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General mirror pairs for gauged linear sigma models

Publication ,  Journal Article
Aspinwall, PS; Plesser, MR
Published in: Journal of High Energy Physics
November 1, 2015

Abstract: We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.

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Published In

Journal of High Energy Physics

DOI

EISSN

1029-8479

ISSN

1126-6708

Publication Date

November 1, 2015

Volume

2015

Issue

11

Start / End Page

1 / 33

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5106 Nuclear and plasma physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0105 Mathematical Physics
 

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Aspinwall, P. S., & Plesser, M. R. (2015). General mirror pairs for gauged linear sigma models. Journal of High Energy Physics, 2015(11), 1–33. https://doi.org/10.1007/JHEP11(2015)029
Aspinwall, P. S., and M. R. Plesser. “General mirror pairs for gauged linear sigma models.” Journal of High Energy Physics 2015, no. 11 (November 1, 2015): 1–33. https://doi.org/10.1007/JHEP11(2015)029.
Aspinwall PS, Plesser MR. General mirror pairs for gauged linear sigma models. Journal of High Energy Physics. 2015 Nov 1;2015(11):1–33.
Aspinwall, P. S., and M. R. Plesser. “General mirror pairs for gauged linear sigma models.” Journal of High Energy Physics, vol. 2015, no. 11, Nov. 2015, pp. 1–33. Scopus, doi:10.1007/JHEP11(2015)029.
Aspinwall PS, Plesser MR. General mirror pairs for gauged linear sigma models. Journal of High Energy Physics. 2015 Nov 1;2015(11):1–33.
Journal cover image

Published In

Journal of High Energy Physics

DOI

EISSN

1029-8479

ISSN

1126-6708

Publication Date

November 1, 2015

Volume

2015

Issue

11

Start / End Page

1 / 33

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5106 Nuclear and plasma physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0105 Mathematical Physics