Localization on the D-brane, two-dimensional gauge theory and matrix models
- Theoretical Physics Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako Saitama 351-0198 (Japan)
We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vacuum expectation value of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the partition function gives a grand canonical ensemble of multi-instanton corrections for four-dimensional N=2 gauge theory in a suitable large N limit. We find two-dimensional gauge theories that provide the instanton partition function for four-dimensional N=2 theories with the hypermultiplets in the adjoint and fundamental representations. We also propose a partition function that gives the instanton contributions to four-dimensional N=2 quiver gauge theory. We discuss the relation between Nekrasov's instanton partition function and the Dijkgraaf-Vafa theory in terms of large N phase transitions of the generalized two-dimensional Yang-Mills theory.
- OSTI ID:
- 20776803
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevD.73.046006; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CORRECTIONS
EUCLIDEAN SPACE
EXPECTATION VALUE
GAUGE INVARIANCE
INSTANTONS
MEMBRANES
PARTITION FUNCTIONS
PHASE TRANSFORMATIONS
POTENTIALS
QUANTUM FIELD THEORY
STRING MODELS
SUPERSYMMETRY
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES
VORTICES
YANG-MILLS THEORY