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Gauge theory description of compactified pp-waves

M. Bertolini, J. de Boer, T. Harmark, E. Imeroni, N. A. Obers

TL;DR

This work introduces new Penrose limits of $AdS_5 \times S^5$ that reveal explicit space-like isometries and, for orbifolded backgrounds, space-like circles and DLCQ directions. It establishes a novel duality between string theory on these pp-waves and triple- or quadruple-scaling limits of $\mathcal{N}=4$ and $\mathcal{N}=2$ quiver gauge theories, including winding sectors, with detailed operator–state maps. The authors compute one-loop anomalous dimensions in the gauge theories and demonstrate exact agreement with the corresponding string spectra for the explored sectors, thereby extending the BMN paradigm to new geometric and supersymmetric contexts. They further explore time-dependent backgrounds and multiple isometries, outlining a broader framework for embeddings of pp-waves in gauge theories and highlighting trajectories toward Matrix/String theory realizations and DLCQ descriptions.

Abstract

We find a new Penrose limit of AdS_5*S^5 that gives the maximally symmetric pp-wave background of type IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N=4 SYM theory. The new Penrose limit, when applied to AdS_5*S^5/Z_M, yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N=2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework.

Gauge theory description of compactified pp-waves

TL;DR

This work introduces new Penrose limits of that reveal explicit space-like isometries and, for orbifolded backgrounds, space-like circles and DLCQ directions. It establishes a novel duality between string theory on these pp-waves and triple- or quadruple-scaling limits of and quiver gauge theories, including winding sectors, with detailed operator–state maps. The authors compute one-loop anomalous dimensions in the gauge theories and demonstrate exact agreement with the corresponding string spectra for the explored sectors, thereby extending the BMN paradigm to new geometric and supersymmetric contexts. They further explore time-dependent backgrounds and multiple isometries, outlining a broader framework for embeddings of pp-waves in gauge theories and highlighting trajectories toward Matrix/String theory realizations and DLCQ descriptions.

Abstract

We find a new Penrose limit of AdS_5*S^5 that gives the maximally symmetric pp-wave background of type IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N=4 SYM theory. The new Penrose limit, when applied to AdS_5*S^5/Z_M, yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N=2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework.

Paper Structure

This paper contains 28 sections, 240 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. New Penrose limits and space-like isometry
  3. Explicit space-like isometry from Penrose limit of ${\rm AdS}_5 \times S^5$
  4. A space-like circle from ${\rm AdS}_5 \times S^5/\mathbb{Z}_M$
  5. Space-like circle and DLCQ from ${\rm AdS}_5 \times S^5/(\mathbb{Z}_{M_1} \times \mathbb{Z}_{M_2})$
  6. Space-like isometry and DLCQ from ${\rm AdS}_5 \times S^5/ \mathbb{Z}_{M}$
  7. String Theory on pp-wave with space-like circle
  8. Bosonic sector
  9. Fermionic sector
  10. The String spectrum
  11. Space-like circle and $\mathcal{N} =2$ quiver gauge theory
  12. Predictions from string theory
  13. Bosonic gauge theory operators without anomalous dimensions
  14. Bosonic gauge theory operators with anomalous dimensions
  15. Anomalous dimensions and comparison with string theory
  16. ...and 13 more sections

Figures (4)

  • Figure 1: The quiver diagram for the $\mathcal{N}=2$ QGT that we consider. Each dot represents a $U(N)$ gauge factor. For the matter fields, we use a ${\mathcal{N}}=1$ notation: each line between dots correspond to a complex scalar of either type ${A}_I$ or ${B}_I$ ($I=1,...,M$), the two making-up the corresponding bifundamental hypermultiplet. Arrows go from fundamental to anti-fundamental representations of the corresponding gauge groups. The fermionic partner of each bosonic field is implicit in the figure.
  • Figure 2: The three relevant graphs contributing to the radiative correction of two point scalar field trace operator ${\cal O}_{(n)}$.
  • Figure 3: One-loop F-term contribution. This diagram includes both $\Phi$ interchange with $A$ or $B$ as well as $A$ and $B$ interchange.
  • Figure 4: The quiver diagram for the orbifold $\mathbb{C}^3/(\mathbb{Z}_5 \times \mathbb{Z}_3)$. Each dot represents a $U(N)$ gauge factor, in double index notation. The red dashed lines correspond to chiral multiplets belonging to ${\bf W}_1$ , the blue lines to chiral multiplets belonging to ${\bf W}_2$ and green ones to chiral multiplets belonging to ${\bf W}_3$. Arrows go from fundamental to anti-fundamental representations.