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Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$

C. Chamon, R. Jackiw, S. -Y. Pi, L. Santos

Abstract

A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory.

Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$

Abstract

A 0+1-dimensional candidate theory for the CFT dual to AdS is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory.

Paper Structure

This paper contains 5 sections, 50 equations.

Table of Contents

  1. Introduction
  2. Review
  3. Puzzle
  4. Operator-state correspondence with neither an invariant vacuum nor a primary operator
  5. Conclusion