Quantum null string holography conjecture

Establish the quantum-level equivalence between minimal null string theory on a regular non-null dilation-orbit patch of a target manifold and the ILST theory on the corresponding projective boundary, thereby proving the null string holography conjecture.

Background

The paper proves a classical equivalence between minimal null string theory on a target space with metric g and the ILST theory on the projective boundary obtained by quotienting the target space along the homothetic dilation orbits. After eliminating the holographic coordinate and the Carroll–Weyl connection, the resulting action is the ILST action for the induced boundary metric.

The unresolved problem is to determine whether this classical correspondence survives quantization. Establishing it would require demonstrating equivalence of the quantized parent and reduced theories, including their functional measures, gauge fixing, and possible anomalies, and would provide the proposed null string analogue of holography.

References

We conjecture that this equivalence also holds as quantum level, which we dub null string holography.

— Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces  (2609.10432 - Sheikh-Jabbari et al., 9 Sep 2026) in Abstract; Section 2.3, immediately following Eq. (S-g-S-ILST-G)

Null string theory on global dS or in a patch we are close to the cosmological horizon or Big Bang ($\eta\to \pm\infty$), needs dealing with homothetic vectors that become null on certain time slices. We postpone a detailed analysis of such cases to a separate publication.

— Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces  (2609.10432 - Sheikh-Jabbari et al., 9 Sep 2026) in Section 3.2, Example II: de Sitter space

Several questions remain open. A complete quantum analysis will require a careful treatment of radial zero modes, global boundary conditions, and the full physical state space. An important next step is to understand the anomaly matching beyond the highest-weight realization and to extend the local correspondence to integrated vertex operators, correlation functions, and higher-genus amplitudes.

— Null string holography in AdS from local BRST descent  (2610.10540 - Duary et al., 7 Oct 2026) in Conclusions and Outlook

Several questions remain open. A complete quantum analysis will require a careful treatment of radial zero modes, global boundary conditions, and the full physical state space. An important next step is to understand the anomaly matching beyond the highest-weight realization and to extend the local correspondence to integrated vertex operators, correlation functions, and higher-genus amplitudes.

— Null string holography in AdS from local BRST descent  (2610.10540 - Duary et al., 7 Oct 2026) in Conclusions and Outlook