Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua

David Berenstein; Robert G. Leigh (UIUC); Vishnu Jejjala

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Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua

David Berenstein, Vishnu Jejjala, Robert G. Leigh (UIUC)

High Energy Physics - Theory · Submitted 9 May 2000

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The authors' main claim Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces.

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arXiv IDhep-th/0005087 (version 1)

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CitationDavid Berenstein, Robert G. Leigh (UIUC), Vishnu Jejjala. "Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua." arXiv:hep-th/0005087 (2000). https://pith.science/paper/2PX776LC

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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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study marginal and relevant supersymmetric deformations of the N=4 super-Yang-Mills theory in four dimensions.	contribution 0.64	0.90	0.05	asserted 0.94
s1	Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces.	contribution 0.95	0.92	0.42	asserted 1.00
s2	The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F-term constraints.	method 0.97	0.72	0.07	asserted 1.00
s3	These field theories are dual to superstring theories propagating on deformations of the AdS_5xS^5 geometry.	background 0.84	0.17	0.06	asserted 1.00
s4	We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces.	contribution 0.93	0.92	0.05	asserted 1.00
s5	The resulting moduli spaces of D-branes have several novel features.	result 0.88	0.76	0.07	asserted 0.93
s6	In particular, they may be interpreted as symmetric products of non-commutative spaces.	interpretation 0.75	0.80	0.13	hedged possibility 1.00
s7	We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality.	result 0.74	0.87	0.08	asserted 1.00
s8	Many features of the dual closed string theory may be identified within the non-commutative algebra.	result 0.59	0.80	0.09	hedged possibility 0.94
s9	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.	result 0.52	0.92	0.16	asserted 0.74

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.99.

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Original 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_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.

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References

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Hidden Symmetries of 4D N=2 Gauge Theories
hep-th 2024-11 conditional novelty 6.0 of 10

The apparently broken SU(4) R-symmetry of the Z2 orbifold of N=4 SYM is recovered as a Lie algebroid and, after marginal deformation, as a Drinfeld-twisted non-associative algebroid under which the planar Lagrangian i...
Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
hep-th 2012-07 conditional novelty 6.0 of 10

The single-trace superconformal index of the holographic quiver gauge theory equals a sum over Kohn-Rossi cohomology of the Sasaki-Einstein base, matching the independent gauge theory computation.
Counting Gauge Invariants: the Plethystic Program
hep-th 2007-01 accept novelty 6.0 of 10

The plethystic exponential and its inverse give a systematic dictionary between the Hilbert series of a Calabi-Yau singularity and the single- and multi-trace gauge invariant operators of its D-brane quiver theory.
String theory dual of the beta-deformed gauge theory
hep-th 2006-03 conditional novelty 6.0 of 10

The authors construct a doubly periodic, SL(2,Z) covariant string dual by replacing the deformation parameter in the Lunin-Maldacena background with an elliptic function.
Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
hep-th 2006-02 conditional novelty 5.0 of 10

The number of conifold singularities in a deformed q-deformed N=4 geometry equals the number of allowed complex-structure deformations, with two fractional branes at each singularity.

Show 1 more citing papers

Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
hep-th 2010-12 accept novelty 2.0 of 10

Across the deformations, orbifolds and open-chain setups surveyed, all-loop integrability survives only where the bulk spin chain is undeformed N=4 SYM and the difference sits in twisted, orbifold or open boundary conditions.

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21 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Uses its method or tool 3 papers

The moduli spaces we found can be seen as a $ℂ^*$-fibration over a basis described by $𝒵𝒜$, so we can use the same reasoning as in [ref] .

Aspects of ABJM orbifolds with discrete torsion · Matching with gravity duals · 0.93
For theories that have couplings of single trace type, there is a general recipe to build the moduli space from the components we have studied so far [ref] .

Aspects of ABJM orbifolds · The complete moduli space · 0.85
Basically, we are going to We describe the algebraic tools developed in [ref] for the three examples we consider in this paper.

Geometric aspects of dibaryon operators · Dibaryon operators in the conifold theory · 0.92

Compares with it 1 paper

Like in the type IIB case [ref] they are related by mirror symmetry.

Aspects of ABJM orbifolds with discrete torsion · Matching with gravity duals · 0.87

Cites it as background 6 papers

The dual $N=1$ field theory arises as an exactly marginal deformation of $N=4$ SYM [ref] .

Three-point correlators: Examples from Lunin-Maldacena background · Introduction · 0.81
An understanding of how $V$ appears in a given field theory has been described in [ref] (for previous work see [ref] ), but one is not guaranteed to get a Calabi-Yau geometry from such a field theory and all the details of when this works are not understood in general.

Geometric aspects of dibaryon operators · Introduction and conclusion · 0.83
For the $=1$ Leigh-Strassler marginal deformations of the $=4$ theory [ref] , the link between the F-term relations and quantum planes was noticed in [ref] , and was further developed in [ref] .

Hidden Symmetries of 4D N=2 Gauge Theories · F- and D- term quantum planes · 0.82

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