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This study extends the integrability approach for one-point functions in AdS/dCFT to higher loop orders. The generalized formula accurately predicts one-loop corrections in supersymmetric Yang-Mills theory, matching dual string theory results.

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Area of Science:

  • High Energy Physics
  • String Theory
  • Quantum Field Theory

Background:

  • The AdS/dCFT correspondence relates quantum field theories to gravitational theories.
  • Integrability methods are powerful tools for studying strongly coupled systems.
  • One-point functions are crucial observables in quantum field theories.

Purpose of the Study:

  • To extend the integrability approach for calculating one-point functions in AdS/dCFT to higher loop orders.
  • To develop a generalized formula for tree-level one-point functions.
  • To verify the formula's accuracy through explicit computations and comparisons with dual string theory.

Main Methods:

  • Asymptotic generalization of a tree-level one-point function formula.
  • Explicit computation using a novel object: an amputated matrix product state.
  • Analysis within the context of the defect version of N=4 supersymmetric Yang-Mills theory and its dual D5-D3 probe-brane system.

Main Results:

  • A natural asymptotic generalization of the tree-level one-point function formula is proposed.
  • The generalized formula correctly encodes one-loop corrections for non-protected operators.
  • The formula yields results consistent with dual string theory in a specific double-scaling limit.

Conclusions:

  • The integrability approach can be successfully extended to higher loop orders for one-point functions in AdS/dCFT.
  • The proposed asymptotic formula provides a powerful tool for studying quantum field theories at strong coupling.
  • This work opens new avenues for investigating quantum phenomena within the AdS/dCFT framework.