SO(10) heterotic M-theory vacua

This talk adapts the available formalism to study a class of heterotic M-theory vacua with SO(10) grand unification group. Compactification to four dimensions with N = 1 supersymmetry is achieved on a torus fibered Calabi-Yau 3-fold Z = X / tau_{X} with first homotopy group pi_{1}(Z) = Z_{2}. Here X is an elliptically fibered Calabi-Yau 3-fold which admits two global sections and \tau_{X} is a freely acting involution on X. The vacua in this class have net number of three generations of chiral fermions in the observable sector and may contain M5-branes in the bulk space which wrap holomorphic curves in Z. Vacua with nonvanishing and vanishing instanton charges in the observable sector are considered. The latter case corresponds to potentially viable matter Yukawa couplings. Since pi_{1}(Z) = Z_{2}, the grand unification group can be broken with Z_{2} Wilson lines. The motivation is to use the above formalism to extend realistic free-fermionic models to the nonperturbative regime. The correspondence between these models and Z_{2} x Z_{2} orbifold compactification of the weakly coupled 10-dimensional heterotic string identifies associated Calabi-Yau 3-folds which possess the structure of the above Z and X. A nonperturbative extension of the top quark Yukawa coupling is discussed.Comment: 9 pages. Invited talk presented at the String Phenomenology 2003 Workshop, IPPP, Durham UK, 29 July - 4 August 200

BPS State Counting in N=8 Supersymmetric String Theory for Pure D-brane Configurations

Exact results for the BPS index are known for a class of BPS dyons in type II string theory compactified on a six dimensional torus. In this paper we set up the problem of counting the same BPS states in a duality frame in which the states carry only Ramond-Ramond charges. We explicitly count the number of states carrying the lowest possible charges and find agreement with the result obtained in other duality frames. Furthermore, we find that after factoring out the supermultiplet structure, each of these states carry zero angular momentum. This is in agreement with the prediction obtained from a representation of these states as supersymmetric black holes.Comment: 26 pages; v2: minor corrections in section 5; v3: typos correcte

Do All BPS Black Hole Microstates Carry Zero Angular Momentum?

From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on $T^6$, represented by four stacks of D-branes wrapped on various cycles of $T^6$. For this system the above conjecture translates to the statement that the moduli space of classical vacua must be a collection of points. Explicit analysis of systems carrying a low number of D-branes supports this conjecture.Comment: LaTeX, 42 pages; v2: minor corrections, some new results adde

R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models

In this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety X. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is either a deformation of the tangent bundle of X or a deformation of a sub-bundle of the tangent bundle of X. Some anomaly-free examples are provided. The curvature constraint imposed by supersymmetry in these models when the superpotential is not holomorphic is reviewed. Constraints of this nature have been used to establish properties of analogues of pullbacks of Mathai–Quillen forms which arise in the correlation functions of the corresponding A-twisted or B-twisted heterotic Landau–Ginzburg models. The analogue most relevant to this paper is a deformation of the pullback of a Mathai–Quillen form. We discuss how this deformation may arise in the class of models studied in this paper. We then comment on how analogues of pullbacks of Mathai–Quillen forms not discussed in previous work may be obtained. Standard Mathai–Quillen formalism is reviewed in an appendix. We also include an appendix which discusses the deformation of the pullback of a Mathai–Quillen form

Super Landau-Ginzburg mirrors and algebraic cycles

We investigate the super Landau-Ginzburg mirrors of gauged linear sigma models which, in an appropriate low energy limit, reduce to nonlinear sigma models with Kaehler supermanifold target spaces of nonnegative super-first Chern class.Comment: 29 pages, 5 figures, uses edited version of jheppub.sty. Dedicated to our dear friend and coauthor Maximilian Kreuzer, who died November 26, 2010. v3: Modifications to the Introduction, Equations (4.2), (5.2), and (6.2), and Remark 8.2. v2: Theorem A.1 and Corollary A.1 corrected; corresponding changes made in Section 4. Minor change in Section 2. Minor changes in Section

Fano hypersurfaces and Calabi-Yau supermanifolds

In this paper, we study the geometrical interpretations associated with Sethi's proposed general correspondence between N = 2 Landau-Ginzburg orbifolds with integral \hat{c} and N = 2 nonlinear sigma models. We focus on the supervarieties associated with \hat{c} = 3 Gepner models. In the process, we test a conjecture regarding the superdimension of the singular locus of these supervarieties. The supervarieties are defined by a hypersurface \widetilde{W} = 0 in a weighted superprojective space and have vanishing super-first Chern class. Here, \widetilde{W} is the modified superpotential obtained by adding as necessary to the Gepner superpotential a boson mass term and/or fermion bilinears so that the superdimension of the supervariety is equal to \hat{c}. When Sethi's proposal calls for adding fermion bilinears, setting the bosonic part of \widetilde{W} (denoted by \widetilde{W}_{bos}) equal to zero defines a Fano hypersurface embedded in a weighted projective space. In this case, if the Newton polytope of \widetilde{W}_{bos} admits a nef partition, then the Landau-Ginzburg orbifold can be given a geometrical interpretation as a nonlinear sigma model on a complete intersection Calabi-Yau manifold. The complete intersection Calabi-Yau manifold should be equivalent to the Calabi-Yau supermanifold prescribed by Sethi's proposal.Comment: 24 pages, uses JHEP3.cls; v2: minor corrections, references adde

Yukawa couplings in SO(10) heterotic M-theory vacua

We demonstrate the existence of a class of N=1 supersymmetric nonperturbative vacua of Horava-Witten M-theory compactified on a torus fibered Calabi-Yau 3-fold Z with first homotopy group \pi_{1}(Z)= Z2, having the following properties: 1) SO(10) grand unification group, 2) net number of three generations of chiral fermions in the observable sector, and 3) potentially viable matter Yukawa couplings. These vacua correspond to semistable holomorphic vector bundles V_{Z} over Z having structure group SU(4)_C, and generically contain M5-branes in the bulk space. The nontrivial first homotopy group allows Wilson line breaking of the SO(10) symmetry. Additionally, we propose how the 11-dimensional Horava-Witten M-theory framework may be used to extend the perturbative calculation of the top quark Yukawa coupling in the realistic free-fermionic models to the nonperturbative regime. The basic argument being that the relevant coupling couples twisted-twisted-untwisted states and can be calculated at the level of the Z2 X Z2 orbifold without resorting to the full three generation models.Comment: 24 pages. Standard LaTe