VTID

Vanishing Theorems and Incomplete Deformations for Vacuum Data in N=4 SYM

This project investigates the conditions under which 1-point functions vanish in N=4 Super Yang-Mills theory and systematically characterizes the structures that permit nonzero values under various deformations.

Key Results

  1. Unified vanishing theorem: In the Poincare-invariant, conformally invariant, source-free vacuum of N=4 SYM, the 1-point functions of all operators in the family C_ex (local scalar primaries, conserved currents, and the energy-momentum tensor) vanish.

  2. Deformation analysis: Under deformations (relevant deformations, finite temperature, finite chemical potential, vacuum selection, time-dependent backgrounds, etc.), we systematize the conditions under which nonzero 1-point functions are permitted.

  3. Four-layer classification: We classify observables into four layers and prove that the vanishing theorem is specific to Layer I (local 1-point data); Layers II-IV carry nontrivial data even in the symmetric vacuum.

  4. Layer-resolved response theorem: Representative deformations trigger systematic responses across all four layers. Of the 20 cells formed by representative deformations and the four layers, 19 are supported by literature evidence, explicit computation, or the QFT-on-de Sitter framework.

Resources