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Title: Non-vanishing superpotentials in heterotic string theory and discrete torsion

Abstract

Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finitemore » part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other« less

Authors:
 [1];  [2]
  1. Univ. of Western Australia, Crawley, WA (Australia). School of Physics
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1360741
Grant/Contract Number:
SC0007901
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Superstring Vacua; Superstrings and Heterotic Strings

Citation Formats

Buchbinder, Evgeny I., and Ovrut, Burt A.. Non-vanishing superpotentials in heterotic string theory and discrete torsion. United States: N. p., 2017. Web. doi:10.1007/JHEP01(2017)038.
Buchbinder, Evgeny I., & Ovrut, Burt A.. Non-vanishing superpotentials in heterotic string theory and discrete torsion. United States. doi:10.1007/JHEP01(2017)038.
Buchbinder, Evgeny I., and Ovrut, Burt A.. Tue . "Non-vanishing superpotentials in heterotic string theory and discrete torsion". United States. doi:10.1007/JHEP01(2017)038. https://www.osti.gov/servlets/purl/1360741.
@article{osti_1360741,
title = {Non-vanishing superpotentials in heterotic string theory and discrete torsion},
author = {Buchbinder, Evgeny I. and Ovrut, Burt A.},
abstractNote = {Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other},
doi = {10.1007/JHEP01(2017)038},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2017,
place = {United States},
year = {Tue Jan 10 00:00:00 EST 2017},
month = {Tue Jan 10 00:00:00 EST 2017}
}

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  • Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less
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