On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors

Abstract

Including world-sheet orientation-reversing automorphisms in the orbifold program, we recently reported the twisted operator algebra and twisted KZ equations in each open-string sector of the general WZW orientation orbifold. In this paper we work out the corresponding classical description of these sectors, including the {\it WZW orientation-orbifold action} -- which is naturally defined on the solid half cylinder -- and its associated WZW orientation-orbifold branes. As a generalization, we also obtain the {\it sigma-model orientation-orbifold action}, which describes a much larger class of open-string orientation-orbifold sectors. As special cases, this class includes twisted open-string {\it free boson} examples, the open-string WZW sectors above and the open-string sectors of the {\it general coset orientation orbifold}. Finally, we derive the {\it orientation- orbifold Einstein equations}, in terms of twisted Einstein tensors -- which hold when the twisted open-string sigma-model sectors are 1-loop conformal.

77 pages, typos corrected

References in corpus (7)

• 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)
• More About All Current-Algebraic Orbifolds
• Twisted Einstein Tensors and Orbifold Geometry
• Hamiltonian Formulation of Open WZW Strings

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• The General Twisted Open WZW String
• E10 Orbifolds
• 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 Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 II. The Twisted BRST Systems of \hatc=52 Matter
• 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 $\mathbf{c}=26$ 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
• On Homological and Homotopical Algebra of Supersymmetries and Integrability in String Theory