Calabi-Yau metrics for quotients and complete intersections

doi:10.1088/1126-6708/2008/05/080

Title: Calabi-Yau metrics for quotients and complete intersections

Abstract

We extend previous computations of Calabi-Yau metrics on projective hypersurfaces to free quotients, complete intersections, and free quotients of complete intersections. In particular, we construct these metrics on generic quintics, four-generation quotients of the quintic, Schoen Calabi-Yau complete intersections and the quotient of a Schoen manifold with Z₃ x Z₃ fundamental group that was previously used to construct a heterotic standard model. Various numerical investigations into the dependence of Donaldson's algorithm on the integration scheme, as well as on the Kähler and complex structure moduli, are also performed.

Authors:

Braun, Volker ^[1]; Brelidze, Tamaz ^[1]; Douglas, Michael R. ^[2]; Ovrut, Burt A. ^[1]

Univ. of Pennsylvania, Philadelphia, PA (United States)
Rutgers Univ., Piscataway, NJ (United States)

Publication Date:: 2008-05-22

Research Org.:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1201591

Grant/Contract Number:: FG02-95ER40893

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2008; Journal Issue: 05; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Calabi-Yau metrics; mathematical physics; particle physics and field theory

Citation Formats


                    Braun, Volker, Brelidze, Tamaz, Douglas, Michael R., and Ovrut, Burt A. Calabi-Yau metrics for quotients and complete intersections.  United States: N. p., 2008. 
        Web.  doi:10.1088/1126-6708/2008/05/080.

Copy to clipboard


                    Braun, Volker, Brelidze, Tamaz, Douglas, Michael R., & Ovrut, Burt A. Calabi-Yau metrics for quotients and complete intersections.  United States.  doi:10.1088/1126-6708/2008/05/080.

Copy to clipboard


                    Braun, Volker, Brelidze, Tamaz, Douglas, Michael R., and Ovrut, Burt A. Thu .  
        "Calabi-Yau metrics for quotients and complete intersections".  United States.  doi:10.1088/1126-6708/2008/05/080.  https://www.osti.gov/servlets/purl/1201591.

Copy to clipboard


                    
@article{osti_1201591,

  title        = {Calabi-Yau metrics for quotients and complete intersections},

  author       = {Braun, Volker and Brelidze, Tamaz and Douglas, Michael R. and Ovrut, Burt A.},

  abstractNote = {We extend previous computations of Calabi-Yau metrics on projective hypersurfaces to free quotients, complete intersections, and free quotients of complete intersections. In particular, we construct these metrics on generic quintics, four-generation quotients of the quintic, Schoen Calabi-Yau complete intersections and the quotient of a Schoen manifold with Z₃ x Z₃ fundamental group that was previously used to construct a heterotic standard model. Various numerical investigations into the dependence of Donaldson's algorithm on the integration scheme, as well as on the Kähler and complex structure moduli, are also performed.},

  doi          = {10.1088/1126-6708/2008/05/080},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 05,

  volume       = 2008,

  place        = {United States},

  year         = {2008},

  month        = {5}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: 10.1088/1126-6708/2008/05/080

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 26 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
journal, December 2007

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio
Journal of High Energy Physics, Vol. 2007, Issue 12
DOI: 10.1088/1126-6708/2007/12/083

Worldsheet instantons, torsion curves and non-perturbative superpotentials
journal, June 2007

Braun, Volker; Kreuzer, Maximilian; Ovrut, Burt A.
Physics Letters B, Vol. 649, Issue 4
DOI: 10.1016/j.physletb.2007.03.066

An <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="italic">SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>5</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> heterotic standard model
journal, February 2006

Bouchard, Vincent; Donagi, Ron
Physics Letters B, Vol. 633, Issue 6
DOI: 10.1016/j.physletb.2005.12.042

Torus-Fibered Calabi-Yau threefolds with non-trivial fundamental group
journal, May 2003

Ovrut, Burt A.; Reinbacher, René; Pantev, Tony
Journal of High Energy Physics, Vol. 2003, Issue 05
DOI: 10.1088/1126-6708/2003/05/040

Vector bundle extensions, sheaf cohomology, and the heterotic standard model
journal, January 2006

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Advances in Theoretical and Mathematical Physics, Vol. 10, Issue 4
DOI: 10.4310/atmp.2006.v10.n4.a3

