Wilson Loops at Large N and the Quantum M2-Brane

Area of Science:

• High-energy physics
• String theory
• Quantum field theory

Background:

• The U(N)_k × U(N)_{-k} ABJM theory is a quantum field theory with a holographic dual description in M-theory.
• Wilson loop operators are crucial for probing properties of quantum field theories.

Purpose of the Study:

• To compare the Wilson loop expectation value in the ABJM theory with its dual M2-brane description.
• To verify the holographic duality by examining both leading and subleading terms.

Main Methods:

• Utilizing the localization result for the 1/2-BPS circular Wilson loop in the ABJM theory.
• Comparing the quantum field theory result with the classical and one-loop contributions of the wrapped M2-brane solution in AdS4 × S7/Zk.

Main Results:

• The leading large N exponential factor of the Wilson loop expectation value is matched by the M2-brane's classical action.
• The subleading k-dependent prefactor is exactly reproduced by the one-loop term of the M2-brane partition function, including Kaluza-Klein modes.

Conclusions:

• This work presents the first exact matching of the overall numerical prefactor for a Wilson loop expectation value against its dual holographic prediction.
• The findings provide evidence for a consistent quantum M2-brane computation and suggest avenues for future research and generalizations.