E. Sobko

Continuous quivers enable exact Wilson loop calculation, reveal an emergent dimension, and raise tantalising questions on dual strings.

Four-dimensional circular quivers often arise as discretized versions of space-time and as holographic duals in string theory. But within such theories, calculating observable quantities for general couplings is challenging. We introduce a new class of continuous quivers that are exactly solvable for any smooth profile of couplings and uncover an emergent fifth dimension that raises intriguing questions for theorists.

We consider half-BPS Wilson loops in N = 2 long circular quiver gauge theories at large-N with continuous limit shape of ’t Hooft couplings. In the limit of an infinite number of nodes L, the solution to the localisation matrix model is given by Wigner semicircles for any profile of couplings. Higher-order corrections in 1/L can be calculated iteratively. 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.

Continuous quivers

Continuous Quivers