## Periodic Report Summary 1 - QFT@FC (Quantum Field Theory at Finite Coupling)

The constituents of atoms in nature are quarks and gluons. The quarks source a color ﬂux between them that results in the strong nuclear force, conﬁning them together. The same gluonic color ﬂux controls almost any strong interaction dynamics in the theory of gluons, namely quantum chromodynamics. Hence, to understand fundamental phenomena that originate from strong coupling dynamics we need to understand the dynamics of the color ﬂux. Recently a new tool has emerged, in which the color ﬂux is described by a two dimensional string. The string naturally lives in a holographic higher dimensional space-time. Excitingly, in some cases the dynamic of the string tuns out to by integrable, namely solvable.

This goal of this proposal is to use the integrable string dynamics for solving a certain interacting gauge theory in four dimensions for any strength of the interaction. That theory is expected to play an analogues role in Quantum Field Theory (QFT) to the one played by the Hydrogen atom in Chemistry. Namely, it will serve as a base ground for our physical understanding of strongly interacting theories in general. In this proposal the PI is focusing on the computation of the two most fundamental non-local observables in any QFT. These are scattering amplitudes and Wilson loops.

Since the beginning of the project, signiﬁcant progress has been made:

1 The PI have studied scattering amplitudes and Wilson loops using integrability methods. He has reviled how to extend the use of this method for computing amplitudes with any possible helicity conﬁguration of the external particles. He has also boot-strapped the necessary building block for computing these amplitudes with arbitrary helicity at ﬁnite value of the coupling.

2 The PI has provide a ﬁnite coupling prediction for all the terms in the expansion of the six gluon amplitudes around the collinear limit. These furnish for the ﬁrst time a non-perturbative representation of the full amplitudes.

3 One of the main ingredients in the computation of scattering amplitudes using integrable methods is the group theoretical structures by which the relevant building blocks are glued together into the physical amplitude. The PI has provided a simple expression for all these structures.

4 Many diﬀerent observables in QFT are known to factoriez into simpler pieces in a certain kinematical limits. The PI have understood how such limits are all controlled by few simple building block which are associated with null propagation. Using integrability methods, he has computed these building block at ﬁnite coupling. By combining them together in diﬀerent ways, he has derived ﬁnite coupling prediction several observables.

In addition to the signiﬁcant scientiﬁc progress, the proposal and its implementation aids the PI with his integration at Tel Aviv University. In particular, the PI has two undergraduate student, one postdoc that is arriving soon and numerous visitors and experts that have visited the group in the past two years. The program thus strongly supports the theoretical activities at Tel Aviv university, which have commenced with the arrival of the PI.

This goal of this proposal is to use the integrable string dynamics for solving a certain interacting gauge theory in four dimensions for any strength of the interaction. That theory is expected to play an analogues role in Quantum Field Theory (QFT) to the one played by the Hydrogen atom in Chemistry. Namely, it will serve as a base ground for our physical understanding of strongly interacting theories in general. In this proposal the PI is focusing on the computation of the two most fundamental non-local observables in any QFT. These are scattering amplitudes and Wilson loops.

Since the beginning of the project, signiﬁcant progress has been made:

1 The PI have studied scattering amplitudes and Wilson loops using integrability methods. He has reviled how to extend the use of this method for computing amplitudes with any possible helicity conﬁguration of the external particles. He has also boot-strapped the necessary building block for computing these amplitudes with arbitrary helicity at ﬁnite value of the coupling.

2 The PI has provide a ﬁnite coupling prediction for all the terms in the expansion of the six gluon amplitudes around the collinear limit. These furnish for the ﬁrst time a non-perturbative representation of the full amplitudes.

3 One of the main ingredients in the computation of scattering amplitudes using integrable methods is the group theoretical structures by which the relevant building blocks are glued together into the physical amplitude. The PI has provided a simple expression for all these structures.

4 Many diﬀerent observables in QFT are known to factoriez into simpler pieces in a certain kinematical limits. The PI have understood how such limits are all controlled by few simple building block which are associated with null propagation. Using integrability methods, he has computed these building block at ﬁnite coupling. By combining them together in diﬀerent ways, he has derived ﬁnite coupling prediction several observables.

In addition to the signiﬁcant scientiﬁc progress, the proposal and its implementation aids the PI with his integration at Tel Aviv University. In particular, the PI has two undergraduate student, one postdoc that is arriving soon and numerous visitors and experts that have visited the group in the past two years. The program thus strongly supports the theoretical activities at Tel Aviv university, which have commenced with the arrival of the PI.