SL(2, Z) action on three-dimensional conformal field theories with abelian symmetry

Edward Witten

Research output: Chapter in Book/Report/Conference proceedingChapter

72 Scopus citations

Abstract

On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2, Z). The generator S of SL(2, Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2, Z) action in three dimensions is related by the AdS/CFT correspondence to SL(2, Z) duality of low energy U(1) gauge fields in four dimensions.

Original languageEnglish (US)
Title of host publicationFrom Fields to Strings
Subtitle of host publicationCircumnavigating Theoretical Physics: Ian Kogan Memorial Collection
PublisherWorld Scientific Publishing Co.
Pages1173-1200
Number of pages28
Volume1
ISBN (Electronic)9789812775344
ISBN (Print)9789812389558
DOIs
StatePublished - Jan 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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