Higher order couplings from heterotic orbifold theory

Kang Sin Choi; Tatsuo Kobayashi

doi:10.1016/j.nuclphysb.2008.01.016

Higher order couplings from heterotic orbifold theory

Kang Sin Choi, Tatsuo Kobayashi

Scranton Honors Program

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kähler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.

Original language	English
Pages (from-to)	295-321
Number of pages	27
Journal	Nuclear Physics, Section B
Volume	797
Issue number	1-2
DOIs	https://doi.org/10.1016/j.nuclphysb.2008.01.016
State	Published - 1 Jul 2008

Bibliographical note

Funding Information:
We are grateful to Steve Abel, Massimo Bianchi, Jihn E. Kim, Hans-Peter Nilles, Saul Ramos-Sanchez, Michael Ratz, Robert Richter and Patrick K.S. Vaudrevange for discussion. K.S.C. thanks to Yukawa Institute for hospitality, where part of the work is done. K.S.C. is supported in part by the European Union 6th framework program MRTN-CT-2004-503069 “Quest for unification”, MRTN-CT-2004-005104 “ForcesUniverse”, MRTN-CT-2006-035863 “UniverseNet” and SFB-Transregio 33 “The Dark Univerese” by Deutsche Forschungsgemeinschaft (DFG). T.K. is supported in part by the Grand-in-Aid for Scientific Research #1754025 and the Grant-in-Aid for the 21st Century COE “The Center for Diversity and Universality in Physics” from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Keywords

Heterotic string
Higher order coupling
Orbifold compactification
Yukawa coupling

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10.1016/j.nuclphysb.2008.01.016

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title = "Higher order couplings from heterotic orbifold theory",

abstract = "We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from K{\"a}hler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.",

keywords = "Heterotic string, Higher order coupling, Orbifold compactification, Yukawa coupling",

author = "Choi, {Kang Sin} and Tatsuo Kobayashi",

note = "Funding Information: We are grateful to Steve Abel, Massimo Bianchi, Jihn E. Kim, Hans-Peter Nilles, Saul Ramos-Sanchez, Michael Ratz, Robert Richter and Patrick K.S. Vaudrevange for discussion. K.S.C. thanks to Yukawa Institute for hospitality, where part of the work is done. K.S.C. is supported in part by the European Union 6th framework program MRTN-CT-2004-503069 “Quest for unification”, MRTN-CT-2004-005104 “ForcesUniverse”, MRTN-CT-2006-035863 “UniverseNet” and SFB-Transregio 33 “The Dark Univerese” by Deutsche Forschungsgemeinschaft (DFG). T.K. is supported in part by the Grand-in-Aid for Scientific Research #1754025 and the Grant-in-Aid for the 21st Century COE “The Center for Diversity and Universality in Physics” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. ",

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N2 - We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kähler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.

AB - We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kähler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.

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Higher order couplings from heterotic orbifold theory

Abstract

Bibliographical note

Keywords

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