Deconstruction of the Maldacena–Núñez compactification

Abstract

We demonstrate a classical equivalence between the large-N limit of the Higgsed N = 1 * SUSY U (N ) Yang-Mills theory and the MaldacenaNúñez twisted compactification of a six dimensional gauge theory on a two-sphere. A direct comparison of the actions and spectra of the two theories reveals them to be identical. We also propose a gauge theory limit which should describe the corresponding spherical compactification of Little String Theory.

Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

“…Moreover, the only diagrams contributing to the coefficients g 5 , g 6 of the "nonlocal" terms are nonplanar, and thus logarithmically divergent but suppressed by 1 N compared to the other (planar) diagrams. This justifies the explicit factors 1 N in (4) and (8). Finally, the only one-loop diagram contributing to g 3 is also logarithmically divergent.…”

Confinement, phase transitions and non-locality in the entanglement entropy

“…This is of course correct, but the point is subtle. Indeed, as Andrews and Dorey [40] have shown (in the perturbative regime), the field theory is completely equivalent to four-dimensional N = 1 * Yang-Mills, expanded at a particular point of its Higgs branch, which is a well-defined 4-d QFT. Also, the same sort of KK-modes appear if we compactify a stack of D4 branes on S 1 and in that confining model the phase transition is present, see [11] and section 2.…”

Remarks on the string dual toN=1supersymmetric QCD

“…It is precisely the twisting in the compactification that preserves only four supercharges. The weakly coupled massless spectrum and multiplicities were studied in detail in [13]. The theory contains a massless vector multiplet plus a tower of massive chiral and massive vector multiplets, usually called "Kaluza-Klein (KK) modes".…”

“…Generically, the Lagrangian describing the weakly coupled theory (see [13] for the quadratic part of the Lagrangian), consists of a massless vector multiplet plus an infinite set of KK multiplets. Denoting the massless vector multiplet and its curvature by (V, W α ), the massive vector multiplets by V k (its curvature by W k ) and massive chiral multiplets as Φ k , the action is…”

“…The only available solution was originally found (in part analytically and in part numerically) in [9]. The configuration of the dilaton, metric (in Einstein frame) and RR three form are given by 13) whereω i are the left-invariant forms of SU (2) ω 1 = cos ψdθ + sin ψ sinθdφ , ω 2 = − sin ψdθ + cos ψ sinθdφ , 14) and the BPS equations defining the functions h, g, k, a, b, φ as presented in Appendix B of [9] and appear quite involved; we will not quote them here because in the following sections we will present them in a unified way with the type A BPS equations written above eqs.(2.9)-(2.12). It was argued in [9] and [12] that the type N backgrounds faithfully capture non-perturbative physics for any value of the number of flavors N f > 0.…”