, and we build the map that relates the charge lattices and moduli of the compactification of the E_8 x E_8 and Spin(32)/Z_2 heterotic theories.

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arXiv2020

Gaugino mass term for D-branes and Generalized Complex Geometry

We compute the four-dimensional gaugino mass for a Dp-brane extended in spacetime and wrapping a cycle on the internal geometry in a warped compactification with fluxes. Motivated by the backreaction of gaugino bilinear VEVs, we use Generalized Complex Geometry to characterize the internal geometry as well as the cycle wrapped by the brane. We find that the RR fluxes and the non-closure of the generalized complex structures combine in the gaugino mass terms in the same form as they do in the bulk superpotential, while for the NSNS fluxes there is a crucial minus sign in the component normal to the brane. Our expression extends the known result for D3 and D7-branes in Calabi-Yau manifolds, where the gaugino masses are induced respectively by the imaginary anti-self dual and imaginary self-dual components of the complex 3-form flux $G_3$.

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arXiv2019

Kähler moduli stabilization from ten dimensions

We describe the back-reaction of gaugino condensates in supersymmetric AdS$_4$ Type II String Theory compactifications with fluxes. We use generalized complex geometry to capture the modification of the ten-dimensional supersymmetry equations and show that the cosmological constant prevents the cycle wrapped by the branes with gaugino condensation from shrinking to zero size. Thus, unlike in ordinary geometric transitions in flat space, the volume of this cycle remains finite. For D7 branes with gaugino condensation, this gives a ten-dimensional account of Kähler moduli stabilization. Furthermore, by matching the ten-dimensional supergravity solutions near and far from the cycle wrapped by the D7 branes, we find a relation between the size of this cycle and the cosmological constant. This relation agrees with the supersymmetric AdS vacuum condition obtained by KKLT using effective field theory.

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arXiv2019

Uplifting Runaways

We find a mechanism by which antibranes placed in a warped deformed conifold throat can destroy the stabilization of the size of the sphere at the tip, collapsing it to zero size. This conifold destabilization mechanism can be avoided by turning on a large amount of flux on the sphere, but tadpole cancelation makes this incompatible with a hierarchy of scales in a Type IIB flux compactification. This indicates that antibrane uplift cannot be used to construct stable de Sitter vacua with a small cosmological constant in perturbative String Theory. The values of V and V' for these KKLT-like scenarios can be parametrically small, but we find that V'/V is still consistent with the de Sitter swampland conjecture. Our results also suggest that there should exist a Klebanov-Strassler black hole, holographically dual to a deconfined phase with spontaneously broken chiral symmetry.

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arXiv2018

A new twist on heterotic string compactifications

A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We show the gauge symmetry groups that arise at special points, in figures of slices of the 17-dimensional moduli space of Wilson lines and circle radii. We then study the target space realization of the duality symmetry. Although the global continuous duality symmetries of dimensionally reduced heterotic supergravity are completely broken by the structure constants of the maximally enhanced gauge groups, the low energy effective action can be written in a manifestly duality covariant form using heterotic double field theory. As a byproduct, we show that a unique deformation of the generalized diffeomorphisms accounts for both $SO(32)$ and $E_8\times E_8$ heterotic effective field theories, which can thus be considered two different backgrounds of the same double field theory even before compactification. Finally we discuss the spontaneous gauge symmetry breaking and Higgs mechanism that occurs when slightly perturbing the background fields, both from the string and the field theory perspectives.

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arXiv2017

The bosonic string on string-size tori from double field theory

We construct the effective action for toroidal compactifications of bosonic string theory from generalized Scherk-Schwarz reductions of double field theory. The enhanced gauge symmetry arising at special points in moduli space is incorporated into this framework by promoting the $O(k,k)$ duality group of $k$-tori compactifications to $O(n,n)$, $n$ being the dimension of the enhanced gauge group, which allows to account for the full massless sector of the theory. We show that the effective action reproduces the right masses of scalar and vector fields when moving sligthly away from the points of maximal symmetry enhancement. The neighborhood of the enhancement points in moduli space can be neatly explored by spontaneous symmetry breaking. We generically discuss toroidal compactifications of arbitrary dimensions and maximally enhanced gauge groups, and then inspect more closely the example of $T^2$ at the $SU(3)_L \times SU(3)_R$ point, which is the simplest setup containing all the non trivialities of the generic case. We show that the entire moduli space can be described in a unified way by considering compactifications on higher dimensional tori.

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arXiv2016

Generalized geometric vacua with eight supercharges

We investigate compactifications of type II and M-theory down to $AdS_5$ with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped $AdS_5$ background imply the generalized integrability conditions.

