Quantum Deconstruction of a 5D SYM and its Moduli Space

TL;DR

This paper reconstructs a five-dimensional supersymmetric Yang-Mills theory from a four-dimensional quiver model, analyzing its moduli space and phase structure, and compares it with string theory UV completions to reveal intrinsic properties.

Contribution

It introduces a deconstruction approach for 5D SYM with specific Chern-Simons level, elucidates its moduli space, and compares different UV completions to identify intrinsic features.

Findings

The 5D coupling h is non-negative and cannot be continued to negative values.

The moduli space is identical across different UV completions, with no flop transitions.

The phase structure is constrained, reflecting intrinsic properties of the SU(M) SYM with k=M.

Abstract

We deconstruct the fifth dimension of the 5D SYM theory with SU(M) gauge symmetry and Chern-Simons level k=M and show how the 5D moduli space follows from the non-perturbative analysis of the 4D quiver theory. The 5D coupling h=1/(g_5)^2 of the un-broken SU(M) is allowed to take any non-negative values, but it cannot be continued to h<0 and there are no transitions to other phases of the theory. The alternative UV completions of the same 5D SYM -- via M theory on the C^3/Z_2M orbifold or via the dual five-brane web in type IIB string theory -- have identical moduli spaces: h >= 0 only, and no flop transitions. We claim these are intrinsic properties of the SU(M) SYM theory with k=M.