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Large central charge in superconformal field theories implies numerous scalar operators. This finding, derived from Coulomb branch operator analysis, has holographic implications for anti-de Sitter space supergravity.

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Area of Science:

  • High-energy theoretical physics
  • Quantum field theory
  • String theory and supergravity

Background:

  • Unitary, interacting four-dimensional N=2 superconformal field theories (SCFTs) are complex systems with rich mathematical structures.
  • Understanding the operator content and spectral properties of these theories, especially at large central charge (c), is crucial for theoretical advancements.

Purpose of the Study:

  • To provide an elementary proof for the existence of a specific number of single-trace, scalar superconformal primary operators in four-dimensional N=2 SCFTs at large c.
  • To establish a refined bound on the spectral density related to the asymptotic growth rate of the central charge.
  • To explore the holographic implications of these findings in the context of anti-de Sitter space (AdS) supergravity.

Main Methods:

  • An elementary proof technique is employed, building upon established results concerning the structure of Coulomb branch operators.
  • The study analyzes the spectral density and its relationship with the central charge's asymptotic growth.
  • Holographic interpretation is used to translate field theory results into statements about AdS supergravity.

Main Results:

  • It is proven that for large central charge c, there exist at least sqrt[c] single-trace, scalar superconformal primary operators with dimensions Δ≲sqrt[c].
  • A stronger, refined bound on the spectral density is derived.
  • Holographically, this implies bounds on scale separation in semiclassical AdS_{5} half-maximal supergravity, requiring an infinite tower of charged scalar states below the black hole threshold.

Conclusions:

  • The existence of a substantial number of scalar operators is a fundamental property of large-c N=2 SCFTs.
  • The holographic duals of such theories must exhibit specific features, including a rich spectrum of low-energy states.
  • AdS_{5} pure supergravity is ruled out as an asymptotic limit for certain sequences in theory space, though the general holographic question remains open.