Strings vs Spins on the Null Orbifold

Abstract

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the ${\alpha }^{\prime }\to \infty$ limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.

arXiv comment27 pages, 5 figures, v2: comments about boundary conditions added, strengthening the conclusion

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Cited by in corpus (3)

• Chiral Higher Spin Gravity
• 3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography