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Twisted Backgrounds, PP-Waves and Nonlocal Field Theories

Mohsen Alishahiha, Ori J. Ganor

TL;DR

This work develops a framework to study nonlocal field theories arising from twisted, plane-wave–like deformations of string/M-theory backgrounds and analyzes their holographic duals. By constructing geometries with geometrical, T-/U-duals, and lightlike twists, the authors reveal dipole and discpole nonlocalities and compute Wilson loop/surface observables to diagnose nonlocal interactions. Key findings include the explicit gravity duals for dipole and discpole theories, the emergence of open Wilson lines/surfaces, and the persistence of R-charge constraints in nonlocal settings, especially in lightlike deformations where simplifications appear in the worldsheet dynamics. The results provide valuable insights into nonlocal holography and the role of center-of-mulitple gauge groups, with implications for little string theory and related nonlocal CFTs.

Abstract

We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.

Twisted Backgrounds, PP-Waves and Nonlocal Field Theories

TL;DR

This work develops a framework to study nonlocal field theories arising from twisted, plane-wave–like deformations of string/M-theory backgrounds and analyzes their holographic duals. By constructing geometries with geometrical, T-/U-duals, and lightlike twists, the authors reveal dipole and discpole nonlocalities and compute Wilson loop/surface observables to diagnose nonlocal interactions. Key findings include the explicit gravity duals for dipole and discpole theories, the emergence of open Wilson lines/surfaces, and the persistence of R-charge constraints in nonlocal settings, especially in lightlike deformations where simplifications appear in the worldsheet dynamics. The results provide valuable insights into nonlocal holography and the role of center-of-mulitple gauge groups, with implications for little string theory and related nonlocal CFTs.

Abstract

We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.

Paper Structure

This paper contains 31 sections, 96 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Construction of twisted backgrounds
  3. Geometrical twists
  4. T-duals and U-duals of twists
  5. Notation
  6. Supergravity solutions of generalized twisted backgrounds
  7. Fundamental string twist
  8. Generalized twists
  9. Lightlike twists
  10. Probing with branes and new nonlocal theories
  11. Fundamental string twists
  12. D-brane twists
  13. Supergravity solutions of D-branes and NS5-branes and the large $N$ limit
  14. Review of the supergravity dual of dipole theory
  15. Lightlike dipole theory
  16. ...and 16 more sections

Figures (9)

  • Figure 1: Four different orientations of the membrane in $AdS$. The nonlocality is in directions $x_4,x_5.$
  • Figure 2: The boundary of the nonlocal dipole theory is a fibration of the $x$ (horizontal) direction over an internal $\fb$ (vertical) direction with identification of points separated by $2\pi L$.
  • Figure 3: Open Wilson line with R-charge. The opening is a vector in the $x$ direction with length proportional to the R-charge.
  • Figure 4: Open Wilson surface with R-charge. The boundary traces out a closed curve in the $x_4,x_5$ plane that bounds an area proportional to the R-charge. The opening (depicted as a cross hatched square) could be of any shape.
  • Figure 5: Correlation function of open Wilson lines. It can be nonzero if $\vec{L}_1 + \vec{L}_2 + \vec{L}_3 = 0.$
  • ...and 4 more figures