Holography of Non-relativistic String on AdS5xS5

TL;DR

This work demonstrates that a non-relativistic string in $AdS_5\times S^5$, viewed as fluctuations around an $AdS_2$ Wilson line, has a complete spectral match with a one-dimensional conformal quantum mechanics, and that NR string normalizable modes can reproduce CQM wavefunctions and correlators. It argues for an AdS$_2$/CFT$_1$ sector embedded in AdS$_5$/CFT$_4$ via a double holography framework and establishes a GKPW-type relation by coupling NR string non-normalizable modes to sources on a straight Wilson line. The analysis identifies precise mappings between AdS$_2$ masses and CQM couplings, clarifies boundary regularization, and shows how Wilson-line deformations arise from NN mode insertions, offering a concrete holographic bridge between defect/string dynamics and one-dimensional quantum mechanics. The work also outlines future directions to derive the CQM from $\mathcal{N}=4$ SYM, extend to circular Wilson loops, and explore higher-order fluctuations and representations of Wilson lines.

Abstract

We discuss a holographic dual of a non-relativistic (NR) string on AdS5xS5. The NR string can be regarded as a semiclassical string around an AdS2 classical solution corresponding to a straight Wilson line in the gauge-theory side. The quadratic action with respect to the fluctuations is composed of free massive and massless scalars, and free massive fermions on the AdS2 world-sheet. We show that the complete agreement of the spectra between the NR string and a conformal quantum mechanics (CQM). Then we show a holographic relation between normalizable modes of the NR string and wave functions in the CQM. Then it may be argued from this result that an AdS2/CFT1 would be realized in AdS5/CFT4. We can really discuss a GKPW-type relation by considering non-normalizable modes of the NR string in Euclidean signature. Those modes give a source term insertion to the Wilson line, which can also be regarded as a small deformation of it.

Figures (3)

• Figure 1: The potentials for $H$ and $L_0$ .
• Figure 2: The restriction of the insertion points of the operators onto the Wilson line $C$ . In general the operators may be inserted everywhere on $\mathbb{R}^4$ .
• Figure 3: A contribution of the third-order fluctuation