Abstract
By compactifying gauge theories on a lower dimensional manifold, we often find many interesting relationships between a geometry and a supersymmetric quantum field theory. In this paper we consider conformal field theories obtained from twisted compactification on a Riemann surface with a boundary. Various kinds of supersymmetric boundary conditions are exchanged under S-duality. To consider these transformations one need to take into account boundary degrees of freedom. So we study how the degrees of freedom can be added at the boundary of the Riemann surface. In this paper I show that this introduction of the boundary fields can be done preserving supersymmetry by means of 2-dimensional superfields.
Highlights
Example, under the S-duality transformation the NS5-like boundary condition (2.10) is transformed into the D5-like boundary condition [20]
Various kinds of supersymmetric boundary conditions are exchanged under S-duality
We study how these degrees of freedom can be added at the boundary of the Riemann surface
Summary
Our theory is constructed on the space R1,1 × Σg. The first factor R1,1 is a flat space with metric gmn = diag(−1, +1) and the second factor is a Riemann surface with genus g. ∇μXA := ∂μXA + i[Aμ, XA] , ∇μΨ := ∂μΨ + i[Aμ, Ψ] By twisting this action, we obtain the Lagrangian which is invariant under the supersymmetry transformation: δAμ = iǫΓμΨ , δXA′ = iǫΓAΨ , δΨ. In order to preserve the supersymmetries on such a curved space, we usually need to twist the theory. According to the previous work [21], we know N = (2, 2) supersymmetry is obtained from the no boundary with N = (4, 4) case. These supersymmetries are generated by the parameter satisfying, Γ2345ǫ = −ǫ , Γ3579ǫ = +ǫ.
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