Chiral Composite Linear Dilaton as String Dual to Two-Dimensional Yang-Mills

TL;DR

This paper proposes and analyzes a bosonic worldsheet dual to large $N_c$ chiral 2d YM, built from a $eta$-$ar{eta}$ system plus a chiral composite linear dilaton (CLD). By localizing the worldsheet path integral on Mandelstam maps, it derives explicit expressions for $n$-point correlators, and computes two-, three-, and four-point string amplitudes that are shown to match the corresponding 2d YM amplitudes, providing a nontrivial check of the duality. The key technical advances include a detailed derivation of the Mandelstam formula in this noncritical setting, the consistent computation of the $eta$-$eta$ OPE, and a KLT-like factorization of the four-point amplitude, all while addressing regularization and renormalization subtleties. The results establish a concrete, computable noncritical string framework for chiral 2d YM, offering insights into confinement mechanisms and potential links to nonrelativistic string theories and topological duals. Overall, the work provides a rigorous bridge between a solvable gauge theory and a novel string-theoretic description, with implications for understanding holography-like dualities in lower dimensions.

Abstract

Two-dimensional Yang-Mills theory (2d YM) is arguably the simplest confining gauge theory and its large $N_c$ expansion has a structure of the genus expansion in string theory. Nevertheless various aspects of its worldsheet description have not been fully understood. In this paper, we elaborate on a bosonic string dual to large $N_c$ chiral 2d YM at finite 't Hooft coupling, proposed in our earlier work. The worldsheet theory consists of $β$-$γ$ system deformed by linear dilaton action built from a composite of $γ$. It can be seen as a noncritical version of nonrelativistic string theory introduced by Gomis and Ooguri. We provide a detailed analysis of the worldsheet operator product expansion and the computation of three- and four-point scattering amplitudes.

Figures (8)

• Figure 1: Octopus diagram computing the tensionful term in the worldsheet action, expressed as a boundary integral along the cuts and encircling the branch points.
• Figure 2: The string diagram for three point amplitude with $Z_1$ being the interaction point where $\partial \rho$ vanishes.
• Figure 3: Four-point amplitudes in chiral 2d YM with $s-, t-$ and $u$-channel exchanges
• Figure 4: A six-point string tree diagram where the interaction point at which the $k$-th string interacts is denoted by $Z_I^{(k)}$ .
• Figure 5: To regulate the divergences in $\Gamma[\rho]$ to compute the string amplitudes, we excise small discs on the worldsheet surface around the insertion points of the vertex operators $\{z_k\}_{k=1}^{n}$, the insertion points $\{Z_I\}_{I=1}^{n-2}$, and the point at infinity $(z_{\infty},\bar{z}_{\infty})$ .