A Simple Worldsheet Black Hole

TL;DR

The paper investigates the worldsheet theory of confining strings in two-dimensional massive adjoint QCD, showing a non-trivial planar S-matrix with zigzag configurations that create non-locality and a black-hole–like complementarity. It formulates the worldsheet as a θ-vacuum subsector, analyzes two-particle states, and demonstrates how confinement resolves apparent state-counting puzzles while producing a non-local, complementary description. The work also connects the worldsheet S-matrix to gravitational dressing and T\bar{T} deformations, discusses a special SUSY point $m^2 = g^2 N/\pi$ with potential integrability, and highlights the broader implication that confining strings can exhibit gravity-like features in a controlled setting.

Abstract

We study worldsheet theory of confining strings in two-dimensional massive adjoint QCD. Similarly to confining strings in higher dimensions this theory exhibits a non-trivial $S$-matrix surviving even in the strict planar limit. In the process of two-particle scattering a zigzag is formed on the worldsheet. It leads to an interesting non-locality and exhibits some properties of a quantum black hole. Ordinarily, identical quantum particles do not carry identity. On the worldsheet they acquire off-shell identity due to strings attached. Identity implies complementarity. We discuss similarities and differences of the worldsheet scattering with the $T\bar{T}$ deformation. We also propose a promising candidate for a supersymmetric model with integrable confining strings.

Figures (8)

• Figure 1: A long string wound around the cylinder is created by a Polyakov loop ${\cal O}_P$. In lattice simulations a finite volume spectrum of the worldsheet theory is determined from the exponential falloff of two-point correlators, $\langle {\cal O}^\dagger_P(\tau) {\cal O}_P(0) =\sum_n e^{-E_n\tau}$.
• Figure 2: A one-particle state on the worldsheet may be represented as a free quark with two conjugate flux lines emanating in opposite directions and terminating at the boundary charges at infinity.
• Figure 3: Meson states are created by double-trace operators and decouple from worldsheet excitations in the planar limit.
• Figure 4: $|L\rangle$ and $|R\rangle$ sectors arise as a consequence of the color ordering. Note that the ordering of quarks in space does not need to agree with the color ordering. This leads to a possibility of zigzag configurations, as shown on the top.
• Figure 5: Potential describing a two-particle collision in the $|L\rangle$-sector.