RECORD
Structure constants of $\beta$ deformed super Yang-Mills
High Energy Physics - Theory · Submitted 15 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We study the structure constants of the ${\cal N}=1$ beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the $AdS_5\times S^5$ geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the structure constants of the ${\cal N}=1$ beta deformed theory perturbatively and at strong coupling. | contribution 0.99 | 0.95 | 0.05 | asserted 0.75 |
| s1 | We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. | result 0.97 | 0.95 | 0.15 | asserted 1.00 |
| s2 | This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. | interpretation 0.91 | 0.87 | 0.14 | asserted 0.97 |
| s3 | We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. | contribution 0.71 | 0.93 | 0.04 | asserted 0.83 |
| s4 | We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. | contribution 0.79 | 0.96 | 0.05 | asserted 1.00 |
| s5 | We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the $AdS_5\times S^5$ geometry. | result 1.00 | 0.94 | 0.30 | asserted 1.00 |
| s6 | This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. | interpretation 0.99 | 0.81 | 0.67 | hedged possibility 0.88 |
| s7 | We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. | result 0.98 | 0.93 | 0.05 | asserted 1.00 |
| s8 | This is in accordance with the prediction of the R-symmetry Ward identity. | interpretation 0.97 | 0.32 | 0.05 | hedged possibility 0.69 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We study the structure constants of the ${\cal N}=1$ beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the $AdS_5\times S^5$ geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.
Human review
How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 2 papers
-
In order to check the results of the hexagon approach with a field-theory computation, we make use of the results of [ref] and [ref] for undeformed and $β$-deformed $𝒩=4$ SYM theory, respectively.
Higher-rank sectors in the hexagon formalism and marginal deformations · Asymptotic one-loop corrections · 0.93
-
This argument ties the non-renormalization of the 3-point extremal functions to the non-renormalization of the Kälher potential on moduli space and seems to be different in spirit to the arguments on Harmonic superspace [ref] (see also [ref] and references therein and see also [ref] for the study of $β$-deformations).
Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra · Discussion · 0.91
What it cites · 18 sentences without a confident label
Uses the method or tool of 3 papers
-
We then use the method developed by [ref] to evaluate the structure constant of this supergravity mode with geodesics carrying R-charge $(J, J, J)$.
Holographic three-point functions of semiclassical states · Introduction · 0.99
-
Following the same method developed by [ref] and implemented for the case of the three point function involving vectors in [ref] , we evaluate the amplitude [equation] where $x$ refers to the co-ordinates on the boundary of the $AdS_5$. $S_string$ is given by [equation] and $h_MN, β_MN$ is the supergravity mode corresponding to the R-current given in ([ref]).
Correlators of massive string states with conserved currents · Ward identity at strong coupling · 0.95
-
The three point function of the chiral primaries in the Lunin-Maldacena background were evaluated in the limit when two of the chiral primaries have large R-charges and are semi-classical using the methods of [ref] .
On correlation functions of operators dual to classical spinning string states · Conclusions · 0.96
Compares with 2 papers
-
In [ref] the authors evaluated the three point function of a chiral primary and two heavy (non-chiral) operators using integrability in a certain large charge limit and showed that this agreed with that obtained at strong coupling in [ref] .
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match · Introduction · 0.81
-
In [ref] the authors evaluated the three point function of a chiral primary and two heavy (non-chiral) operators using integrability in a certain large charge limit and showed that this agreed with that obtained at strong coupling in [ref] .
Holographic three-point functions of semiclassical states · Introduction · 0.81
Cites as background 14 papers
-
Finally in [ref] methods which use integrability of planar $N=4$ Yang-Mills have been developed to evaluate structure constants.
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match · Introduction · 0.80
-
Finally in [ref] methods which use integrability of planar $N=4$ Yang-Mills have been developed to evaluate structure constants.
Tailoring Three-Point Functions and Integrability · Introduction · 0.80
-
Finally in [ref] methods which use integrability of planar $N=4$ Yang-Mills have been developed to evaluate structure constants.
N=4 SYM structure constants as determinants · Introduction · 0.80
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.