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Open Strings on Plane waves and their Yang-Mills duals

D. Berenstein, E. Gava, J. Maldacena, K. S. Narain, H. Nastase

TL;DR

The paper analyzes the Penrose (plane-wave) limit of $AdS_5\times S^5/Z_2$ in type I' theory with D3-D7-O7, yielding a duality between an ${\cal N}=2$ ${\rm Sp}(N)$ gauge theory and string theory on an orientifolded plane-wave background. It identifies closed-string states with gauge-invariant operators $\mathrm{Tr}[(Z\Omega)^J]$ and open-string states with operators of the form $Q\Omega(Z\Omega)^JQ$, and derives the corresponding string bit Hamiltonian from gauge-theory F-terms, showing how Dirichlet and Neumann boundary conditions arise for open strings. The approach extends the BMN correspondence to theories with fundamental matter, demonstrating how unoriented string sectors are captured by gauge-invariant operators in the ${\rm Sp}(N)$ theory and how their anomalous dimensions reproduce string excitations in the orientifolded plane-wave. This provides a concrete framework for matching gauge theory data to open and closed string states in orientifold backgrounds and suggests directions for exploring open strings ending on baryons or giant gravitons in this setup.

Abstract

We study the plane wave limit of $AdS_5\times S^5/Z_2$ which arises as the near horizon geometry of D3-branes at an orientifold 7-plane in type I' theory. We analyze string theory in the resulting plane wave background which contains open strings. We identify gauge invariant operators in the dual $Sp(N)$ gauge theory with unoriented closed and open string states.

Open Strings on Plane waves and their Yang-Mills duals

TL;DR

The paper analyzes the Penrose (plane-wave) limit of in type I' theory with D3-D7-O7, yielding a duality between an gauge theory and string theory on an orientifolded plane-wave background. It identifies closed-string states with gauge-invariant operators and open-string states with operators of the form , and derives the corresponding string bit Hamiltonian from gauge-theory F-terms, showing how Dirichlet and Neumann boundary conditions arise for open strings. The approach extends the BMN correspondence to theories with fundamental matter, demonstrating how unoriented string sectors are captured by gauge-invariant operators in the theory and how their anomalous dimensions reproduce string excitations in the orientifolded plane-wave. This provides a concrete framework for matching gauge theory data to open and closed string states in orientifold backgrounds and suggests directions for exploring open strings ending on baryons or giant gravitons in this setup.

Abstract

We study the plane wave limit of which arises as the near horizon geometry of D3-branes at an orientifold 7-plane in type I' theory. We analyze string theory in the resulting plane wave background which contains open strings. We identify gauge invariant operators in the dual gauge theory with unoriented closed and open string states.

Paper Structure

This paper contains 6 sections, 32 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The orientifold of a plane wave
  3. The orientifolded plane wave as a limit of $AdS_5\times S^5/Z_2$.
  4. The gauge theory
  5. The string bit hamiltonian
  6. Conclusions

Figures (2)

  • Figure 1: The corrections involving D terms, photons and self-energies cancel each other if all fields are holomorphic. They do not exchange the position of the fields. We denoted the propagator of the auxiliary $D$ field by a doted line, this is just a delta function in position space.
  • Figure 2: The diagrams involving F terms give non vanishing contributions which involve terms exchanging the position of the fields. We denoted the propagator of the auxiliary $F$ field by a doted line, this is just a delta function in position space.