New Discrete States in Two-Dimensional Supergravity

TL;DR

This paper explores new discrete states in two-dimensional superstring theory, revealing an enlarged algebra of currents that relates to volume-preserving diffeomorphisms and suggests holographic connections to higher-dimensional field theories.

Contribution

It introduces a new class of discrete states in 2D superstrings with an algebra related to SDiff(N), extending known structures and providing explicit structure constants for N=3.

Findings

New discrete states form SU(N) multiplets with ghost numbers from -N to N-2.

Structure constants for N=3 are expressed via SU(3) Clebsch-Gordan coefficients.

Algebra conjectured to be isomorphic to SDiff(N), indicating holographic relations.

Abstract

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.