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Qubit Construction in 6D SCFTs

Jonathan J. Heckman

Abstract

We consider a class of 6D superconformal field theories (SCFTs) which have a large $N$ limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without $AdS$ duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a $T^2$.

Qubit Construction in 6D SCFTs

Abstract

We consider a class of 6D superconformal field theories (SCFTs) which have a large limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a .

Paper Structure

This paper contains 7 sections, 27 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Qubits in 6D SCFTs
  3. Entanglement and 6D RG Flows
  4. Tensor Branch Flows
  5. Higgs Branch Flows
  6. Interpolation
  7. Qubit Manipulation

Figures (3)

  • Figure 1: Depiction of a tensor branch flow from the UV to the IR. In the M5-brane picture (left) this involves separating a stack of $N = N_1 + N_2$ M5-branes into two stacks. In the associated spin chain (right), the resulting spins separate into two decoupled sectors. There can still be significant entanglement between the two sectors.
  • Figure 2: Depiction of a multi-throat spacetime generated by pulling $N = N_1 + ... + N_k$ M5-branes apart into separate stacks. Starting from a configuration of spins in the parent theory, we get a multi-party entangled state in the IR theory.
  • Figure 3: Example of qubit manipulation as a function of RG time / trajectory time in a moduli space flow with local coordinate $z$. The starting point is to separate M5-branes from one another. This is followed by a general Bloch sphere / $SU(2)_{\mathcal{R}}$ rotation. After this, the M5-branes are recombined. In the case of 6D SCFTs this is followed by a projection onto the zero momentum sector of the 1D spin chain Hilbert space.