Duality of the Fermionic 2d Black Hole and N = 2 Liouville Theory as Mirror Symmetry

By K. Hori, A. Kapustin. 2001

279 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dda097b67dee20d7a007d3dfd98a9e2690456894

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. Y. Nakayama
2. C. Vafa
3. T. Nishioka
4. T. Takayanagi
5. Hirosi Ooguri
6. David Tong
7. I. Brunner
8. K. Hori

In Statistical and Nonlinear Physics

1. C. Vafa
2. T. Nishioka
3. Hirosi Ooguri
4. Y. Nakayama
5. T. Takayanagi
6. I. Brunner
7. David Tong
8. K. Hori

Citations in the corpus

• Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories (2006, methodology): “This computation has been performed in several examples — Landau-Ginzburg models [27], N = (0, 2) Abelian linear sigma models (where only T−-T− OPE matters [28]), and N = (2, 2) Abelian linear sigma models [29].”
• Orientifolds and mirror symmetry (2003, background): “In fact, in a closely related SL(2,R)/U(1) gauged WZW model, one can find a mirror transform to a LG model whose superpotential reflects the instanton effects [78].”
• The holographic dual of AdS3 × S3 × S3 × S1 (2014, methodology): “This method has been used to compute the central charge in a number of examples, including N = (0, 2) models [17] and N = (2, 2) Landau-Ginzburg theories [18], Liouville theories [19] and non-Abelian gauge theories [20].”
• NS5-Branes, T-Duality and Worldsheet Instantons (2002, methodology): “ theory. It has N = (4,4) supersymmetry (or 8 non-chiral supercharges) in d= 1 + 1 dimensions, and may be thought of as the N = (4,4) extension of the theories discussed recently by Hori and Kapustin [7]. There are three superfield representations of the N = (4,4) supersymmetry algebra: a vector mult”
• Worldsheet derivation of a large N duality (2002, background): “More recently, this equivalence was proven directly using mirror symmetry in [35].”
• AdS bubbles, entropy and closed string tachyons (2006, background): “The FZZ duality leads to the equivalent background with the following non-trivial metric and dilaton [68] ds(2) = −(dx0)(2) + (dx1)(2) + 1 Q2 tanh(2)(Qx1)(dθ) (2), gs = e0 cosh(Qx1) , (4.”
• Liouville Field Theory — A decade after the revolution (2004, background): “In [419], it was shown that the mild assumption of the reality of the current uniquely chooses a = 0.”