Duality, quotients, and currents

218

427

Abstract:We prove the equivalence of the SL(2, R)/ U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.

“…In other words, the lowest component of the dual superfield is a dynamical theta-angle. Using the method of [31,1], we find that the dual action is…”

Section: The Dual Theorymentioning

confidence: 99%

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

Hori

Kapustin

2001

218

427

“…Consider now the integration over X m for arbitrary W , following [3], [4], [7]. On a general Riemann surface W , X m (σ) can be written in terms of a function x m (σ) and a winding term, so that…”

Section: Large Gauge Transformations and Global Structurementioning

confidence: 99%

Global aspects of T-duality, gauged sigma models and T-folds

Hull

2007

116

205

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to Tduality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

“…The T-dual or mirror Landau-Ginzburg model based on an twisted chiral superfield [36] flows to the anti-diagonal minimal model. This can be written as a Z Z k orbifold of the model in equation (3.1).…”

Section: Landau-ginzburg Potentials For Minimal Modelsmentioning

confidence: 99%

Non-compact Gepner models, Landau-Ginzburg orbifolds and mirror symmetry

Ashok

Benichou

Troost

2008

We study non-compact Gepner models that preserve sixteen or eight supercharges in type II string theories. In particular, we develop an orbifolded Landau-Ginzburg description of these models analogous to the Landau-Ginzburg formulation of compact Gepner models. The Landau-Ginzburg description provides an easy and direct access to the geometry of the singularity associated to the non-compact Gepner models. Using these tools, we are able to give an intuitive account of the chiral rings of the models, and of the massless moduli in particular. By studying orbifolds of the singular linear dilaton models, we describe mirror pairs of non-compact Gepner models by suitably adapting the Greene-Plesser construction of mirror pairs for the compact case. For particular models, we take a large level, low curvature limit in which we can analyze corrections to a flat space orbifold approximation of the non-compact Gepner models. This gives rise to a counting of moduli which differs from the toric counting in a subtle way.