Twisted Einstein Tensors and Orbifold Geometry

Abstract

Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space geometry is emphasized for the WZW orbifolds - while for the sigma model orbifolds we construct the corresponding {\it sigma model orbifold action}, which includes the previously-known general WZW orbifold action and general coset orbifold action as special cases. We focus throughout on the {\it twisted Einstein tensors} with diagonal monodromy, including the twisted Einstein metric, the twisted B field and the twisted torsion field of each orbifold sector. Finally, we present strong evidence for a conjectured set of {\it twisted Einstein equations} which should describe those sigma model orbifolds in this class which are also 1-loop conformal.

67 pages, typos corrected

References in corpus (5)

• The Operator Algebra and Twisted KZ Equations of WZW Orbifolds
• Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)
• The General Coset Orbifold Action
• The Outer-Automorphic WZW Orbifolds on so(2n), including Five Triality Orbifolds on so(8)
• Extended Operator Algebra and Reducibility in the WZW Permutation Orbifolds

Cited by in corpus (12)

• The General Twisted Open WZW String
• On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors
• A Basic Class of Twisted Open WZW Strings
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26. I.Extended Actions and New Twisted World-Sheet Gravities
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds
• The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $c=26$ III. The Spectra of $\hat{c}=52$ Strings
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 II. The Twisted BRST Systems of \hatc=52 Matter
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c}=26$ V. Cyclic Permutation Orbifolds
• The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions
• The Orbifold-String Theories of Permutation-Type: III. Lorentzian and Euclidean Space-Times in a Large Example
• The Lorentzian Space-Times of the Orientation-Orbifold String Systems