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Burt A. Ovrut - One of the best experts on this subject based on the ideXlab platform.
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numerical hermitian yang mills connections and Vector Bundle stability in heterotic theories
Journal of High Energy Physics, 2010Co-Authors: Lara B Anderson, Volker Braun, Robert L Karp, Burt A. OvrutAbstract:A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic Vector Bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad Bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable Bundles. In a variety of examples, it is shown that the failure of these Bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a Vector Bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
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Vector Bundle extensions sheaf cohomology and the heterotic standard model
arXiv: High Energy Physics - Theory, 2005Co-Authors: Volker Braun, Burt A. Ovrut, Yanghui He, Tony PantevAbstract: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.
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The Moduli of reducible Vector Bundles
Journal of High Energy Physics, 2004Co-Authors: Yanghui He, Burt A. Ovrut, René ReinbacherAbstract:A procedure for computing the dimensions of the moduli spaces of reducible, holomorphic Vector Bundles on elliptically fibered Calabi-Yau threefolds X is presented. This procedure is applied to poly-stable rank n+m Bundles of the form V + pi* M, where V is a stable Vector Bundle with structure group SU(n) on X and M is a stable Vector Bundle with structure group SU(m) on the base surface B of X. Such Bundles arise from small instanton transitions involving five-branes wrapped on fibers of the elliptic fibration. The structure and physical meaning of these transitions are discussed.
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pfaffians superpotentials and Vector Bundle moduli
Comptes Rendus Physique, 2003Co-Authors: Burt A. OvrutAbstract:Abstract We present a method for explicitly computing the non-perturbative superpotentials associated with the Vector Bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic Vector Bundle over an elliptically fibered Calabi–Yau threefold. Superpotentials of Vector Bundle moduli potentially have important implications for small instanton phase transitions and the vacuum stability and cosmology of superstrings and M-theory. To cite this article: B.A. Ovrut, C. R. Physique 4 (2003).
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superpotentials for Vector Bundle moduli
Nuclear Physics, 2003Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:We present a method for explicitly computing the non-perturbative superpotentials associated with the Vector Bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic Vector Bundle over an elliptically fibered Calabi–Yau threefold. For specificity, the Vector Bundle moduli superpotential, for a Vector Bundle with structure group G=SU(3), generated by a heterotic superstring wrapped once over an isolated curve in a Calabi–Yau threefold with base B=F1, is explicitly calculated. Its locus of critical points is discussed. Superpotentials of Vector Bundle moduli potentially have important implications for small instanton phase transitions and the vacuum stability and cosmology of superstrings and M-theory.
Indranil Biswas - One of the best experts on this subject based on the ideXlab platform.
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fourier mukai transformation and logarithmic higgs Bundles on punctual hilbert schemes
Journal of Geometry and Physics, 2020Co-Authors: Indranil Biswas, Andreas KrugAbstract:Abstract Given a Vector Bundle E on a smooth projective curve or surface X carrying the structure of a V -twisted Hitchin pair for some Vector Bundle V , we observe that the associated tautological Bundle E [ n ] on the punctual Hilbert scheme of points X [ n ] has an induced structure of a ( ( V ∨ ) [ n ] ) ∨ -twisted Hitchin pair, where ( V ∨ ) [ n ] is a Vector Bundle on X [ n ] constructed using the dual V ∨ of V . In particular, a Higgs Bundle on X induces a logarithmic Higgs Bundle on the Hilbert scheme X [ n ] . We then show that the known results on stability of tautological Bundles and reconstruction from tautological Bundles generalize to tautological Hitchin pairs.
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fourier mukai transformation and logarithmic higgs Bundles on punctual hilbert schemes
arXiv: Algebraic Geometry, 2019Co-Authors: Indranil Biswas, Andreas KrugAbstract:Given a Vector Bundle $E$ on a smooth projective curve or surface $X$ carrying the structure of a $V$-twisted Hitchin pair for some Vector Bundle $V$, we observe that the associated tautological Bundle $E^{[n]}$ on the punctual Hilbert scheme of points $X^{[n]}$ has an induced structure of a $((V^\vee)^{[n]})^\vee$-twisted Hitchin pair, where $(V^\vee)^{[n]}$ is a Vector Bundle on $X^{[n]}$ constructed using the dual $V^\vee$ of $V$. In particular, a Higgs Bundle on $X$ induces a logarithmic Higgs Bundle on the Hilbert scheme $X^{[n]}$. We then show that the known results on stability of tautological Bundles and reconstruction from tautological Bundles generalize to tautological Hitchin pairs.
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Equivariant Vector Bundles and logarithmic connections on toric varieties
Journal of Algebra, 2013Co-Authors: Indranil Biswas, Vicente Muñoz, Jonatan SánchezAbstract:Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic Vector Bundle on X. We prove that the following three statements are equivalent: • The holomorphic Vector Bundle E admits an equivariant structure. • The holomorphic Vector Bundle E admits an integrable logarithmic connection singular over D. • The holomorphic Vector Bundle E admits a logarithmic connection singular over D. We show that an equivariant Vector Bundle on X has a tautological integrable logarithmic connection singular over D. This is used in computing the Chern classes of the equivariant Vector Bundles on X. We also prove a version of the above result for holomorphic Vector Bundles on log parallelizable G-pairs (X,D), where G is a simply connected complex affine algebraic group.
