arXiv subjects

Andre Lukas

Publications and source records attributed to Andre Lukas.

At least 91 records · Page 5Linked to original sources

arXiv2009

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.

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arXiv2009

M-theory on Calabi-Yau Five-Folds

We study the compactification of M-theory on Calabi-Yau five-folds and the resulting N=2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an N=2 super-space action. We find that the Kahler and complex structure moduli of the five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1,3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional N=2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukov-type formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional N=2 supersymmetry and supergravity to the level of generality required for our purposes.

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arXiv2009

Yukawa Couplings in Heterotic Compactification

We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not restricted to, the recently classified positive monads over favourable complete intersection Calabi-Yau three-folds. Since the algorithm is based on manipulating polynomials it can be easily implemented on a computer. This makes the automated investigation of Yukawa couplings for large classes of smooth heterotic compactifications a viable possibility.

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arXiv2008

An Abundance of Heterotic Vacua

We explicitly construct the largest dataset to date of heterotic vacua arising from stable vector bundles on Calabi-Yau threefolds. Focusing on elliptically fibered Calabi-Yau manifolds with spectral cover bundles, we show that the number of heterotic models with non-zero number of generations is finite. We classify these models according to the complex base of their Calabi-Yau threefold and to the unification gauge group that they preserve in four dimensions. This database of the order of $10^7$ models, which includes potential Standard Model candidates, is subjected to some preliminary statistical analyses. The additional constraint that there should be three net generations of particles gives a dramatic reduction of the number of vacua.

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arXiv2008

Monad Bundles in Heterotic String Compactifications

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.

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arXiv2007

Heterotic String Compactifications on Half-flat Manifolds II

In this paper, we continue the analysis of heterotic string compactifications on half-flat mirror manifolds by including the 10-dimensional gauge fields. It is argued, that the heterotic Bianchi identity is solved by a variant of the standard embedding. Then, the resulting gauge group in four dimensions is still E6 despite the fact that the Levi-Civita connection has SO(6) holonomy. We derive the associated four-dimensional effective theories including matter field terms for such compactifications. The results are also extended to more general manifolds with SU(3) structure.

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arXiv2007

A New Method for Finding Vacua in String Phenomenology

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.

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arXiv2007

Heterotic Compactification, An Algorithmic Approach

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. Using a combination of analytic methods and computer algebra we prove stability for all such bundles and compute the complete particle spectrum, including gauge singlets. In particular, we find that the number of anti-generations vanishes for all our bundles and that the spectrum is manifestly moduli-dependent.

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arXiv2007

Perturbative Anti-Brane Potentials in Heterotic M-theory

We derive the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes is explicitly included. To first order in the heterotic strong-coupling expansion, we find that the forces on branes and anti-branes vanish and that the KKLT procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential. However, there are additional non-supersymmetric corrections to the gauge-kinetic functions and matter terms. The new correction to the gauge kinetic functions is important in a discussion of moduli stabilization. At second order in the strong-coupling expansion, we find that the forces on the branes and anti-branes become non-vanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter of the strong-coupling expansion, they are relatively weak. This suggests that moduli stabilization in heterotic models with anti-branes is achievable.

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arXiv2006

Four-dimensional Effective M-theory on a Singular G_2 Manifold

We reduce M-theory on a G_2 orbifold with co-dimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional super-Yang-Mills theory, as derived in a previous paper. The resulting four-dimensional theory has N=1 supersymmetry with non-Abelian N=4 gauge theory sub-sectors. We present explicit formulae for the Kahler potential, gauge-kinetic function and superpotential. In the four-dimensional theory, blowing-up of the orbifold is described by a Higgs effect induced by continuation along D-flat directions. Using this interpretation, we show that our results are consistent with the corresponding ones obtained for smooth G_2 spaces. In addition, we consider the effects of switching on flux and Wilson lines on singular loci of the G_2 space, and we discuss the relation to N=4 SYM theory.

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arXiv2006

Cosmological Solutions of Low-Energy Heterotic M-Theory

We derive a set of exact cosmological solutions to the D=4, N=1 supergravity description of heterotic M-theory. Having identified a new and exact SU(3) Toda model solution, we then apply symmetry transformations to both this solution and to a previously known SU(2) Toda model, in order to derive two further sets of new cosmological solutions. In the symmetry-transformed SU(3) Toda case we find an unusual "bouncing" motion for the M5 brane, such that this brane can be made to reverse direction part way through its evolution. This bounce occurs purely through the interaction of non-standard kinetic terms, as there are no explicit potentials in the action. We also present a perturbation calculation which demonstrates that, in a simple static limit, heterotic M-theory possesses a scale-invariant isocurvature mode. This mode persists in certain asymptotic limits of all the solutions we have derived, including the bouncing solution.

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arXiv2006

Moduli Stabilisation in Heterotic String Compactifications

In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalised half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N=1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalised models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification.

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arXiv2006

M-Theory on the Orbifold C^2/Z_N

We construct M-theory on the orbifold C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading non-trivial order in the 11-dimensional Newton constant. This action provides the starting point for a reduction of M-theory on G_2 spaces with co-dimension four singularities.

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arXiv2005

Type IIB Conifold Transitions in Cosmology

We study four-dimensional low energy effective actions for conifold transitions of Calabi-Yau spaces in the context of IIB supergravity. The actions are constucted by examining the mass of D3-branes wrapped on collapsing/expanding three-cycles. We then study the cosmology of the conifold transition, including consequences for moduli stabilization, taking into account the effect of the additional states which become light at the transition. We find, the degree to which the additional states are excited is essential for whether the transition is dynamically realized.

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arXiv2005

Classification and Moduli Kahler Potentials of G_2 Manifolds

Compact manifolds of G_2 holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kahler potential for M-theory on the resulting class of G_2 manifolds with blown up co-dimension four singularities.

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arXiv2004

Non-perturbative vacua for M-theory on G2 manifolds

We study moduli stabilization in the context of M-theory on compact manifolds with G2 holonomy, using superpotentials from flux and membrane instantons, and recent results for the Khaeler potential of such models. The existence of minima with negative cosmological constant, stabilizing all moduli, is established. While most of these minima preserve supersymmetry, we also find examples with broken supersymmetry. Supersymmetric vacua with vanishing cosmological constant can also be obtained after a suitable tuning of parameters.

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arXiv2004

G_2 Domain Walls in M-theory

M-theory is considered in its low-energy limit on a G_2 manifold with non-vanishing flux. Using the Killing spinor equations for linear flux, an explicit set of first-order bosonic equations for supersymmetric solutions is found. These solutions describe a warped product of a domain wall in four-dimensional space-time and a deformed G_2 manifold. It is shown how these domain walls arise from the perspective of the associated four-dimensional N=1 effective supergravity theories. We also discuss the inclusion of membrane and M5-brane sources.

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arXiv2004

Heterotic on Half-flat

We study the effective action of the heterotic string compactified on particular half-flat manifolds which arise in the context of mirror symmetry with NS-NS flux. We explicitly derive the superpotential and Kahler potential at lowest order in alpha' by a reduction of the bosonic action. The superpotential contains new terms depending on the Kahler moduli which originate from the intrinsic geometrical flux of the half-flat manifolds. A generalized Gukov formula, valid for all manifolds with SU(3) structure, is derived from the gravitino mass term. For the half-flat manifolds it leads to a superpotential in agreement with our explicit bosonic calculation. We also discuss the inclusion of gauge fields.

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