1993/04/29 by John H. Schwarz, Ashoke Sen · 430 citations
Mathematics · Physics and Astronomy · #Action (physics) #Antisymmetric tensor #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Duality (order theory) #Gauge theory #Geometry #Heterotic string theory #Homogeneous space #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Symmetry (geometry) #Theoretical physics #hep-th
paper · pdf · doi:10.1016/0550-3213(94)90053-1
published in Nuclear Physics B 411(1), 35-63 (Elsevier BV) · phyzzx.tex, 31 pages, NSF-ITP-93-46
arxiv created 1993/04/29 · openalex publication_date 1994/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is frequently useful to construct dual descriptions of theories containing antisymmetric tensor fields by introducing a new potential whose curl gives the dual field strength, thereby interchanging field equations with Bianchi identities. We describe a general procedure for constructing actions containing both potentials at the same time, such that the dual relationship of the field strengths arises as an equation of motion. The price for doing this is the sacrifice of manifest Lorentz invariance or general coordinate invariance, though both symmetries can be realized nonetheless. There are various examples of global symmetries that have been realized as symmetries of field equations but not actions. These can be elevated to symmetries of the action by our method. The main example that we focus on is the low-energy effective action description of the heterotic string theory compactified on a six-torus to four dimensions. We show that the SL(2,R) symmetry, whose SL(2,Z) subgroup has been conjectured to be an exact symmetry of the full string theory, can be realized on the action in a way that brings out a remarkable similarity to the target space duality symmetry O(6,22). Our analysis indicates that SL(2,Z) symmetry may arise naturally in a dual formulation of the theory.