arXiv subjects

Eirik Eik Svanes

Publications and source records attributed to Eirik Eik Svanes.

34 records · Page 2Linked to original sources

arXiv2020

$T^3$-Invariant Heterotic Hull-Strominger Solutions

We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the $T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on $\mathbb{R}^3$ satisfying a certain co-closure condition. We give a number of abelian and non-abelian examples, and also compute the back-reaction on the geometry through the non-trivial $α'$-corrected heterotic Bianchi identity, which includes an important correction to the equations for the complex flat connection. These are all new local solutions to the Hull-Strominger system on $T^3\times\mathbb{R}^3$. We also propose a method for computing the spectrum of certain non-abelian models, in close analogy with the Morse-Witten complex of the abelian 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

Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_\infty$ algebra

We consider finite deformations of the Hull--Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer--Cartan equation that controls the moduli. The resulting complex effective action generalises that of both Kodaira--Spencer and holomorphic Chern--Simons theory. The supersymmetric locus of this action is described by an $L_3$ algebra.

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arXiv2017

Marginal deformations of heterotic $G_2$ sigma models

Recently, the infinitesimal moduli space of heterotic $G_2$ compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST operator. This BRST operator is nilpotent if and only if the target space geometry satisfies the heterotic supersymmetry conditions. We relate this to the supergravity approach by showing that the corresponding cohomologies are indeed isomorphic. We work at tree-level in $α'$ perturbation theory and study general geometries, in particular with non-vanishing torsion.

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arXiv2017

Heterotic Hyper-Kahler Flux Backgrounds

We study Heterotic supergravity on Hyper-Kahler manifolds in the presence of non-trivial warping and three form flux with Abelian bundles in the large charge limit. We find exact, regular solutions for multi-centered Gibbons-Hawking spaces and Atiyah-Hitchin manifolds. In the case of Atiyah-Hitchin, regularity requires that the circle at infinity is of the same order as the instanton number, which is taken to be large. Alternatively there may be a non-trivial density of smeared five branes at the bolt.

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arXiv2017

On Heterotic Vacua with Fermionic Expectation Values

We study heterotic backgrounds with non-trivial $H$-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear $Σ_{MNP}={\rm tr}\:\barχΓ_{MNP}χ$. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form $Σ_{mnp}$ that must be a singlet of the holonomy group. This condition does not hold anymore when an internal $H$-flux is turned on and ${\cal O}(α')$ effects are included. In this paper we study flux compactifications to three and four-dimensions on $G$-structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate.

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arXiv2016

The Heterotic Superpotential and Moduli

We study the four-dimensional effective theory arising from ten-dimensional heterotic supergravity compactified on manifolds with torsion. In particular, given the heterotic superpotential appropriately corrected at $\mathcal{O}(α')$ to account for the Green-Schwarz anomaly cancellation mechanism, we investigate properties of four-dimensional Minkowski vacua of this theory. Considering the restrictions arising from F-terms and D-terms we identify the infinitesimal massless moduli space of the theory. We show that it agrees with the results that have recently been obtained from a ten-dimensional perspective where supersymmetric Minkowski solutions including the Bianchi identity correspond to an integrable holomorphic structure, with infinitesimal moduli calculated by its first cohomology. As has recently been noted, interplay of complex structure and bundle deformations through holomorphic and anomaly constraints can lead to fewer moduli than may have been expected. We derive a relation between the number of complex structure and bundle moduli removed from the low energy theory in this way, and give conditions for there to be no complex structure moduli or bundle moduli remaining in the low energy theory. The link between Yukawa couplings and obstruction theory is also briefly discussed.

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arXiv2016

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical $G_2$ cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H^1_{\check{d}_A}(Y,\mathrm{End}(V))$ plus the moduli of the $G_2$ structure preserving the instanton condition. The latter piece is contained in $H^1_{\check{d}_θ}(Y,TY)$, and is given by the kernel of a map ${\cal\check F}$ which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map ${\cal\check F}$ is given in terms of the curvature of the bundle and maps $H^1_{\check{d}_θ}(Y,TY)$ into $H^2_{\check{d}_A}(Y,\mathrm{End}(V))$, and moreover can be used to define a cohomology on an extension bundle of $TY$ by $\mathrm{End}(V)$. We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on $(Y,V)$ when $α'=0$.

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arXiv2016

Inflationary Potentials from the Exact Renormalisation Group

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. We assume that the theory contains a scalar mode with suppressed coupling to other UV fields, and that higher derivative couplings are suppressed. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the $ϕ^4$ theory.

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arXiv2016

$Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity

We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a $Spin(7)$ manifold, which leads to a $1/4$-BPS four-dimensional supersymmetric perturbative vacuum breaking all but one supercharge. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to maximal symmetry by some non-perturbative or higher-order effect.

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arXiv2016

The Abelian Heterotic Conifold

We study heterotic supergravity on the conifold and its Z2 orbifold with Abelian gauge fields and three-form flux. At large distances, these solutions are locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for the decoupled near horizon region where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but we obtain a solution on the (unorbifolded) resolved conifold.