The exact MSSM spectrum from string theory
journal, May 2006

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2006, Issue 05
DOI: 10.1088/1126-6708/2006/05/043

The Particle Spectrum of Heterotic Compactifications
journal, December 2004

Donagi, Ron; He, Yang-Hui; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2004, Issue 12
DOI: 10.1088/1126-6708/2004/12/054

Standard-model bundles on non-simply connected Calabi-Yau threefolds
journal, August 2001

Donagi, Ron; Ovrut, Burt A.; Pantev, Tony
Journal of High Energy Physics, Vol. 2001, Issue 08
DOI: 10.1088/1126-6708/2001/08/053

Scalar Curvature and Projective Embeddings, I
journal, November 2001

Donaldson, S. K.
Journal of Differential Geometry, Vol. 59, Issue 3
DOI: 10.4310/jdg/1090349449

On fiber products of rational elliptic surfaces with section
journal, June 1988

Schoen, Chad
Mathematische Zeitschrift, Vol. 197, Issue 2
DOI: 10.1007/bf01215188

A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
journal, July 1991

Candelas, Philip; De La Ossa, Xenia C.; Green, Paul S.
Nuclear Physics B, Vol. 359, Issue 1
DOI: 10.1016/0550-3213(91)90292-6

Worldsheet instantons and torsion curves. Part A: direct computation
journal, October 2007

Braun, Volker; Ovrut, Burt A.; Kreuzer, Maximilian
Journal of High Energy Physics, Vol. 2007, Issue 10
DOI: 10.1088/1126-6708/2007/10/022

E6 symmetry breaking in the superstring theory
journal, August 1985

Breit, J. D.; Ovrut, Burt A.; Segré, Gino C.
Physics Letters B, Vol. 158, Issue 1
DOI: 10.1016/0370-2693(85)90734-8

Worldsheet instantons and torsion curves. Part B: mirror symmetry
journal, October 2007

Braun, Volker; Ovrut, Burt A.; Kreuzer, Maximilian
Journal of High Energy Physics, Vol. 2007, Issue 10
DOI: 10.1088/1126-6708/2007/10/023

Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory
journal, July 2002

Buchbinder, Evgeny I.; Donagi, Ron; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2002, Issue 07
DOI: 10.1088/1126-6708/2002/07/066

Symmetry breaking patterns in superstring models
journal, January 1985

Witten, Edward
Nuclear Physics B, Vol. 258
DOI: 10.1016/0550-3213(85)90603-0

Mirror manifolds in higher dimension
journal, November 1995

Greene, Brian R.; Morrison, David R.; Plesser, M. Ronen
Communications in Mathematical Physics, Vol. 173, Issue 3
DOI: 10.1007/bf02101657

Yukawa couplings in heterotic standard models
journal, April 2006

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2006, Issue 04
DOI: 10.1088/1126-6708/2006/04/019

Numerical Ricci-flat metrics on K3
journal, November 2005

Headrick, Matthew; Wiseman, Toby
Classical and Quantum Gravity, Vol. 22, Issue 23
DOI: 10.1088/0264-9381/22/23/002

Counting gauge invariants: the plethystic program
journal, March 2007

Feng, Bo; Hanany, Amihay; He, Yang-Hui
Journal of High Energy Physics, Vol. 2007, Issue 03
DOI: 10.1088/1126-6708/2007/03/090

Vacuum configurations for superstrings
journal, January 1985

Candelas, P.; Horowitz, Gary T.; Strominger, Andrew
Nuclear Physics B, Vol. 258
DOI: 10.1016/0550-3213(85)90602-9

A Standard Model from the E ₈ × E ₈ heterotic superstring
journal, June 2005

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2005, Issue 06
DOI: 10.1088/1126-6708/2005/06/039

A heterotic standard model
journal, July 2005

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Physics Letters B, Vol. 618, Issue 1-4
DOI: 10.1016/j.physletb.2005.05.007

Numerical Calabi–Yau metrics
journal, March 2008

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio
Journal of Mathematical Physics, Vol. 49, Issue 3
DOI: 10.1063/1.2888403

Elliptic Calabi-Yau Threefolds with Z ₃ × Z ₃ Wilson Lines
journal, December 2004

Braun, Volker; Ovrut, Burt A.; Pantev, Tony
Journal of High Energy Physics, Vol. 2004, Issue 12
DOI: 10.1088/1126-6708/2004/12/062

On a set of polarized Kähler metrics on algebraic manifolds
journal, January 1990

