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Gauge theory loop operators and liouville theory (2009).
| Content Provider | CiteSeerX |
|---|---|
| Author | Drukker, Nadav Gomis, Jaume Okuda, Takuya Teschner, Jörg |
| Abstract | We propose a correspondence between loop operators in a family of four dimensional N = 2 gauge theories on S 4 – including Wilson, ’t Hooft and dyonic operators – and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N = 2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun’s formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of ’t Hooft and dyonic loop operators in these N = 2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmüller theory as the quantum operators representing the length of geodesics. We |
| File Format | |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Subject Keyword | Liouville Theory Pi-strings-144 Gauge Theory Loop Operator Gauge Theory Liouville Loop Operator Liouville Correlators Beautiful Relation Loop Operator Riemann Surface Liouville Theory Loop Operator Partition Function Liouville Loop Operator Reproduces Pestun Wilson Loop Operator Corresponding Gauge Theory Dyonic Loop Operator Quantum Operator Quantum Teichm Ller Theory Dyonic Operator Modular Transformation Gauge Theory Loop Operator Expectation Value Conjectured Action Simple Geometric Interpretation Explicit Prediction Exact Expectation Value |
| Content Type | Text |