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arXiv2015

Connections, Field Redefinitions and Heterotic Supergravity

We study heterotic supergravity at $\mathcal{O}(α')$, first described in detail in 1989 by Bergshoeff and de Roo. In particular, we discuss an ambiguity of a connection choice on the tangent bundle. It is well known that at $\mathcal{O}(α')$ the Hull connection gives a consistent supergravity theory with supersymmetry transformations given in the usual way. We consider deformations of this connection corresponding to field redefinitions, and the necessary corrections to the supersymmetry transformations. We are interested in the moduli space of such field redefinitions which allow for supersymmetric solutions to the equations of motion. We show that for solutions on $M_4\times X$, where $M_4$ is Minkowski and $X$ is compact, the moduli space of infinitesimal field redefinitions is given by $H^{(0,1)}(X,\textrm{End}(TX))$. This space corresponds to infinitesimally close connections for which the equations of motion are satisfied. The setup suggests a symmetry between the gauge connection and the tangent bundle connection, as also employed by Bergshoeff and de Roo. We argue that this symmetry should be kept to higher orders in $α'$, and propose a natural choice for the corresponding tangent bundle connection used in curvature computations. In particular, the Hull connection should be corrected at second and higher orders in $α'$ from this point of view.

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arXiv2015

The Massless Spectrum of Heterotic Compactifications

We discuss the four-dimensional massless spectrum of supersymmetric Minkowski compactifications of ten-dimensional heterotic supergravity, including the anomaly cancelation condition. This can be calculated from restrictions arising from F-term conditions in a four-dimensional effective theory. The results agree with computations of the infinitesimal moduli space recently performed from a ten-dimensional perspective. The paper is based on a talk given by Eirik Eik Svanes in Leuven for the workshop on "The String Theory Universe".

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arXiv2015

Heterotic Moduli Stabilisation and Non-Supersymmetric Vacua

We study moduli stabilisation in four-dimensional $N=1$ supergravity theories which originate from compactifications of the heterotic string on certain manifolds with $SU(3)$ structure. These theories have a non-trivial superpotential generated from geometric flux and, in general, D-terms associated to anomalous $U(1)$ symmetries. We show that, at the perturbative level, there are no supersymmetry preserving vacua. However, subject to a certain technical condition on the D-terms which aligns the extrema of the F-term and D-term potentials, $\partial_iV_F=\partial_iV_D=0$, we find at the perturbative level analytic stable AdS vacua which break supersymmetry. As a result, all T-moduli and the dilaton are stabilised perturbatively with supersymmetry broken at a high scale. We also show numerically that similar vacua can be found when the technical condition on the D-term is relaxed. These vacua persist in the presence of non-perturbative effects. In all cases, the vacua remain AdS.

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arXiv2015

Moduli in General $SU(3)$-Structure Heterotic Compactifications

In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time $X$ is a six-dimensional manifold of what we refer to as a heterotic $SU(3)$-structure. We show that this system can be put in terms of a holomorphic operator $\bar D$ on a bundle $\mathcal{Q}=T^*X\oplus\mathrm{End}(TX)\oplus\mathrm{End}(V)\oplus TX$, defined by a series of extensions. We proceed to compute the infinitesimal deformation space of this structure, given by $T\mathcal{M}=H^{(0,1)}(\mathcal{Q})$, which constitutes the infinitesimal spectrum of the four-dimensional theory. In doing so, we find an over counting of moduli by $H^{(0,1)}(\mathrm{End}(TX))$, which can be reinterpreted as $\mathcal{O}(α')$ field redefinitions. We next consider non-maximally symmetric domain wall compactifications of the form $M_{10}=M_3\times Y$, where $M_3$ is three-dimensional Minkowski space, and $Y=\mathbb{R}\times X$ is a seven-dimensional non-compact manifold with a $G_2$-structure. Here $X$ is a six dimensional compact space of half-flat $SU(3)$-structure, non-trivially fibered over $\mathbb{R}$. By focusing on coset compactifications, we show that the compact space $X$ can be endowed with non-trivial torsion, which can be used in a combination with $α'$-effects to stabilise all geometric moduli. The domain wall can further be lifted to a maximally symmetric AdS vacuum by inclusion of non-perturbative effects. Finally, we consider domain wall compactifications where $X$ is a Calabi-Yau. We show that by considering such compactifications, one can evade the usual no-go theorems for flux in Calabi-Yau compactifications, allowing flux to be used as a tool in such compactifications, even when $X$ is Kähler.

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arXiv2013

Heterotic Calabi-Yau Compactifications with Flux

Compactifications of the heterotic string with NS flux normally require non Calabi-Yau internal spaces which are complex but no longer Kähler. We point out that this conclusion rests on the assumption of a maximally symmetric four-dimensional space-time and can be avoided if this assumption is relaxed. Specifically, it is shown that an internal Calabi-Yau manifold is consistent with the presence of NS flux provided four-dimensional space-time is taken to be a domain wall. These Calabi-Yau domain wall solutions can still be associated with a covariant four-dimensional N=1 supergravity. In this four-dimensional context, the domain wall arises as the "simplest" solution to the effective supergravity due to the presence of a flux potential with a runaway direction. Our main message is that NS flux is a legitimate ingredient for moduli stabilization in heterotic Calabi-Yau models. Ultimately, the success of such models depends on the ability to stabilize the runaway direction and thereby "lift" the domain wall to a maximally supersymmetric vacuum.

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