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arXiv2016

Exactly marginal deformations from exceptional generalised geometry

We apply exceptional generalised geometry to the study of exactly marginal deformations of $\mathcal{N}=1$ SCFTs that are dual to generic AdS$_5$ flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any $\mathcal{N}=2$ AdS$_5$ flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

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arXiv2016

D3-brane model building and the supertrace rule

A common way to obtain standard-model-like Lagrangians in string theory is to place D3-branes inside flux compactifications. The bosonic and fermionic masses and couplings of the resulting gauge theory are determined by the ten-dimensional metric and the fluxes, respectively, and the breaking of supersymmetry is soft. However, not any soft-supersymmetry-breaking Lagrangian can be obtained this way since the string theory equations of motion impose certain relations between the soft couplings. We show that for D3-branes in background fluxes, these relations imply that the sums of the squares of the boson and of the fermion masses are equal and that, furthermore, one- and two-loop quantum corrections do not spoil this equality. This makes the use of D3-branes for constructing computationally controllable models for physics beyond the standard model problematic.

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arXiv2015

Fermionic and bosonic mass deformations of N=4 SYM and their bulk supergravity dual

We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of N=4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation-theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral operator) is a stringy excitation with dimension of order $(g_s N)^{1/4}$ and the existence of non-stringy supergravity flows describing theories where this trace is nonzero, by showing that the stringy mode does not parameterize the sum of the squares of the boson masses but rather its departure from the trace of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can only describe holographically theories where the sums of the squares of the bosonic and fermionic masses are equal, which is consistent with the weakly-coupled result that only such theories can have a conformal UV fixed point.

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arXiv2015

M-theory moduli spaces and torsion-free structures

Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of $Spin(7)$-structures on an eight-dimensional $S^{1}$-bundle to the set of $G_{2}$-structures on the base space, fully characterizing the $G_{2}$-torsion clases when the total space is equipped with a torsion-free $Spin(7)$-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of M-theory compactifications.

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arXiv2014

Giant Tachyons in the Landscape

We study the dynamics of localized and fully backreacting anti-D3 branes at the tip of the Klebanov-Strassler geometry. We use a non-supersymmetric version of the Polchinski-Strassler analysis to compute the potential for anti-D3 branes to polarize into all kinds of five-brane shells in all possible directions. We find that generically there is a direction along which the brane-brane interaction is repulsive, which implies that anti-D3 branes are tachyonic. Hence, even though anti-D3 branes can polarize into five-branes, the solution will most likely be unstable. This indicates that anti-D3 brane uplift may not result in stable de Sitter vacua.

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arXiv2014

Spin(7)-manifolds in compactifications to four dimensions

We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold $\mathcal{M}_{8}$ equipped with a particular set of tensors $\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ a family of $G_{2}$-structure seven-dimensional manifolds as the leaves of a codimension-one foliation. Under a different set of assumptions, $\mathfrak{S}$ allows to make $\mathcal{M}_{8}$ into a principal $S^{1}$ bundle, which is equipped with a topological $Spin(7)$-structure if the base is equipped with a topological $G_{2}$-structure. We also show that $\mathfrak{S}$ can be naturally used to describe regular as well as a singular elliptic fibrations on $\mathcal{M}_{8}$, which may be relevant for F-theory applications, and prove several mathematical results concerning the relation between topological $G_{2}$-structures in seven dimensions and topological $Spin(7)$-structures in eight dimensions.

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arXiv2014

Tachyonic Anti-M2 Branes

We study the dynamics of anti-M2 branes in a warped Stenzel solution with M2 charges dissolved in fluxes by taking into account their full backreaction on the geometry. The resulting supergravity solution has a singular magnetic four-form flux in the near-brane region. We examine the possible resolution of this singularity via the polarization of anti-M2 branes into M5 branes, and compute the corresponding polarization potential for branes smeared on the finite-size four-sphere at the tip of the Stenzel space. We find that the potential has no minimum. We then use the potential for smeared branes to compute the one corresponding to a stack of localized anti-M2 branes, and use this potential to compute the force between two anti-M2 branes at tip of the Stenzel space. We find that this force, which is zero in the probe approximation, is in fact repulsive. This surprising result points to a tachyonic instability of anti-M2 branes in backgrounds with M2 brane charge dissolved in flux.

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arXiv2014

The gauge structure of Exceptional Field Theories and the tensor hierarchy

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.

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arXiv2013

The quantization problem in Scherk-Schwarz compactifications

We re-examine the quantization of structure constants, or equivalently the choice of lattice in the so-called flat group reductions, introduced originally by Scherk and Schwarz. Depending on this choice, the vacuum either breaks supersymmetry and lifts certain moduli, or preserves all supercharges and is identical to the one obtained from the torus reduction. Nonetheless the low-energy effective theory proposed originally by Scherk and Schwarz is a gauged supergravity that describes supersymmetry breaking and moduli lifting for all values of the structure constants. When the vacuum does not break supersymmetry, such a description turns out to be an artifact of the consistent truncation to left-invariant forms as illustrated for the example of ISO(2). We furthermore discuss the construction of flat groups in d dimensions and find that the Scherk--Schwarz algorithm is exhaustive. A classification of flat groups up to six dimensions and a discussion of all possible lattices is presented.

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