Strongly coupled QFT dynamics via TQFT coupling
Mithat Ünsal
Abstract
A bstract We consider a class of quantum field theories and quantum mechanics, which we couple to ℤ N topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤ N TQFT structure arises naturally from turning on a classical background field for a ℤ N 0- or 1-form global symmetry. In SU( N ) Yang-Mills theory coupled to ℤ N TQFT, the non-perturbative expansion parameter is exp[ −S I /N ] = exp[ − 8 π 2 /g 2 N ] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU( N ) theory, we must use PSU( N ) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU( N ). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T 3 × $$ {S}_L^1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msubsup> </mml:math> can be interpreted as tunneling events in the ’t Hooft flux background in the PSU( N ) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large- N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$ \mathbbm{CP} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>CP</mml:mi> </mml:math> 1 model, and mass gap for arbitrary θ in $$ \mathbbm{CP} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>CP</mml:mi> </mml:math> N− 1 , N ≥ 3 on ℝ 2 .