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# Publications

- Computations of Some K-groups
[ps.gz,
pdf,
to appear in the Oberwolfach Reports]

- Heterotic Standard Model Moduli
[arXiv]

**Authors:**Volker Braun, Yang Hui-He, Burt A. Ovrut, Tony Pantev,**Abstract:**In previous papers, we introduced a heterotic standard model and discussed its basic properties. The Calabi-Yau threefold has, generically, three Kahler and three complex structure moduli. The observable sector of this vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields. The hidden sector has no charged matter in the strongly coupled string and only minimal matter for weak coupling. Additionally, the spectrum of both sectors will contain vector bundle moduli. The exact number of such moduli was conjectured to be small, but was not explicitly computed. In this paper, we rectify this and present a formalism for computing the number of vector bundle moduli. Using this formalism, the number of moduli in both the observable and strongly coupled hidden sectors is explicitly calculated. - Vector Bundle Extensions, Sheaf Cohomology,
and the Heterotic Standard Model
[arXiv]

**Authors:**Volker Braun, Yang Hui-He, Burt A. Ovrut, Tony Pantev,**Abstract:**Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua. - A Standard Model from the E
_{8}× E_{8}Heterotic Superstring [arXiv]

**Authors:**Volker Braun, Yang Hui-He, Burt A. Ovrut, Tony Pantev,**Abstract:**In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In this paper, the requisite vector bundles are formulated; specifically, stable, holomorphic bundles with structure group SU(N) on smooth Calabi-Yau threefolds with Z_{3}× Z_{3}fundamental group. A method for computing bundle cohomology is presented and used to evaluate the cohomology groups of the standard model bundles. It is shown how to determine the Z_{3}× Z_{3}action on these groups. Finally, using an explicit method of "doublet-triplet splitting", the low-energy particle spectrum is computed. - A Heterotic Standard Model
[arXiv]

**Authors:**Volker Braun, Yang Hui-He, Burt A. Ovrut, Tony Pantev,**Abstract:**Within the context of the E_{8}× E_{8}heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the existence of simple, realistic N=1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU(3)_{C}× SU(2)_{L}× U(1)_{Y}× U(1)_{B-L}, three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter. The hidden sector contains non-Abelian gauge fields and moduli. In the strong coupling case there is no exotic matter, whereas for weak coupling there are a small number of additional matter multiplets in the hidden sector. The construction exploits a mechanism for "splitting" multiplets. The minimal nature and rarity of these vacua suggest the possible theoretical and experimental relevance of spontaneously broken U(1)_{B-L}gauge symmetry and two Higgs-Higgs conjugate pairs. The U(1)_{B-L}symmetry helps to naturally suppress the rate of nucleon decay. - Elliptic Calabi-Yau Threefolds with
Z
_{3}× Z_{3}Wilson Lines [arXiv]

**Authors:**Volker Braun, Burt A. Ovrut, Tony Pantev, Renè Reinbacher**Abstract:**A torus fibered Calabi-Yau threefold with first homotopy group Z_{3}× Z_{3}is constructed as a free quotient of a fiber product of two dP_{9}surfaces. Calabi-Yau threefolds of this type admit Z_{3}× Z_{3}Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three generation models of particle physics with a right handed neutrino and a U(1)_{B-L}gauge factor, in addition to the SU(3)_{C}× SU(2)_{L}× U(1)_{Y}standard model gauge group. This factor helps to naturally suppress nucleon decay. The moduli space and Dolbeault cohomology of the threefold is also discussed. - Minimal Models and K-theory
[ps.gz,
pdf,
to appear in the Oberwolfach Reports]

**Authors:**Volker Braun, Sakura Schäfer-Nameki - Supersymmetric WZW models and twisted K-theory of SO(3)
[arXiv]

**Authors:**Volker Braun, Sakura Schäfer-Nameki**Abstract:**We present an encompassing treatment of D-brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K-theories and find complete agreement with the CFT analysis of D-brane charges. The K-theoretical computation in particular elucidates some important aspects of N=1 supersymmetric WZW models on non-simply connected Lie groups. - Twisted K-Theory of Lie Groups
[arXiv]
**Abstract:**I determine the twisted K-theory of all compact simply connected Lie groups. The computation reduces via the Freed-Hopkins-Telemann theorem to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze the exceptions noted by Bouwknegt et al. - On Berenstein-Douglas-Seiberg Duality
[arXiv]
**Abstract:**I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed. - The Standard Model on the Quintic
[arXiv]

**Authors:**Ralph Blumenhagen, Volker Braun, Boris Kors, Dieter Lust - K-theory and exceptional holonomy in string theory
[edoc.hu-berlin.de,
ps.gz,
pdf,
src]

PhD Thesis (Humboldt University Berlin)**Abstract:**In this thesis I consider various aspects of string theory compactifications, especially for nontrivial internal manifolds.The first part is dedicated to the application of K-theory to the study of D-branes. It is the generalized cohomology theory which classifies the possible charges on a given spacetime. A natural question is whether there is any difference between K-theory and the usual description via (de Rahm) cohomology/homology. For this I present a Calabi-Yau manifold which illustrates this difference.

