Bootstrap using labelled f-graphs, double-triangle and triangle rules, integrated correlators, and 10D hidden symmetry uniquely fixes three-loop mixed GGOO correlators in N=4 SYM, reproducing known two-loop results and yielding new three-loop terms for the maximal determinant operator.
Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the three-loop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the three-loop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the three-loop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the three-point function of two half-BPS operators and one Konishi operator at three-loop level. We use the same technique to work out a compact form for the four-loop four-point integrand and discuss the generalisation to higher loops.
fields
hep-th 4representative citing papers
ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.
citing papers explorer
-
Bootstrapping Giant Graviton Correlators
Bootstrap using labelled f-graphs, double-triangle and triangle rules, integrated correlators, and 10D hidden symmetry uniquely fixes three-loop mixed GGOO correlators in N=4 SYM, reproducing known two-loop results and yielding new three-loop terms for the maximal determinant operator.
-
Loops and legs: ABJM amplitudes from $f$-graphs
ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.
-
Notes on off-shell conformal integrals and correlation functions at five points
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
-
Leading singularities and chambers of Correlahedron
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.