Marginal and relevant deformations of /N=4 field theories and non-commutative moduli spaces of vacua

By D. Berenstein, Vishnu Jejjala, R. Leigh. 2000

158 citations recorded by the source corpus.

Abstract 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 5 ×S 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.

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

View Paper: https://www.semanticscholar.org/paper/f1745223eeaddafd8247afa34102b148effa08b0

How researchers see this paper

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

In Astronomy and Astrophysics

1. S. Frolov
2. A. Tseytlin
3. R. Roiban
4. K. Zoubos
5. R. Dijkgraaf
6. N. Beisert
7. G. Arutyunov
8. C. Vafa

In Nuclear and High Energy Physics

1. S. Frolov
2. A. Tseytlin
3. R. Roiban
4. N. Beisert
5. G. Arutyunov
6. K. Zoubos
7. M. Staudacher
8. L. Alday

In Statistical and Nonlinear Physics

1. S. Frolov
2. R. Dijkgraaf
3. K. Zoubos
4. R. Roiban
5. A. Tseytlin
6. C. Vafa
7. Marcos Mariño
8. D. Berenstein

Citations in the corpus

• Deformations of N = 4 SYM and integrable spin chain models (2004, background): “For the particular case of q a root of unity q = exp(2πit/k), with t, k coprime, we have r = 1 and we want to check that the spectrum of states with zero energy (BPS states) corresponds to the calculation done in [26].”
• Lax pair for strings in Lunin-Maldacena background (2005, background): “In a recent paper [1], Lunin and Maldacena have found a supergravity background which they have conjectured to be dual to a marginal deformation of N = 4 SYM sometimes called a β deformation [2, 3, 4, 5, 6, 7, 8].”
• A Perturbative Window into Non-Perturbative Physics (2002, background): “(The relation of this to non-commutativity in spacetime has been noted in [48].”
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, background): “q being a k-th root of unity) the dual background is actually an AdS5 × S/Zk × Zk orbifold [8].”
• Counting gauge invariants: The Plethystic program (2007, unknown): “also [33] for a non-commutative perspective).”
• Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “The argument is the same as originally given for rational deformation parameter in [33], see also [1].”