Tian, Gang
Journal of Differential Geometry, Vol. 32, Issue 1
DOI: 10.4310/jdg/1214445039

The spectra of heterotic standard model vacua
journal, June 2005

Donagi, Ron; He, Yang-Hui; Ovrut, Burt A.
Journal of High Energy Physics, Vol. 2005, Issue 06
DOI: 10.1088/1126-6708/2005/06/070

Moduli dependent spectra of heterotic compactifications
journal, September 2004

Donagi, Ron; He, Yang-Hui; Ovrut, Burt A.
Physics Letters B, Vol. 598, Issue 3-4
DOI: 10.1016/j.physletb.2004.08.010

Mirror manifolds in higher dimension
journal, November 1995

Greene, Brian R.; Morrison, David R.; Plesser, M. Ronen
Communications in Mathematical Physics, Vol. 173, Issue 3
DOI: 10.1007/BF02101657

On fiber products of rational elliptic surfaces with section
journal, June 1988

Schoen, Chad
Mathematische Zeitschrift, Vol. 197, Issue 2
DOI: 10.1007/BF01215188

Vector bundle extensions, sheaf cohomology, and the heterotic standard model
journal, January 2006

Braun, Volker; He, Yang-Hui; Ovrut, Burt A.
Advances in Theoretical and Mathematical Physics, Vol. 10, Issue 4
DOI: 10.4310/ATMP.2006.v10.n4.a3

Works referencing / citing this record:

Stability walls in heterotic theories
journal, September 2009

Anderson, Lara B.; Gray, James; Lukas, Andre
Journal of High Energy Physics, Vol. 2009, Issue 09
DOI: 10.1088/1126-6708/2009/09/026

Similar Records in DOE PAGES and OSTI.GOV collections:

Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds

Journal Article Buchbinder, Evgeny ; Lukas, Andre ; Ovrut, Burt ; ... - Journal of High Energy Physics (Online)

We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by Beasley and Witten shows that these instanton contributions cancel among curves within a given homology class for Calabi-Yau manifolds that can be described as hypersurfaces or complete intersections in projective or toric ambient spaces. We provide a prescription that identifies allmore »« less
Cited by 4
DOI: 10.1007/jhep10(2017)032

Full Text Available
Numerical Calabi-Yau metrics

Journal Article Douglas, Michael R ; I.H.E.S., Le Bois-Marie, Bures-sur-Yvette 91440 ; Karp, Robert L ; ... - Journal of Mathematical Physics

We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.
DOI: 10.1063/1.2888403
Calabi-Yau manifolds, Landau-Ginzburg orbifolds and mirror symmetry

Miscellaneous Berglund, N P.G.

When compactifying the ten-dimensional heterotic string theory to the four-dimensional spacetime the extra degrees of freedom has to form an N=2 superconformal field theory. One way of realization is in terms of Calabi-Yau manifolds of complex dimension three. An alternative description is as N=2 superconformal Landau-Ginzburg models. This thesis will use both of these compactification schemes in studying properties of the heterotic string vacua. The author develops a method for describing the massless spectrum in one and the same framework for any complete intersection Calabi-Yau threefold. This geometric approach, though classical, is in one to one correspondence with the Landau-Ginzburgmore »« less
Stabilizing all geometric moduli in heterotic Calabi-Yau vacua

Journal Article Anderson, Lara B. ; Gray, James ; Lukas, Andre ; ... - Physical Review. D, Particles, Fields, Gravitation and Cosmology

We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kähler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the moduli are combined with non-perturbative corrections. We argue that, for appropriate gauge bundles, all complex structure and a large number of other moduli can be perturbatively stabilized - in the most restrictive case, leaving only one combination of Kähler moduli and the dilaton as a flat direction. At this stage, the remaining modulimore »« less
Cited by 40
DOI: 10.1103/PhysRevD.83.106011

Full Text Available
Heterotic string compactification on conformal field theories and Calabi-Yau manifolds

Miscellaneous Lynker, M

The compactification of the Heterotic String from the ten dimensions in which it can consistently propagate down to the four dimensions is observed to be one of the central problems in String Theory. Two such compactification schemes as well as the resulting space of groundstates are discussed in this thesis. First a nongeometric scheme originally formulated by Gepner and then a more geometric approach using Calabi-Yau manifolds is discussed and the connection between them is explored. The first approach bypasses the geometrical construction of the internal sector. Instead, one replaces the coordinate fields and their supersymmetric partners by a generalmore »« less

