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## Quantum conformal algebras and closed conformal field theory

Citations: | 19 - 9 self |

### Citations

5631 | The Large-N limit of superconformal field theories and supergravity,
- Maldacena
- 1999
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Citation Context ... it is suitable for an algebraic/axiomatic investigation. It is expected to be relevant both physically and mathematically. For example, in [2] (sect. 4.5) we argued, using the AdS/CFT correspondence =-=[5]-=-, in particular the results of [6], that the limit in which the TT OPE closes should be the strongly coupled large-Nc limit. In the present paper we argue something similar about finite N=2 theories. ... |

2757 |
Gauge theory correlators from noncritical string theory,
- Gubser, Klebanov, et al.
- 1998
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Citation Context ...xiomatic investigation. It is expected to be relevant both physically and mathematically. For example, in [2] (sect. 4.5) we argued, using the AdS/CFT correspondence [5], in particular the results of =-=[6]-=-, that the limit in which the TT OPE closes should be the strongly coupled large-Nc limit. In the present paper we argue something similar about finite N=2 theories. The plan of the paper is as follow... |

164 | Nonperturbative formulas for central functions of supersymmetric gauge theories,” Nucl.Phys. B526
- Anselmi, Freedman, et al.
- 1998
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Citation Context ...imensional conformal field theory. Thirdly, we show in the next section that · a closed algebra is determined uniquely by two central charges: c and a. The two central charges, called c and a in ref. =-=[13]-=- take different values in the N=2 algebra, precisely 4 : c = 1 6 (2N2 c − 1), a = 1 24 (7N2 c − 5), (9) and equal values in the N=4 algebra, c = a = 1 4 (N2 c − 1) if the gauge group is SU(Nc). We rec... |

30 |
A class of finite four-dimensional supersymmetric field theories, Phys
- Howe, Stelle, et al.
- 1983
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Citation Context ...hypermultiplets in the fundamental representation. The beta-function is just one-loop owing to N=2 supersymmetry. Precisely, it is proportional to Nc − 1 2 Nf, so it vanishes identically for Nf = 2Nc =-=[8]-=-. Combining the free-vector and freehypermultiplet quantum conformal algebras is not as straightforward as it might seem. The algebra is much richer than the N=4 one and some non-trivial work is requi... |

25 | Central functions and their physical implications
- Anselmi
- 1998
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Citation Context .... The currents are easily defined at non-zero coupling g by covariantizing the derivative appearing in A S 1 , i.e. AS 1 → −2iM←→ D µN. The matrix of two-point functions has the form (see for example =-=[11]-=-) 〈Σ i µ(x)Σ j 1 ν(0)〉 = (|x|µ) hik(g2 ) πµν ( (1) c kl (g2) |x| 4 ) 1 (|x|µ) hjl(g2 ) ( 1 4π2 ) 2 . (4) To calculate the lowest order of the matrix hij(g 2 ) of anomalous dimensions it is sufficient ... |

24 |
A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT4
- Anselmi, Grisaru, et al.
- 1997
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Citation Context ...epresentation, the conformal window is the interval 3/2Nc < Nf < 3Nc. In the limit where both Nc and Nf are large, but the ratio Nc/Nf is fixed and arbitrary in this window, the TT OPE does not close =-=[10]-=- and r is bounded by [14] r ∼ g 2 Nc < 8π 2 , 3 To our present knowledge, the stronger version of this statement, i.e. its extension to open algebras, might hold also. However, this is a more difficul... |

22 | The N = 4 quantum conformal algebra
- Anselmi
- 1999
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Citation Context ... consequence is that c and a have different subleading corrections. The closed algebra simplifies considerably at c = a, where it coincides with the N=4 one. CERN-TH/98-363 November, 1998. 1Recently =-=[1, 2]-=- we developed techniques to study the operator product expansion of the stress-energy tensor, with the purpose of acquiring a deeper knowledge of conformal field theories in four dimensions and quantu... |

18 | Theory of higher spin tensor currents and central charges
- Anselmi
- 1999
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Citation Context ...6 (1) The lowest components of each current multiplet (T2, Λ3, Ξ4, ∆5, Υ6, Ω7) have the same form. The normalization is fixed in such a way that these components have also the same overall factor. In =-=[2]-=- we used a different convention: we fixed the normalization of each current by demanding that the coefficients of AF and J S be 1. Here we have to be more precise and keep track of the relative factor... |

15 |
Positivity constraints for anomalous dimensions
- Nachtmann
- 1973
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Citation Context ...ill be very fruitful for both. It was observed in [1] that the relevant features of the algebra do not change with the value of the coupling constant. This was proved using a theorem due to Nachtmann =-=[4]-=-, found 1973 in the context of the theory of deep inelastic scattering. Only at special values g∗ of the coupling constant can the algebra change considerably. One special point is of course the free-... |

10 |
Introducing supersymmetry, Phys. Rep
- Sohnius
- 1985
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Citation Context ...theory (sects. 5 and 6), give the complete OPE algebra in the N=2 case (section 6) and discuss aspects of the N=1 closed quantum 2conformal algebra. For supersymmetry, we use the notation of Sohnius =-=[7]-=-, converted to the Euclidean framework via δµν → −δµν, T V,F,S → −T V,F,S (these are the vector, spinor and scalar contributions to the stress-tensor), εµνρσ → −iεµνρσ and γµ,γ5 → −iγµ, −iγ5. Moreover... |

6 |
the recent papers
- See
- 2013
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Citation Context ...f c and a are [13] c = (3Nv + Nχ), a = (9Nv + Nχ), where 24 48 Nv and Nχ are the numbers of vector and chiral multiplets. 6 This situation should be described also by the formalism of N=4 superfields =-=[17]-=-. Claimed by its authors to hold generically in N=4 supersymmetric Yang-Mills theory, this formally can actually be correct only in the closed limit of theories with c = a + O(1). 13Tµ(x) Tν(y) = Tµν... |

3 | for example T. Muta, Foundations of quantum chromodynamics. An introduction to perturbative methods in gauge theories, World Scientific - See - 1987 |

3 |
Non chiral primary superfields
- Andrianopoli, Ferrara
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Citation Context ...turned on by the interaction. Operators of classes ii) and iii) can often be derived from those of class i) by using supersymmetry. This is the case, for example, of the N=4 quantum conformal algebra =-=[12]-=-. The anomalous dimensions are of course the same as those of their class i)-partners, so that our discussion covers them and the conclusions that we derive are unaffected. 1 I am grateful to S. Ferra... |

3 | Matching conditions and duality in N=1 susy gauge theories - Kogan, Shifman, et al. |

1 |
Explicit supersymmetry breaking can preserve finiteness in rigid N=2 supersymmetric theories
- Parkes, West
- 1983
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Citation Context ...et appears in the quantum conformal algebra. T1 is the SU(2)invariant R-current, and its anomaly vanishes because it is proportional to the beta-function. 6T0 is one of the finite mass perturbations =-=[9]-=-. Our picture gives a nice argument for the finiteness of such a mass term, which follows directly from the finiteness of the stress-tensor. The next observation is that the T -multiplet has to be par... |

1 |
Exactly marginal operators and duality in four dimensional N=1 supersymmetric gauge theory, Nucl. Phys. B447
- Lucchesi
- 1997
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Citation Context ...ith a point at infinity, the parameter in question being the radius r of the ball or, equivalently, the coupling constant g2Nc. N=1 finite families of this type are for example those studied in refs. =-=[16]-=-. 6 OPE structure of closed conformal field theory. The basic rule to determine the quantum conformal algebra of closed conformal field theory is as follows. One first studies the free-field OPE of an... |