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Title: Intrinsic non-commutativity of closed string theory

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 non-commutativity 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 non-commutativity was not emphasized previously in the existing literature. This non-commutativity can be thought of as a central extension of the zero-mode 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.
 [1] ;  [2] ;  [3]
  1. Perimeter Inst. for Theoretical Physics, Waterloo (Canada)
  2. Univ. of Illinois, Urbana, IL (United States). Dept. of Physics
  3. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
SC0015655; FG02-13ER41917
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 1029-8479
Springer Berlin
Research Org:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org:
USDOE; Natural Sciences and Engineering Research Council of Canada (NSERC); Julian Schwinger Foundation
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Non-Commutative Geometry; String Duality
OSTI Identifier: