# Overview

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One of the most important problems in mathematical physics is the study of strongly coupled field theories of the sort we use to describe the strong interactions (QCD) and condensed matter systems (CMT). Theorists have very few tools at their disposal, each of which accompanied by its attendant limitations. Perturbative (i.e., weak coupling) computations can probe a large part of the parameter space of QCD. However, these results are valid only at temperatures well above the deconfinement temperature, and at large values of the baryon number chemical potential $mu$ in order for the QCD coupling to be small, and thus the perturbation theory valid. These exclusions limit the applicability to regions of parameter space explored in heavy ion collisions at RHIC and LHC.

AdS/CFT is one prominent tool for studying strongly coupled systems which is especially suited for studying QCD at low energies where we know that the system is strongly coupled. In fact all perturbative techniques fail there and so far there has not been any analytic control on the low energy regimes of QCD. Lattice gauge theories have their own limitations. Another way to study strongly coupled system is integrability. Many important condensed matter systems (such as those described by minimal 2D CFTs) are essentially integrable near a critical point. Likewise, QCD scattering amplitudes include contributions which can be computed using N=4 Yang-Mills (which is integrable in the planar limit).

Applying AdS/CFT to QCD and CMT are examples par excellence of “perturbing away” from the exact results available in integrable sectors, under the control of the general framework of gauge/gravity duality, to obtain experimentally verifiable predictions. Even though QCD is neither conformal, nor supersymmetric, nor has a “large” number of colors, recent progress in this area, however, has provided us with strong hints to overcome these limitations, and move towards models of gauge-gravity duality that are not supersymmetric, and are non-conformal. There has also been a tremendous amount of activity studying gravity duals of strongly coupled condensed matter systems, especially topological phases of matter.

The workshop will unify themes related to the connection of AdS/CFT with QCD and condensed matter physics, for example color glass condensate and color superconductivity phase of QCD using appropriate gravity duals and the techniques from integrability.