Mother Moose: Generating Extra Dimensions from Simple Groups at Large N

TL;DR

The paper establishes a framework to relate four-dimensional gauge theories with simple groups to higher-dimensional theories in the large $N$ limit, using orbifold projections and Higgsing to generate extra dimensions and KK towers. By combining orbifolding (planar equivalence) with moose/quiver constructions and careful coupling rescalings, it shows how a 4D theory can reproduce the correlators of a $(d+1)$-dimensional theory, and extends this idea to connect to AdS/CFT and higher-dimensional gravity duals. A concrete SUSY example demonstrates how a 4D mother theory orbifolded to a 4D daughter on a Higgs branch yields a 5D theory, with explicit mass spectra and scale relations that reproduce a flat extra dimension, and with precise conditions under which the five-dimensional interpretation and gravity dual are valid. The work provides a versatile mechanism to derive higher-dimensional physics from four-dimensional, simple-group theories and to compute higher-dimensional correlators from classical gravity solutions, with potential extensions to even higher dimensions via additional orbifoldings and brane configurations.

Abstract

We show that there exists a correspondence between four dimensional gauge theories with simple groups and higher dimensional gauge theories at large N. As an example, we show that a four dimensional {N}=2 supersymmetric SU(N) gauge theory, on the Higgs branch, has the same correlators as a five dimensional SU(N) gauge theory in the limit of large N provided the couplings are appropriately rescaled. We show that our results can be applied to the AdS/CFT correspondence to derive correlators of five or more dimensional gauge theories from solutions of five dimensional supergravity in the large t'Hooft coupling limit.

Figures (2)

• Figure 1: Typical moose diagram
• Figure 2: The pattern of orbifolding and symmetry breaking. The mother theory is on the left and the daughter on the right.