Intrinsic noncommutativity of closed string theory
Abstract
We show that the proper interpretation of the cocycle operators appearing in the physical vertex operators of compactified strings is that the closed string target is noncommutative. We track down the appearance of this noncommutativity to the Polyakov action of the at closed string in the presence of translational monodromies (i.e., windings). Here, in view of the unexpected nature of this result, we present detailed calculations from a variety of points of view, including a careful understanding of the consequences of mutual locality in the vertex operator algebra, as well as a detailed analysis of the symplectic structure of the Polyakov string. Finally, we also underscore why this noncommutativity was not emphasized previously in the existing literature. This noncommutativity can be thought of as a central extension of the zeromode operator algebra, an effect set by the string length scale $$ it is present even in trivial backgrounds. Clearly, this result indicates that the α'→0 limit is more subtle than usually assumed.
 Authors:

 Perimeter Inst. for Theoretical Physics, Waterloo (Canada)
 Univ. of Illinois, Urbana, IL (United States). Dept. of Physics
 Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Univ. of Illinois at UrbanaChampaign, IL (United States)
 Sponsoring Org.:
 USDOE; Natural Sciences and Engineering Research Council of Canada (NSERC); Julian Schwinger Foundation
 OSTI Identifier:
 1425953
 Grant/Contract Number:
 SC0015655; FG0213ER41917
 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: 2017; Journal Issue: 9; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; NonCommutative Geometry; String Duality
Citation Formats
Freidel, Laurent, Leigh, Robert G., and Minic, Djordje. Intrinsic noncommutativity of closed string theory. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)060.
Freidel, Laurent, Leigh, Robert G., & Minic, Djordje. Intrinsic noncommutativity of closed string theory. United States. doi:10.1007/JHEP09(2017)060.
Freidel, Laurent, Leigh, Robert G., and Minic, Djordje. Thu .
"Intrinsic noncommutativity of closed string theory". United States. doi:10.1007/JHEP09(2017)060. https://www.osti.gov/servlets/purl/1425953.
@article{osti_1425953,
title = {Intrinsic noncommutativity of closed string theory},
author = {Freidel, Laurent and Leigh, Robert G. and Minic, Djordje},
abstractNote = {We show that the proper interpretation of the cocycle operators appearing in the physical vertex operators of compactified strings is that the closed string target is noncommutative. We track down the appearance of this noncommutativity to the Polyakov action of the at closed string in the presence of translational monodromies (i.e., windings). Here, in view of the unexpected nature of this result, we present detailed calculations from a variety of points of view, including a careful understanding of the consequences of mutual locality in the vertex operator algebra, as well as a detailed analysis of the symplectic structure of the Polyakov string. Finally, we also underscore why this noncommutativity was not emphasized previously in the existing literature. This noncommutativity can be thought of as a central extension of the zeromode operator algebra, an effect set by the string length scale $$ it is present even in trivial backgrounds. Clearly, this result indicates that the α'→0 limit is more subtle than usually assumed.},
doi = {10.1007/JHEP09(2017)060},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2017,
place = {United States},
year = {2017},
month = {9}
}
Web of Science
Works referenced in this record:
Noncommutative geometry and Matrix theory
journal, February 1998
 Connes, Alain; Douglas, Michael R.; Schwarz, Albert
 Journal of High Energy Physics, Vol. 1998, Issue 02
Born reciprocity in string theory and the nature of spacetime
journal, March 2014
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 Physics Letters B, Vol. 730
A physical interpretation of cocycle factors in vertex operator representations
journal, November 1989
 Sakamoto, Makoto
 Physics Letters B, Vol. 231, Issue 3
String theory and noncommutative geometry
journal, September 1999
 Seiberg, Nathan; Witten, Edward
 Journal of High Energy Physics, Vol. 1999, Issue 09
Quantum field theory on noncommutative spaces
journal, May 2003
 Szabo, R.
 Physics Reports, Vol. 378, Issue 4
Quantum gravity, dynamical phasespace and string theory
journal, October 2014
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 International Journal of Modern Physics D, Vol. 23, Issue 12
A note on toroidal compactification of heterotic string theory
journal, January 1987
 Narain, K. S.; Sarmadi, M. H.; Witten, E.
 Nuclear Physics B, Vol. 279, Issue 34
Projective characters of degree one and the inflationrestriction sequence
journal, April 1989
 Higgs, R. J.
 Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 46, Issue 2
Cocycle Properties of String Theories on Orbifolds
journal, January 1992
 Horiguchi, Tsutomu; Sakamoto, Makoto; Tabuse, Masayoshi
 Progress of Theoretical Physics Supplement, Vol. 110
Topological Terms in String Theory on Orbifolds
journal, February 1995
 Sakamoto, M.; Tachibana, M.
 Progress of Theoretical Physics, Vol. 93, Issue 2
String emission from twisted sectors: Cocycle operators and modular background symmetries
journal, August 1992
 Erler, J.; Jungnickel, D.; Lauer, J.
 Annals of Physics, Vol. 217, Issue 2
Double field theory
journal, September 2009
 Hull, Chris; Zwiebach, Barton
 Journal of High Energy Physics, Vol. 2009, Issue 09
Local subsystems in gauge theory and gravity
journal, September 2016
 Donnelly, William; Freidel, Laurent
 Journal of High Energy Physics, Vol. 2016, Issue 9
Dbranes and the noncommutative torus
journal, February 1998
 Douglas, Michael R.; Hull, Chris
 Journal of High Energy Physics, Vol. 1998, Issue 02
Noncommutative field theory
journal, November 2001
 Douglas, Michael; Nekrasov, Nikita
 Reviews of Modern Physics, Vol. 73, Issue 4
Metastring theory and modular spacetime
journal, June 2015
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 Journal of High Energy Physics, Vol. 2015, Issue 6
Doubled geometry and Tfolds
journal, July 2007
 Hull, Christopher M.
 Journal of High Energy Physics, Vol. 2007, Issue 07
Topological aspects of an antisymmetric background field on orbifolds
journal, February 1994
 Sakamoto, Makoto
 Nuclear Physics B, Vol. 414, Issue 12
Modular spacetime
journal, October 2015
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 International Journal of Modern Physics D, Vol. 24, Issue 12
Modular Spacetime and Metastring Theory
journal, January 2017
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 Journal of Physics: Conference Series, Vol. 804
New heterotic string theories in uncompactified dimensions < 10
journal, March 1986
 Narain, K. S.
 Physics Letters B, Vol. 169, Issue 1
Renormalisation of ?4Theory on Noncommutative ?4 in the Matrix Base
journal, February 2005
 Grosse, Harald; Wulkenhaar, Raimar
 Communications in Mathematical Physics, Vol. 256, Issue 2
String Geometry and the Noncommutative Torus
journal, October 1999
 Landi, Giovanni; Lizzi, Fedele; Szabo, Richard J.
 Communications in Mathematical Physics, Vol. 206, Issue 3
Asymmetric orbifolds
journal, January 1987
 Narain, K. S.; Sarmadi, M. H.; Vafa, C.
 Nuclear Physics B, Vol. 288