Heterotic (0,2) Gepner Models and Related Geometries (2009)
On the sad occasion of contributing to the memorial volume ``Fundamental Interactions'' for my teacher Wolfgang Kummer I decided to recollect and extend some unpublished notes from the mid 90s when I...
The making of Calabi-Yau spaces: Beyond toric hypersurfaces (2009)
While Calabi-Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader...
Fano hypersurfaces and Calabi-Yau supermanifolds (2008)
Garavuso, Richard S., Kreuzer, Maximilian, Noll, Alexander
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...
Four-modulus "Swiss Cheese" chiral models (2008)
Collinucci, Andres, Kreuzer, Maximilian, Mayrhofer, Christoph, Walliser, Nils-Ole
We study the 'Large Volume Scenario' on explicit, new, compact, four-modulus Calabi-Yau manifolds. We pay special attention to the chirality problem pointed out by Blumenhagen, Moster and Plauschinn....
On the combinatorial classification of toric log del Pezzo surfaces (2008)
Kasprzyk, Alexander M., Kreuzer, Maximilian, Nill, Benjamin
Toric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. An upper bound on the volume and on the number of...
On the Statistics of Lattice Polytopes (2008)
We use the notions of reflexivity and of reflexive dimensions in order to introduce probability measures for lattice polytopes and initiate the investigation of their statistical properties. Examples...
Albrecht Klemm, Maximilian Kreuzer, Erwin Riegler, Emanuel Scheidegger
Calabi-Yau spaces and threshold corrections
Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions (2008)
Batyrev, Victor, Kreuzer, Maximilian
We construct a surprisingly large class of new Calabi-Yau 3-folds $X$ with small Picard numbers and propose a construction of their mirrors $X^*$ using smoothings of toric hypersurfaces with conifold...
Worldsheet Instantons and Torsion Curves (2008)
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt A., Scheidegger, Emanuel
We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation...
Worldsheet Instantons and Torsion Curves (2008)
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt, Scheidegger, Emanuel
We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation...
Supported by the Austrian Federal Ministry of Education, Science and Culture (2008)
Sebastian Guttenberg, Manfred Herbst, Maximilian Kreuzer, Radoslav Rashkov, Sebastian Guttenberg, Manfred Herbst, ...
Key words Noncommutative geometry, D-branes, deformation quantization
Non-topological non-commutativity in string theory (2007)
Guttenberg, Sebastian, Herbst, Manfred, Kreuzer, Maximilian, Rashkov, Radoslav
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields...
Max-Planck-Institut fur Mathematik in den Naturwissenschaften Leipzig (2007)
Superstring Brst Cohomology, Friedemann Br, Er Kling, Friedemann Brandt, Alexander Kling, Maximilian Kreuzer, ...
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Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry (2007)
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt A., Scheidegger, Emanuel
We apply mirror symmetry to the problem of counting holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. As we found in Part A [hep-th/0703182], the integral homology...
Worldsheet Instantons and Torsion Curves, Part A: Direct Computation (2007)
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt A., Scheidegger, Emanuel
As a first step towards studying vector bundle moduli in realistic heterotic compactifications, we identify all holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines....
Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials (2007)
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt A., Scheidegger, Emanuel
As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov-Witten invariants for a Calabi-Yau threefold with fundamental group...
Classification of toric Fano 5-folds (2007)
Kreuzer, Maximilian, Nill, Benjamin
We obtain 866 isomorphism classes of five-dimensional nonsingular toric Fano varieties using a computer program and the database of four-dimensional reflexive polytopes. The algorithm is based on the...
Toric Geometry and Calabi-Yau Compactifications (2006)
These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last...
Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds (2005)
Batyrev, Victor, Kreuzer, Maximilian
In this paper, we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among 473 800 776...
On the Covariant Quantization of Type II Superstrings (2004)
Guttenberg, Sebastian, Knapp, Johanna, Kreuzer, Maximilian
In a series of papers Grassi, Policastro, Porrati and van Nieuwenhuizen have introduced a new method to covariantly quantize the GS-superstring by constructing a resolution of the pure spinor...
NS Fivebrane and Tachyon Condensation (2003)
Ghoshal, Debashis, Jatkar, Dileep P., Kreuzer, Maximilian
We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of...
PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry (2002)
Kreuzer, Maximilian, Skarke, Harald
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and...
