Emergent Dimensions in Exactly Solvable Models

 I will show how to calculate the 1/N expansion of the vacuum energy in the two-dimensional SU(N) Principal Chiral Model (PCM) for a certain profile of external fields. By combining this expansion with the strong-coupling regime, I will identify a double-scaling limit that bears striking similarities to the c=1 string theory, suggesting that the double-scaled PCM is dual to a non-critical string theory with a (2+1)-dimensional target space, where the additional dimension emerges dynamically from the SU(N) Dynkin diagram. 

  Developing this idea further, I will show how to solve the large-N PCM for an arbitrary set of external fields and at any interaction strength - a unique result of this kind for an asymptotically free quantum field theory. The solution reproduces the one-loop perturbative calculation at weak coupling, and in the strong-coupling regime reveals an emergent spatial dimension arising from the continuum limit of the SU(N) Dynkin diagram.

  In the second part of my talk, I will show that the calculation of the expectation value of half-BPS circular Wilson loops in N=2 superconformal A_L quiver gauge theories simplifies drastically in the large-L limit, similarly to the PCM case. Combining large L with a strong coupling regime we identify a double scaling limit that describes dynamics along a fifth dimension which emerges dynamically from the quiver diagram. We solve the resulting integro-differential equation exactly for a certain range of parameters.