Year: 2026
Type: article
Abstract: A bstract Motivated by the observation that 2 + 2 = 4, we consider four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories on S 2 × Σ, turning on a suitable rigid supergravity background. On the one hand, reduction of a four-dimensional theory T on a Riemann surface Σ leads to a family $$ \mathcal{F}\left[T,\Sigma \right] $$ F T Σ of two-dimensional (2, 2) unitary SCFTs, a two-dimensional analog of the four-dimensional theories of class $$ \mathcal{S} $$ S . On the other hand, reduction on S 2 yields a non-unitary two-dimensional CFT $$ \mathcal{C}\left[T\right] $$ C T whose chiral algebra is the same as the one associated to T by the standard SCFT/VOA correspondence. This construction upgrades the vertex operator algebra to a full-fledged two-dimensional CFT. What’s more, it leads to a novel 2d/2d correspondence, a “2 + 2 = 4” analog of the “4 + 2 = 6” AGT correspondence: the S 2 partition function of $$ \mathcal{F}\left[T;\Sigma \right] $$ F T Σ is computed by correlation functions of $$ \mathcal{C}\left[T\right] $$ C T on Σ. The elliptic genus of $$ \mathcal{F}\left[T;\Sigma \right] $$ F T Σ is instead computed by a topological QFT $$ \mathcal{E}\left[T\right] $$ E T on Σ. A central question is whether one can give a purely two-dimensional presentation of the family $$ \mathcal{F}\left[T;\Sigma \right] $$ F T Σ of (2, 2) theories. We propose an algorithm to realize the (2, 2) theories as gauged linear sigma models when T is an Argyres-Douglas theory of type ( A 1 , A 2 k ) and Σ an n -punctured sphere. We perform stringent checks of our conjecture for k = 1 and k = 2.
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: Theoretical Physics
OpenAlex ID: W7214918677