Abstract
We construct a class of codimension-2 solutions in supergravity that realize T-folds with arbitrary $O(2,2,\mathbb{Z})$ monodromy and we develop a geometric point of view in which the monodromy is identified with a product of Dehn twists of an auxiliary surface $\Sigma$ fibered on a base $\mathcal{B}$. These defects, that we call T-fects, are identified by the monodromy of the mapping torus obtained by fibering $\Sigma$ over the boundary of a small disk encircling a degeneration. We determine all possible local geometries by solving the corresponding Cauchy-Riemann equations, that imply the equations of motion for a semi-flat metric ansatz. We discuss the relation with the F-theoretic approach and we consider a generalization to the T-duality group of the heterotic theory with a Wilson line.
Highlights
Obtain the four-dimensional theory with parameter τ by compactifying a six-dimensional (2, 0) theory on R4 × T 2 [1]
We construct a class of codimension-2 solutions in supergravity that realize T-folds with arbitrary O(2, 2, Z) monodromy and we develop a geometric point of view in which the monodromy is identified with a product of Dehn twists of an auxiliary surface Σ fibered on a base B
The monodromy can be factorized as a product of Dehn twists, and the total space of the fibration is a 3-manifold Nφ, known as the mapping torus for Σ = T 2, whose geometry is determined by the type of torus diffeomorphism φ
Summary
We begin by considering a T 2 fibration over a base B. The fiber torus can be either part of the ten dimensional space-time, or be an auxiliary space that geometrizes an SL(2, Z) duality group, as in F-theory [8]. We will first consider torus bundles with B a circle, and later we will study fibrations over a two dimensional base, where the circle becomes contractible. The case B = P1 was introduced in [15] and it can be understood, for the heterotic theory, from a duality with F-theory [11] This is the most interesting situation, since if one describes the auxiliary Tρ2 fibration as an elliptic. We will later generalize our results beyond torus fibrations, motivated by the heterotic T-duality group with a single Wilson line. We note that some of the results we obtain can be applied in more general contexts as well
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