Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-09
Nucl.Phys. B589 (2000) 196-248
Physics
High Energy Physics
High Energy Physics - Theory
60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmath
Scientific paper
10.1016/S0550-3213(00)00394-1
We study marginal and relevant supersymmetric deformations of the N=4 super-Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F-term constraints. These field theories are dual to superstring theories propagating on deformations of the AdS_5xS^5 geometry. We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces. The resulting moduli spaces of D-branes have several novel features. In particular, they may be interpreted as symmetric products of non-commutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality. Many features of the dual closed string theory may be identified within the non-commutative algebra. In particular, we make progress towards understanding the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete anomalies based on the non-commutative geometry.
Berenstein David
Jejjala Vishnu
Leigh Robert G.
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