Similar Records

Title: Calabi-Yau metrics for quotients and complete intersections

Abstract

Citation Formats

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic journal, December 2007

Worldsheet instantons, torsion curves and non-perturbative superpotentials journal, June 2007

Torus-Fibered Calabi-Yau threefolds with non-trivial fundamental group journal, May 2003

Vector bundle extensions, sheaf cohomology, and the heterotic standard model journal, January 2006

The exact MSSM spectrum from string theory journal, May 2006

The Particle Spectrum of Heterotic Compactifications journal, December 2004

Standard-model bundles on non-simply connected Calabi-Yau threefolds journal, August 2001

Scalar Curvature and Projective Embeddings, I journal, November 2001

On fiber products of rational elliptic surfaces with section journal, June 1988

A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory journal, July 1991

Worldsheet instantons and torsion curves. Part A: direct computation journal, October 2007

E6 symmetry breaking in the superstring theory journal, August 1985

Worldsheet instantons and torsion curves. Part B: mirror symmetry journal, October 2007

Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory journal, July 2002

Symmetry breaking patterns in superstring models journal, January 1985

Mirror manifolds in higher dimension journal, November 1995

Yukawa couplings in heterotic standard models journal, April 2006

Numerical Ricci-flat metrics on K3 journal, November 2005

Counting gauge invariants: the plethystic program journal, March 2007

Vacuum configurations for superstrings journal, January 1985

A Standard Model from the E 8 × E 8 heterotic superstring journal, June 2005

A heterotic standard model journal, July 2005

Numerical Calabi–Yau metrics journal, March 2008

Elliptic Calabi-Yau Threefolds with Z 3 × Z 3 Wilson Lines journal, December 2004

On a set of polarized Kähler metrics on algebraic manifolds journal, January 1990

The spectra of heterotic standard model vacua journal, June 2005

Moduli dependent spectra of heterotic compactifications journal, September 2004

Mirror manifolds in higher dimension journal, November 1995

On fiber products of rational elliptic surfaces with section journal, June 1988

Vector bundle extensions, sheaf cohomology, and the heterotic standard model journal, January 2006

Stability walls in heterotic theories journal, September 2009

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
journal, December 2007

Worldsheet instantons, torsion curves and non-perturbative superpotentials
journal, June 2007

Torus-Fibered Calabi-Yau threefolds with non-trivial fundamental group
journal, May 2003

Vector bundle extensions, sheaf cohomology, and the heterotic standard model
journal, January 2006

The exact MSSM spectrum from string theory
journal, May 2006

The Particle Spectrum of Heterotic Compactifications
journal, December 2004

Standard-model bundles on non-simply connected Calabi-Yau threefolds
journal, August 2001

Scalar Curvature and Projective Embeddings, I
journal, November 2001

On fiber products of rational elliptic surfaces with section
journal, June 1988

A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
journal, July 1991

Worldsheet instantons and torsion curves. Part A: direct computation
journal, October 2007

E6 symmetry breaking in the superstring theory
journal, August 1985

Worldsheet instantons and torsion curves. Part B: mirror symmetry
journal, October 2007

Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory
journal, July 2002

Symmetry breaking patterns in superstring models
journal, January 1985

Mirror manifolds in higher dimension
journal, November 1995

Yukawa couplings in heterotic standard models
journal, April 2006

Numerical Ricci-flat metrics on K3
journal, November 2005

Counting gauge invariants: the plethystic program
journal, March 2007

Vacuum configurations for superstrings
journal, January 1985

A Standard Model from the E ₈ × E ₈ heterotic superstring
journal, June 2005

A heterotic standard model
journal, July 2005

Numerical Calabi–Yau metrics
journal, March 2008

Elliptic Calabi-Yau Threefolds with Z ₃ × Z ₃ Wilson Lines
journal, December 2004

On a set of polarized Kähler metrics on algebraic manifolds
journal, January 1990

The spectra of heterotic standard model vacua
journal, June 2005

Moduli dependent spectra of heterotic compactifications
journal, September 2004

Mirror manifolds in higher dimension
journal, November 1995

On fiber products of rational elliptic surfaces with section
journal, June 1988

Vector bundle extensions, sheaf cohomology, and the heterotic standard model
journal, January 2006

Stability walls in heterotic theories
journal, September 2009