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Semistability criterion for parabolic Vector Bundles on curves
arXiv: Algebraic Geometry, 2011Co-Authors: Indranil Biswas, Ajneet DhillonAbstract:We give a cohomological criterion for a parabolic vec- tor Bundle on a curve to be semistable. It says that a parabolic Vector Bundle E∗ with rational parabolic weights is semistable if and only if there is another parabolic Vector Bundle F∗ with rational parabolic weights such that the cohomologies of the Vector Bundle underlying the parabolic tensor product E∗ ⊗F ∗ vanish. This criterion general- izes the known semistability criterion of Faltings for Vector Bundles on curves and significantly improves the result in (Bis07).
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Generalization of a criterion for semistable Vector Bundles
Finite Fields and Their Applications, 2009Co-Authors: Indranil Biswas, Georg HeinAbstract:It is known that a Vector Bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a Vector Bundle F on Y such that both H^0(X,[email protected]?F) and H^1(X,[email protected]?F) vanishes. We extend this criterion for semistability to Vector Bundles on curves defined over perfect fields. Let X be a geometrically irreducible smooth projective curve defined over a perfect field k, and let E be a Vector Bundle on X. We prove that E is semistable if and only if there is a Vector Bundle F on X such that H^i(X,[email protected]?F)=0 for all i. We also give an explicit bound for the rank of F.
Eli Buchbinder - One of the best experts on this subject based on the ideXlab platform.
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superpotentials for Vector Bundle moduli
Nuclear Physics, 2003Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:We present a method for explicitly computing the non-perturbative superpotentials associated with the Vector Bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic Vector Bundle over an elliptically fibered Calabi–Yau threefold. For specificity, the Vector Bundle moduli superpotential, for a Vector Bundle with structure group G=SU(3), generated by a heterotic superstring wrapped once over an isolated curve in a Calabi–Yau threefold with base B=F1, is explicitly calculated. Its locus of critical points is discussed. Superpotentials of Vector Bundle moduli potentially have important implications for small instanton phase transitions and the vacuum stability and cosmology of superstrings and M-theory.
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Vector Bundle moduli superpotentials in heterotic superstrings and m theory
Journal of High Energy Physics, 2002Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated Vector Bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the Vector Bundle moduli. This method is illustrated by a number of non-trivial examples.
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Vector Bundle moduli and small instanton transitions
Journal of High Energy Physics, 2002Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic Vector Bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B = r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic Vector Bundles over the M5-brane curve and give explicit examples. Vector Bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.
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Vector Bundle Moduli
Russian Physics Journal, 2002Co-Authors: Eli Buchbinder, Burt A. OvrutAbstract:We give the general presciption for calculating the number of moduli of irreducible, stable U ( n ) holomorphic Vector Bundles with positive spectral covers over elliptically fibered Calabi–Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B = F _r. Vector Bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M -theory.
Ron Donagi - One of the best experts on this subject based on the ideXlab platform.
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superpotentials for Vector Bundle moduli
Nuclear Physics, 2003Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:We present a method for explicitly computing the non-perturbative superpotentials associated with the Vector Bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic Vector Bundle over an elliptically fibered Calabi–Yau threefold. For specificity, the Vector Bundle moduli superpotential, for a Vector Bundle with structure group G=SU(3), generated by a heterotic superstring wrapped once over an isolated curve in a Calabi–Yau threefold with base B=F1, is explicitly calculated. Its locus of critical points is discussed. Superpotentials of Vector Bundle moduli potentially have important implications for small instanton phase transitions and the vacuum stability and cosmology of superstrings and M-theory.
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Vector Bundle moduli superpotentials in heterotic superstrings and m theory
Journal of High Energy Physics, 2002Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated Vector Bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the Vector Bundle moduli. This method is illustrated by a number of non-trivial examples.
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Vector Bundle moduli and small instanton transitions
Journal of High Energy Physics, 2002Co-Authors: Eli Buchbinder, Ron Donagi, Burt A. OvrutAbstract:We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic Vector Bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B = r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic Vector Bundles over the M5-brane curve and give explicit examples. Vector Bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.
Yuxin Dong - One of the best experts on this subject based on the ideXlab platform.
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on vanishing theorems for Vector Bundle valued p forms and their applications
Communications in Mathematical Physics, 2011Co-Authors: Yuxin DongAbstract:Let F : [0, ∞) → [0, ∞) be a strictly increasing C 2 function with F(0) = 0. We unify the concepts of F-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce F-Yang-Mills fields, F-degree, F-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When \({F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,}\) and \({1-\sqrt{1-2t},}\) the F-Yang-Mills field becomes an ordinary Yang-Mills field, p-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the E F,g −energy functional (resp. F-Yang-Mills functional) and derive the first variational formula of the E F,g −energy functional (resp. F-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors are naturally linked to F-conservation laws and yield monotonicity formulae, via the coarea formula and comparison theorems in Riemannian geometry. Whereas a “microscopic” approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory, a “macroscopic” version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for p−forms with values in Vector Bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for F−harmonic maps (which include harmonic maps, p-harmonic maps, exponentially harmonic maps, minimal graphs and maximal space-like hypersurfaces, etc.), F−Yang-Mills fields, extended Born-Infeld fields, and generalized Yang-Mills-Born-Infeld fields (with the plus sign and with the minus sign) on manifolds, etc. As another consequence, we obtain the unique constant solution of the constant Dirichlet boundary value problems on starlike domains for Vector Bundle-valued 1-forms satisfying an F-conservation law, generalizing and refining the work of Karcher and Wood on harmonic maps. We also obtain generalized Chern type results for constant mean curvature type equations for p−forms on \({\mathbb{R}^m}\) and on manifolds M with the global doubling property by a different approach. The case p = 0 and \({M=\mathbb{R}^m}\) is due to Chern.
