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BMN-like Matrix Models

Eunwoo Lee

Abstract

We conjecture a family of matrix quantum mechanical models that are holographically dual to discrete light-cone quantization of M-theory in pp-wave-like backgrounds. These backgrounds can be obtained from a Penrose limit of AdS$_4\times X_7$, where $X_7$ is Einstein. The matrix models arise from a classically consistent dimensional reduction of the UV Lagrangians of $\mathcal{N}=1$ superconformal field theories, in close analogy with how the BMN matrix model is obtained by dimensional reduction from $\mathcal{N}=4$ super Yang-Mills theory. We also discuss about supersymmetric black objects in pp-wave background by studying the Witten index and speculate that the area of the horizon is bounded from above for a fixed $N$.

BMN-like Matrix Models

Abstract

We conjecture a family of matrix quantum mechanical models that are holographically dual to discrete light-cone quantization of M-theory in pp-wave-like backgrounds. These backgrounds can be obtained from a Penrose limit of AdS, where is Einstein. The matrix models arise from a classically consistent dimensional reduction of the UV Lagrangians of superconformal field theories, in close analogy with how the BMN matrix model is obtained by dimensional reduction from super Yang-Mills theory. We also discuss about supersymmetric black objects in pp-wave background by studying the Witten index and speculate that the area of the horizon is bounded from above for a fixed .
Paper Structure (21 sections, 106 equations)

This paper contains 21 sections, 106 equations.

Table of Contents

  1. Introduction
  2. BMN matrix model
  3. The pp-wave background
  4. Killing spinor equation
  5. Killing spinor equation in "spherical" coordinates
  6. BMN matrix model from $\mathcal{N}=4$ SYM
  7. Symmetries and Classical Ground States
  8. Supersymmetric black objects in BMN
  9. BMN-like matrix models
  10. Generalized pp-wave
  11. Penrose limit from AdS$_4\times X_7$
  12. BMN truncation from holographic gauge theories
  13. $Y^{p,q}$
  14. $\mathbb{Z}_p$ Orbifold of $\mathcal{N}=4$ SYM
  15. $\beta$ deformed $\mathcal{N}=4$ SYM
  16. ...and 6 more sections