Non-commutative tachyon action and D-brane geometry (2002)
Herbst, Manfred, Kling, Alexander, Kreuzer, Maximilian
We analyse open string correlators in non-constant background fields, including the metric $g$, the antisymmetric $B$-field, and the gauge field $A$. Working with a derivative expansion for the...
Star Products from Open Strings in Curved Backgrounds (2001)
Herbst, Manfred, Kling, Alexander, Kreuzer, Maximilian
We define a non-commutative product for arbitrary gauge and B-field backgrounds in terms of correlation functions of open strings. While off-shell correlations are, of course, not conformally...
Superstring BRST Cohomology (2001)
Brandt, Friedemann, Kling, Alexander, Kreuzer, Maximilian
We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we...
Strings on Calabi--Yau spaces and Toric Geometry (2001)
After a brief introduction into the use of Calabi--Yau varieties in string dualities, and the role of toric geometry in that context, we review the classification of toric Calabi-Yau hypersurfaces...
Toric complete intersections and weighted projective space (2001)
Kreuzer, Maximilian, Riegler, Erwin, Sahakyan, David
It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi--Yau manifolds in toric ambient spaces. We...
Superstring BRST cohomology (2001)
Brandt,Friedemann, Kling,Alexander, Kreuzer,Maximilian
We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we...
Superstring BRST cohomology (2001)
Brandt, Friedemann, Kling, Alexander, Kreuzer, Maximilian
We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we...
Superstring BRST cohomology (2001)
Brandt, Friedemann, Kling, Alexander, Kreuzer, Maximilian
We first derive all world-sheet action functionals for NSR superstring models with local (1,1) supersymmetry and any number of abelian gauge fields. The result includes the well-known superstring...
Actions and symmetries of NSR superstrings and D-strings (2000)
Brandt, Friedemann, Kling, Alexander, Kreuzer, Maximilian
We present all NSR superstring and super-D-string actions invariant under a set of prescribed gauge transformations, and characterize completely their global symmetries. In particular we obtain...
SU(2) WZW D-branes and quantized worldvolume U(1) flux on S^2 (2000)
Kling, Alexander, Kreuzer, Maximilian, Zhou, Jian-Ge
We discuss possible D-brane configurations on SU(2) group manifolds in the sigma model approach. When we turn the boundary conditions of the spacetime fields into the boundary gluing conditions of...
Complete classification of reflexive polyhedra in four dimensions (2000)
Kreuzer, Maximilian, Skarke, Harald
Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and in...
Reflexive polyhedra, weights and toric Calabi-Yau fibrations (2000)
Kreuzer, Maximilian, Skarke, Harald
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive...
Kreuzer, Maximilian, Zhou, Jian-Ge
Background independence of noncommutative Yang-Mills theory on $\mathbb R^n$ is discussed. The quantity $\theta \hat F \theta - \theta$ is found to be background dependent at subleading order, and it...
Maximilian Kreuzer, Harald Skarke
We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case...
ON THE EXTENDED POINCARE POLYNOMIAL (1995)
Kreuzer, Maximilian, Schweigert, Christoph
We show that the numbers of generations and anti-generations of a (2,2) string compactification with diagonal internal theory can be expressed in terms of certain specifications of the elliptic genus...
The Mirror Map for Invertible LG Models (1994)
Calculating the (a,c) ring of the maximal phase orbifold for `invertible' Landau--Ginzburg models, we show that the Berglund--H"ubsch construction works for all potentials of the relevant type. The...
Where are the Mirror Manifolds? (1993)
The recent classification of Landau--Ginzburg potentials and their abelian symmetries focuses attention on a number of models with large positive Euler number for which no mirror partner is known....
All Abelian Symmetries of Landau-Ginzburg Potentials (1992)
Kreuzer, Maximilian, Skarke, Harald
We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg...
On the Landau-Ginzburg description of $(A_1^{(1)})^{\oplus N}$ invariants (1992)
Fuchs, Jürgen, Kreuzer, Maximilian
We search for a \Lg\ interpretation of non-diagonal modular invariants of tensor products of minimal $n=2$ superconformal models, looking in particular at automorphism invariants and at some...
No Mirror Symmetry in Landau-Ginzburg Spectra! (1992)
Kreuzer, Maximilian, Skarke, Harald
We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate the...
On the Classification of Quasihomogeneous Functions (1992)
Kreuzer, Maximilian, Skarke, Harald
We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of...