Instead of compactifying on a complicated smooth manifold one can also consider orbifolds of simple manifolds to get interesting compactifications. These are described by equivariant K-theory. To be able to compare this with the physical prediction I calculate all KO

_{Z2}(R^{p,q}). Furthermore one can consider orientifolds, which suggests the definition of new K-theories. I investigate simple properties of these.In the second part I present compactifications on G

_{2}and Spin(7) manifolds and their description as Gepner models. The SCFT and the geometric description disagree. An explanation for this phenomenon is offered. - Orientifolds and K-theory
[arXiv]

**Authors:**Volker Braun, Bogdan Stefanski, jr**Abstract:**Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for such orientifolds. We find that equivariant Real K-theory can be twisted by elements of a generalised group cohomology. This cohomology classifies all orientifolds just as group cohomology classifies all orbifolds. As an example we consider the Omega x I_{4}orientifolds. We completely determine the equivariant orthogonal K-theory KO_{Z2}(R^{p,q}) and analyse the twisted versions. Agreement is found between K-theory and Boundary Confromal Field Theory (BCFT) results for both integrally- and torsion-charged D-branes. - Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
[arXiv]

**Authors:**Ralph Blumenhagen, Volker Braun, Boris Kors, Dieter Lust**Abstract:**We investigate orientifolds of type II string theory on K3 and Calabi-Yau 3-folds with intersecting D-branes wrapping special Lagrangian cycles. We determine quite generically the chiral massless spectrum in terms of topological invariants and discuss both orbifold examples and algebraic realizations in detail. Intriguingly, the developed techniques provide an elegant way to figure out the chiral sector of orientifold models without computing any explicit string partition function. As a new example we derive a non-supersymmetric Standard-like Model from an orientifold of type IIA on the quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric intersecting brane models on Calabi-Yau manifolds we discuss the D-term and F-term potentials, the effective gauge couplings and the Green-Schwarz mechanism. The mirror symmetric formulation of this construction is provided within type IIB theory. We finally include a short discussion about the lift of these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau 3-folds to M-theory on G_{2}manifolds.Chosen as one of the 5 most significant joint publications of the EC-RTN network "The quantum structure of spacetime and the geometric nature of fundamental interactions".

- Superconformal Field Theories for Compact Manifolds with
Spin(7) Holonomy
[arXiv]

**Authors:**Ralph Blumenhagen, Volker Braun - Superconformal Field Theories for Compact G
_{2}Manifolds [arXiv]

**Authors:**Ralph Blumenhagen, Volker Braun**Abstract:**We present the construction of exactly solvable superconformal field theories describing Type II string models compactified on compact G_{2}manifolds. These models are defined by anti-holomorphic quotients of the form (CY*S^{1})/Z_{2}, where we realize the Calabi-Yau as a Gepner model. In the superconformal field theory the Z_{2}acts as charge conjugation implying that the representation theory of a W(2,4,6,8,10) algebra plays an important role in the construction of these models. Intriguingly, in all three examples we study, including the quintic, the massless spectrum in the Z_{2}twisted sector of the superconformal field theory differs from what one expects from the supergravity computation. This discrepancy is explained by the presence of a discrete NS-NS background two-form flux in the Gepner model. - Bound States of D(2p)-D0 Systems and Supersymmetric p-Cycles
[arXiv]

**Authors:**Ralph Blumenhagen, Volker Braun, Robert Helling - K-Theory Torsion
[arXiv]
**Abstract:**The Chern isomorphism determines the free part of the K-groups from ordinary cohomology. Thus to really understand the implications of K-theory for physics one must look at manifolds with K-torsion. Unfortunately there are not many explicit examples, and usually for very symmetric spaces. Cartesian products of RP^{n}are examples where the order of the torsion part differs between K-theory and ordinary cohomology. The dimension of corresponding branes is also discussed. An example for a Calabi-Yau manifold with K-torsion is given. - Toric Calabi-Yau Fourfolds, Duality Between N=1 Theories and
Divisors that Contribute to the Superpotential
[arXiv]

**Authors:**Volker Braun, Philip Candelas, Xenia de la Ossa, Antonella Grassi - The Moricone of a Calibi-Yau Space from Toric Geometry
[ps.gz,
pdf,
src]

M.A. Thesis (University of Texas at Austin) - On extremal transitions of Calabi-Yau threefolds and
the singularity of the associated 7-space from rolling
[arXiv]

**Authors:**Volker Braun, Chien-Hao Liu