Laurent Hoffmann - Academia.edu (original) (raw)

Papers by Laurent Hoffmann

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT co... more We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

Nuclear Physics B, 2001

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions ... more Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fieldsΦΦ,CC andΦC, the conformal fields which are symmetric traceless tensors of rank l and have dimensions δ = 2 + l or 8 + l + η(l) and η(l) = O(N −2 ) are identified. The unidentified fields have dimension δ = λ + l + η(l) with λ ≥ 10. The anomalous dimensions η(l) are calculated at order O(N −2 ) for both 2 − 1 2 (−ΦΦ +CC) and 2 − 1 2 (ΦC +CΦ) and are found to be the same, proving U (1) Y symmetry. The relevant coupling constants are given at order O(1).

We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furt... more We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U (1) Y symmetry for four-point functions.

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fie... more We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) OIk(x)O^I_k(x)OIk(x) and eventually their derivatives by applying operator product expansions and singling out SO(6) representations. We show that normal products of O_2O_2O_2 operators can be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive mathcalO(frac1N2)\mathcal{O}(\frac{1}{N^2})mathcalO(frac1N2) corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1/2-BPS or 1/4-BPS fields.

Nuclear Physics B, 2002

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fie... more We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) O I k (x) and eventually their derivatives by applying operator product expansions and singling out particular SO(6) representations. We show that normal products of O 2 operators can, to leading order, be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive O( 1 N 2 ) corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1 2 -BPS or 1 4 -BPS fields.

Physics Letters B, 2000

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show ... more We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

Nuclear Physics B, 2000

We develop a method of singularity analysis for conformal graphs which, in particular, is applica... more We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis. 1

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT co... more We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

Nuclear Physics B, 2001

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions ... more Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fieldsΦΦ,CC andΦC, the conformal fields which are symmetric traceless tensors of rank l and have dimensions δ = 2 + l or 8 + l + η(l) and η(l) = O(N −2 ) are identified. The unidentified fields have dimension δ = λ + l + η(l) with λ ≥ 10. The anomalous dimensions η(l) are calculated at order O(N −2 ) for both 2 − 1 2 (−ΦΦ +CC) and 2 − 1 2 (ΦC +CΦ) and are found to be the same, proving U (1) Y symmetry. The relevant coupling constants are given at order O(1).

We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furt... more We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of U (1) Y symmetry for four-point functions.

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fie... more We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) OIk(x)O^I_k(x)OIk(x) and eventually their derivatives by applying operator product expansions and singling out SO(6) representations. We show that normal products of O_2O_2O_2 operators can be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive mathcalO(frac1N2)\mathcal{O}(\frac{1}{N^2})mathcalO(frac1N2) corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1/2-BPS or 1/4-BPS fields.

Nuclear Physics B, 2002

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fie... more We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) O I k (x) and eventually their derivatives by applying operator product expansions and singling out particular SO(6) representations. We show that normal products of O 2 operators can, to leading order, be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive O( 1 N 2 ) corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1 2 -BPS or 1 4 -BPS fields.

Physics Letters B, 2000

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show ... more We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

Nuclear Physics B, 2000

We develop a method of singularity analysis for conformal graphs which, in particular, is applica... more We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis. 1