The PP-Wave Limits of Orbifolded AdS_5x S^5

TL;DR

The paper analyzes Penrose (pp‑wave) limits of orbifolded AdS geometries, showing that $AdS_5\times S^5/Z_{N_2}$ admits two distinct pp‑wave limits: an orbifolded, half‑SUSY variant and the standard maximally supersymmetric one, with the latter becoming independent of $N_2$ in the limit. It constructs the dual ${\cal N}=2$ gauge theory operators in ${\rm SU}(N_1)^{N_2}$ that correspond to string excitations on the orbifolded pp‑wave, identifying untwisted and twisted sectors and the insertion patterns that realize higher excitations via $a_{-n/N_2}^{\mu}$ oscillators. The work also extends the analysis to eleven‑dimensional orbifolds $AdS_4\times S^7/Z_N$ and $AdS_7\times S^4/Z_N$, finding similar dual pictures for $AdS_4\times S^7/Z_N$ with two pp‑wave limits, while $AdS_7\times S^4/Z_N$ allows only the maximal pp‑wave. Together, these results illuminate how orbifold singularities imprint distinct subsectors with potential supersymmetry enhancement and motivate further study of M‑theory pp‑waves and their gauge theory duals.

Abstract

Using the supergravity solution of $N_1$ D3-branes probing $A_{N_2-1}$ singularities we study the pp-wave limit of $AdS_5\times S^5/Z_{N_2}$. We show that there are two different pp-wave limits. One is the orbifold of the pp-wave limit of $AdS_5\times S^5$. In this case there is no symmetry enhancement. The other case is the same as the pp-wave limit of $AdS_5\times S^5$ and therefore we again see the maximal supersymmetry. We will also identify operators in the four dimensional ${\cal N}=2$ $SU(N_1)^{N_2}$ gauge theory which correspond to stringy excitations in the orbifolded pp-wave geometry. The existence of the maximal pp-wave geometry indicates that there is a subsector of the corresponding ${\cal N}=2$ gauge theories which has enhanced ${\cal N}=4$ supersymmetry. We also study the pp-wave limits of $AdS_{7,4}\times S^{4,7}/Z_{N}$.