Week 18.03.2024 – 24.03.2024

CANCELLED due to an unforeseen speaker emergency.

I will describe a surprisingly simple representation of a class of integrated correlation functions of four superconformal primaries in the stress tensor multiplet of N=4 supersymmetric Yang-Mills theory with arbitrary simple gauge group, G. I then present exact formulae for these integrated correlators which are manifestly invariant under GNO electro-magnetic duality. For classical gauge groups, G=SU(N), SO(N), USp(2N), In the large-N limit these correlators are interpreted via holography in terms of the low-energy expansion of type IIB superstring amplitudes in AdS_5XS^5 or an orientifold thereof. In this way I recover the SL(2,Z)-invariant BPS interactions, arising in type IIB superstring amplitudes in the flat-space limit. From the asymptotic nature of the 1/N expansion I furthermore reconstruct non-perturbative contributions which holographically correspond to (p,q)-string world-sheet instantons.

We propose the Gauge Theory Bootstrap, a method to compute the pion S-matrix that describes the strongly coupled low energy physics of QCD and other similar gauge theories. The method looks for the most general S-matrix that matches at low energy the tree level amplitudes of the non-linear sigma model and at high energy, QCD sum rules and form factors. We compute pion scattering phase shifts for all partial waves with angular momentum $\ell<=3$ up to 2 GeV and calculate the low energy ChiPT coefficients. This is a theoretical/numerical calculation that uses as only data the pion mass $m_\pi$, pion decay constant $f_{\pi}$ and the QCD parameters $N_c=3$, $N_f=2$, $m_q$ and $\alpha_s$. All results are in reasonable agreement with experiment. In particular, we find the $\rho(770)$, $f_2(1270)$ and $\rho(1450)$ resonances and some initial indication of particle production near the resonances. The interplay between the UV gauge theory and low energy pion physics is an example of a general situation where we know the microscopic theory as well as the effective theory of long wavelength fluctuations but we want to solve the strongly coupled dynamics at intermediate energies. The bootstrap builds a bridge between the low and high energy by determining the consistent S-matrix that matches both and provides, in this case, a new direction to understand the strongly coupled physics of gauge theories. Based on work with Martin Kruczenski.

an informal in-person seminar by Prof. Herman Verlinde

Cosmological Correlators are one of the physical quantities that are of interest to cosmologists and are also of theoretical interest as they are related to CFT correlators via the AdS/CFT correspondence. These differ from the S-matrix as they are correlation functions computed on a given time slice. In this talk, I will review some progress in computing these in momentum space and also describe its relation to the S-matrix.